Data update
This commit is contained in:
Ingy döt Net
parent
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commit
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7735 changed files with 38060 additions and 199180 deletions
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(notonline)-->
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<span style="color: #7060A8;">requires</span><span style="color: #0000FF;">(</span><span style="color: #000000;">64</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">enum</span> <span style="color: #000000;">X</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">Y</span> <span style="color: #000080;font-style:italic;">-- rational ec point</span>
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<span style="color: #008080;">enum</span> <span style="color: #000000;">A</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">B</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">N</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">G</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">R</span> <span style="color: #000080;font-style:italic;">-- elliptic curve parameters
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-- also signature pair(A,B)</span>
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requires(64)
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enum X, Y -- rational ec point
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enum A, B, N, G, R -- elliptic curve parameters
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-- also signature pair(A,B)
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<span style="color: #008080;">constant</span> <span style="color: #000000;">mxN</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1073741789</span> <span style="color: #000080;font-style:italic;">-- maximum modulus</span>
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<span style="color: #008080;">constant</span> <span style="color: #000000;">mxr</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1073807325</span> <span style="color: #000080;font-style:italic;">-- max order G = mxN + 65536</span>
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<span style="color: #008080;">constant</span> <span style="color: #000000;">inf</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">2147483647</span> <span style="color: #000080;font-style:italic;">-- symbolic infinity</span>
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constant mxN = 1073741789 -- maximum modulus
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constant mxr = 1073807325 -- max order G = mxN + 65536
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constant inf = -2147483647 -- symbolic infinity
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">e</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">},</span><span style="color: #000000;">0</span><span style="color: #0000FF;">}</span> <span style="color: #000080;font-style:italic;">-- single global curve</span>
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<span style="color: #008080;">constant</span> <span style="color: #000000;">zerO</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">inf</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">}</span> <span style="color: #000080;font-style:italic;">-- point at infinity zerO</span>
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sequence e = {0,0,0,{0,0},0} -- single global curve
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constant zerO = {inf,0} -- point at infinity zerO
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<span style="color: #004080;">bool</span> <span style="color: #000000;">inverr</span> <span style="color: #000080;font-style:italic;">-- impossible inverse mod N</span>
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bool inverr -- impossible inverse mod N
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<span style="color: #008080;">function</span> <span style="color: #000000;">exgcd</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">v</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">u</span><span style="color: #0000FF;">)</span>
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<span style="color: #000080;font-style:italic;">-- return mod(v^-1, u)</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">q</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
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<span style="color: #008080;">if</span> <span style="color: #000000;">v</span><span style="color: #0000FF;"><</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #000000;">v</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">u</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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function exgcd(atom v, u)
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-- return mod(v^-1, u)
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atom q, t, r = 0, s = 1
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if v<0 then v += u end if
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<span style="color: #008080;">while</span> <span style="color: #000000;">v</span> <span style="color: #008080;">do</span>
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<span style="color: #000000;">q</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">u</span><span style="color: #0000FF;">/</span><span style="color: #000000;">v</span><span style="color: #0000FF;">)</span>
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<span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">u</span><span style="color: #0000FF;">-</span><span style="color: #000000;">q</span><span style="color: #0000FF;">*</span><span style="color: #000000;">v</span>
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<span style="color: #000000;">u</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">v</span>
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<span style="color: #000000;">v</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">t</span>
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<span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">-</span><span style="color: #000000;">q</span><span style="color: #0000FF;">*</span><span style="color: #000000;">s</span>
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<span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">s</span>
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<span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">t</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
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while v do
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q = floor(u/v)
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t = u-q*v
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u = v
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v = t
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t = r-q*s
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r = s
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s = t
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end while
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<span style="color: #008080;">if</span> <span style="color: #000000;">u</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span>
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<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" impossible inverse mod N, gcd = %d\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">u</span><span style="color: #0000FF;">})</span>
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<span style="color: #000000;">inverr</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">true</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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if u!=1 then
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printf(1," impossible inverse mod N, gcd = %d\n",{u})
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inverr = true
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end if
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<span style="color: #008080;">return</span> <span style="color: #000000;">r</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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return r
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end function
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<span style="color: #008080;">function</span> <span style="color: #000000;">modn</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">)</span>
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<span style="color: #000080;font-style:italic;">-- return mod(a, N)</span>
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<span style="color: #000000;">a</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mod</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">e</span><span style="color: #0000FF;">[</span><span style="color: #000000;">N</span><span style="color: #0000FF;">])</span>
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<span style="color: #008080;">if</span> <span style="color: #000000;">a</span><span style="color: #0000FF;"><</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #000000;">a</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">e</span><span style="color: #0000FF;">[</span><span style="color: #000000;">N</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #008080;">return</span> <span style="color: #000000;">a</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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function modn(atom a)
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-- return mod(a, N)
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a = mod(a,e[N])
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if a<0 then a += e[N] end if
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return a
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end function
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<span style="color: #008080;">function</span> <span style="color: #000000;">modr</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">)</span>
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<span style="color: #000080;font-style:italic;">-- return mod(a, r)</span>
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<span style="color: #000000;">a</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mod</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">e</span><span style="color: #0000FF;">[</span><span style="color: #000000;">R</span><span style="color: #0000FF;">])</span>
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<span style="color: #008080;">if</span> <span style="color: #000000;">a</span><span style="color: #0000FF;"><</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #000000;">a</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">e</span><span style="color: #0000FF;">[</span><span style="color: #000000;">R</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #008080;">return</span> <span style="color: #000000;">a</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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function modr(atom a)
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-- return mod(a, r)
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a = mod(a,e[R])
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if a<0 then a += e[R] end if
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return a
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end function
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<span style="color: #008080;">function</span> <span style="color: #000000;">disc</span><span style="color: #0000FF;">()</span>
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<span style="color: #000080;font-style:italic;">-- return the discriminant of E</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">a</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">e</span><span style="color: #0000FF;">[</span><span style="color: #000000;">A</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">b</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">e</span><span style="color: #0000FF;">[</span><span style="color: #000000;">B</span><span style="color: #0000FF;">],</span>
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<span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">4</span><span style="color: #0000FF;">*</span><span style="color: #000000;">modn</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">*</span><span style="color: #000000;">modn</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">*</span><span style="color: #000000;">a</span><span style="color: #0000FF;">))</span>
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<span style="color: #008080;">return</span> <span style="color: #000000;">modn</span><span style="color: #0000FF;">(-</span><span style="color: #000000;">16</span><span style="color: #0000FF;">*(</span><span style="color: #000000;">c</span><span style="color: #0000FF;">+</span><span style="color: #000000;">27</span><span style="color: #0000FF;">*</span><span style="color: #000000;">modn</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">*</span><span style="color: #000000;">b</span><span style="color: #0000FF;">)))</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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function disc()
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-- return the discriminant of E
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atom a = e[A], b = e[B],
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c = 4*modn(a*modn(a*a))
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return modn(-16*(c+27*modn(b*b)))
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end function
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<span style="color: #008080;">function</span> <span style="color: #000000;">isO</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
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<span style="color: #000080;font-style:italic;">-- return true if P = zerO</span>
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<span style="color: #008080;">return</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">X</span><span style="color: #0000FF;">]=</span><span style="color: #000000;">inf</span> <span style="color: #008080;">and</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">Y</span><span style="color: #0000FF;">]=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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function isO(sequence p)
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-- return true if P = zerO
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return (p[X]=inf and p[Y]=0)
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end function
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<span style="color: #008080;">function</span> <span style="color: #000000;">ison</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
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<span style="color: #000080;font-style:italic;">-- return true if P is on curve E</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
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<span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #000000;">isO</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
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<span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">modn</span><span style="color: #0000FF;">(</span><span style="color: #000000;">e</span><span style="color: #0000FF;">[</span><span style="color: #000000;">B</span><span style="color: #0000FF;">]+</span><span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">X</span><span style="color: #0000FF;">]*</span><span style="color: #000000;">modn</span><span style="color: #0000FF;">(</span><span style="color: #000000;">e</span><span style="color: #0000FF;">[</span><span style="color: #000000;">A</span><span style="color: #0000FF;">]+</span><span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">X</span><span style="color: #0000FF;">]*</span><span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">X</span><span style="color: #0000FF;">]))</span>
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<span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">modn</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">Y</span><span style="color: #0000FF;">]*</span><span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">Y</span><span style="color: #0000FF;">])</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #008080;">return</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">=</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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function ison(sequence p)
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-- return true if P is on curve E
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atom r = 0, s = 0
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if not isO(p) then
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r = modn(e[B]+p[X]*modn(e[A]+p[X]*p[X]))
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s = modn(p[Y]*p[Y])
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end if
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return (r=s)
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end function
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<span style="color: #008080;">procedure</span> <span style="color: #000000;">pprint</span><span style="color: #0000FF;">(</span><span style="color: #004080;">string</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
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<span style="color: #000080;font-style:italic;">-- print point P with prefix f</span>
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<span style="color: #008080;">if</span> <span style="color: #000000;">isO</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
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<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%s (0)\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">f</span><span style="color: #0000FF;">})</span>
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<span style="color: #008080;">else</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">y</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">Y</span><span style="color: #0000FF;">]</span>
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<span style="color: #008080;">if</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">></span><span style="color: #000000;">e</span><span style="color: #0000FF;">[</span><span style="color: #000000;">N</span><span style="color: #0000FF;">]-</span><span style="color: #000000;">y</span> <span style="color: #008080;">then</span> <span style="color: #000000;">y</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">e</span><span style="color: #0000FF;">[</span><span style="color: #000000;">N</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%s (%d,%d)\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">f</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">X</span><span style="color: #0000FF;">],</span><span style="color: #000000;">y</span><span style="color: #0000FF;">})</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
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procedure pprint(string f, sequence p)
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-- print point P with prefix f
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if isO(p) then
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printf(1,"%s (0)\n",{f})
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else
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atom y = p[Y]
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if y>e[N]-y then y -= e[N] end if
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printf(1,"%s (%d,%d)\n",{f,p[X],y})
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end if
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end procedure
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<span style="color: #008080;">function</span> <span style="color: #000000;">padd</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">q</span><span style="color: #0000FF;">)</span>
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<span style="color: #000080;font-style:italic;">-- full ec point addition</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">la</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t</span>
|
||||
function padd(sequence p, q)
|
||||
-- full ec point addition
|
||||
atom la, t
|
||||
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">isO</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #000000;">q</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">isO</span><span style="color: #0000FF;">(</span><span style="color: #000000;">q</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #000000;">p</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
if isO(p) then return q end if
|
||||
if isO(q) then return p end if
|
||||
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">X</span><span style="color: #0000FF;">]!=</span><span style="color: #000000;">q</span><span style="color: #0000FF;">[</span><span style="color: #000000;">X</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span> <span style="color: #000080;font-style:italic;">-- R := P + Q</span>
|
||||
<span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">Y</span><span style="color: #0000FF;">]-</span><span style="color: #000000;">q</span><span style="color: #0000FF;">[</span><span style="color: #000000;">Y</span><span style="color: #0000FF;">]</span>
|
||||
<span style="color: #000000;">la</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">modn</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">*</span><span style="color: #000000;">exgcd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">X</span><span style="color: #0000FF;">]-</span><span style="color: #000000;">q</span><span style="color: #0000FF;">[</span><span style="color: #000000;">X</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">e</span><span style="color: #0000FF;">[</span><span style="color: #000000;">N</span><span style="color: #0000FF;">]))</span>
|
||||
if p[X]!=q[X] then -- R := P + Q
|
||||
t = p[Y]-q[Y]
|
||||
la = modn(t*exgcd(p[X]-q[X], e[N]))
|
||||
|
||||
<span style="color: #008080;">else</span> <span style="color: #000080;font-style:italic;">-- P = Q, R := 2P</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">Y</span><span style="color: #0000FF;">]=</span><span style="color: #000000;">q</span><span style="color: #0000FF;">[</span><span style="color: #000000;">Y</span><span style="color: #0000FF;">])</span> <span style="color: #008080;">and</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">Y</span><span style="color: #0000FF;">]!=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">modn</span><span style="color: #0000FF;">(</span><span style="color: #000000;">3</span><span style="color: #0000FF;">*</span><span style="color: #000000;">modn</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">X</span><span style="color: #0000FF;">]*</span><span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">X</span><span style="color: #0000FF;">])+</span><span style="color: #000000;">e</span><span style="color: #0000FF;">[</span><span style="color: #000000;">A</span><span style="color: #0000FF;">])</span>
|
||||
<span style="color: #000000;">la</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">modn</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">*</span><span style="color: #000000;">exgcd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">*</span><span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">Y</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">e</span><span style="color: #0000FF;">[</span><span style="color: #000000;">N</span><span style="color: #0000FF;">]))</span>
|
||||
<span style="color: #008080;">else</span>
|
||||
<span style="color: #008080;">return</span> <span style="color: #000000;">zerO</span> <span style="color: #000080;font-style:italic;">-- P = -Q, R := O</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
else -- P = Q, R := 2P
|
||||
if (p[Y]=q[Y]) and (p[Y]!=0) then
|
||||
t = modn(3*modn(p[X]*p[X])+e[A])
|
||||
la = modn(t*exgcd(2*p[Y], e[N]))
|
||||
else
|
||||
return zerO -- P = -Q, R := O
|
||||
end if
|
||||
end if
|
||||
|
||||
<span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">modn</span><span style="color: #0000FF;">(</span><span style="color: #000000;">la</span><span style="color: #0000FF;">*</span><span style="color: #000000;">la</span><span style="color: #0000FF;">-</span><span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">X</span><span style="color: #0000FF;">]-</span><span style="color: #000000;">q</span><span style="color: #0000FF;">[</span><span style="color: #000000;">X</span><span style="color: #0000FF;">])</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">zerO</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">r</span><span style="color: #0000FF;">[</span><span style="color: #000000;">Y</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">modn</span><span style="color: #0000FF;">(</span><span style="color: #000000;">la</span><span style="color: #0000FF;">*(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">X</span><span style="color: #0000FF;">]-</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)-</span><span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">Y</span><span style="color: #0000FF;">])</span>
|
||||
<span style="color: #000000;">r</span><span style="color: #0000FF;">[</span><span style="color: #000000;">X</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">t</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">inverr</span> <span style="color: #008080;">then</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">zerO</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">return</span> <span style="color: #000000;">r</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
|
||||
t = modn(la*la-p[X]-q[X])
|
||||
sequence r = deep_copy(zerO)
|
||||
r[Y] = modn(la*(p[X]-t)-p[Y])
|
||||
r[X] = t
|
||||
if inverr then r = zerO end if
|
||||
return r
|
||||
end function
|
||||
|
||||
<span style="color: #008080;">function</span> <span style="color: #000000;">pmul</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000080;font-style:italic;">-- R:= multiple kP</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">zerO</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">q</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">p</span>
|
||||
function pmul(sequence p, atom k)
|
||||
-- R:= multiple kP
|
||||
sequence s = zerO, q = p
|
||||
|
||||
<span style="color: #008080;">while</span> <span style="color: #000000;">k</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #7060A8;">and_bits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">k</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">padd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">q</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">inverr</span> <span style="color: #008080;">then</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">zerO</span><span style="color: #0000FF;">;</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">k</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">q</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">padd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">q</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">q</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
|
||||
<span style="color: #008080;">return</span> <span style="color: #000000;">s</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
|
||||
while k do
|
||||
if and_bits(k,1) then
|
||||
s = padd(s, q)
|
||||
end if
|
||||
if inverr then s = zerO; exit end if
|
||||
k = floor(k/2)
|
||||
q = padd(q, q)
|
||||
end while
|
||||
return s
|
||||
end function
|
||||
|
||||
<span style="color: #008080;">function</span> <span style="color: #000000;">ellinit</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000080;font-style:italic;">-- initialize elliptic curve</span>
|
||||
<span style="color: #004080;">atom</span> <span style="color: #000000;">a</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">b</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span>
|
||||
<span style="color: #000000;">inverr</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">false</span>
|
||||
<span style="color: #000000;">e</span><span style="color: #0000FF;">[</span><span style="color: #000000;">N</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">[</span><span style="color: #000000;">3</span><span style="color: #0000FF;">]</span>
|
||||
function ellinit(sequence i)
|
||||
-- initialize elliptic curve
|
||||
atom a = i[1], b = i[2]
|
||||
inverr = false
|
||||
e[N] = i[3]
|
||||
|
||||
<span style="color: #008080;">if</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">e</span><span style="color: #0000FF;">[</span><span style="color: #000000;">N</span><span style="color: #0000FF;">]<</span><span style="color: #000000;">5</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">or</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">e</span><span style="color: #0000FF;">[</span><span style="color: #000000;">N</span><span style="color: #0000FF;">]></span><span style="color: #000000;">mxN</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
if (e[N]<5) or (e[N]>mxN) then return 0 end if
|
||||
|
||||
<span style="color: #000000;">e</span><span style="color: #0000FF;">[</span><span style="color: #000000;">A</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">modn</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">e</span><span style="color: #0000FF;">[</span><span style="color: #000000;">B</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">modn</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">e</span><span style="color: #0000FF;">[</span><span style="color: #000000;">G</span><span style="color: #0000FF;">][</span><span style="color: #000000;">X</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">modn</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">[</span><span style="color: #000000;">4</span><span style="color: #0000FF;">])</span>
|
||||
<span style="color: #000000;">e</span><span style="color: #0000FF;">[</span><span style="color: #000000;">G</span><span style="color: #0000FF;">][</span><span style="color: #000000;">Y</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">modn</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">[</span><span style="color: #000000;">5</span><span style="color: #0000FF;">])</span>
|
||||
<span style="color: #000000;">e</span><span style="color: #0000FF;">[</span><span style="color: #000000;">R</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">[</span><span style="color: #000000;">6</span><span style="color: #0000FF;">]</span>
|
||||
e[A] = modn(a)
|
||||
e[B] = modn(b)
|
||||
e[G][X] = modn(i[4])
|
||||
e[G][Y] = modn(i[5])
|
||||
e[R] = i[6]
|
||||
|
||||
<span style="color: #008080;">if</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">e</span><span style="color: #0000FF;">[</span><span style="color: #000000;">R</span><span style="color: #0000FF;">]<</span><span style="color: #000000;">5</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">or</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">e</span><span style="color: #0000FF;">[</span><span style="color: #000000;">R</span><span style="color: #0000FF;">]></span><span style="color: #000000;">mxr</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
if (e[R]<5) or (e[R]>mxr) then return 0 end if
|
||||
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"E: y^2 = x^3 + %dx + %d (mod %d)\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">,</span><span style="color: #000000;">e</span><span style="color: #0000FF;">[</span><span style="color: #000000;">N</span><span style="color: #0000FF;">]})</span>
|
||||
<span style="color: #000000;">pprint</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"base point G"</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">e</span><span style="color: #0000FF;">[</span><span style="color: #000000;">G</span><span style="color: #0000FF;">])</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"order(G, E) = %d\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">e</span><span style="color: #0000FF;">[</span><span style="color: #000000;">R</span><span style="color: #0000FF;">]})</span>
|
||||
printf(1,"E: y^2 = x^3 + %dx + %d (mod %d)\n",{a,b,e[N]})
|
||||
pprint("base point G", e[G])
|
||||
printf(1,"order(G, E) = %d\n",{e[R]})
|
||||
|
||||
<span style="color: #008080;">return</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
|
||||
return -1
|
||||
end function
|
||||
|
||||
<span style="color: #008080;">function</span> <span style="color: #000000;">signature</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000080;font-style:italic;">-- signature primitive</span>
|
||||
<span style="color: #004080;">atom</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">u</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">u1</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">V</span>
|
||||
function signature(atom s, f)
|
||||
-- signature primitive
|
||||
atom c, d, u, u1
|
||||
sequence V
|
||||
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"signature computation\n"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">while</span> <span style="color: #004600;">true</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #008080;">while</span> <span style="color: #004600;">true</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #000080;font-style:italic;">-- u = rand(e[R]-1)</span>
|
||||
<span style="color: #000000;">u</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">571533488</span> <span style="color: #000080;font-style:italic;">-- match FreeBASIC output
|
||||
-- u = 605163545 -- match C output</span>
|
||||
<span style="color: #000000;">V</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">pmul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">e</span><span style="color: #0000FF;">[</span><span style="color: #000000;">G</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">u</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">modr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">V</span><span style="color: #0000FF;">[</span><span style="color: #000000;">X</span><span style="color: #0000FF;">])</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
|
||||
printf(1,"signature computation\n")
|
||||
while true do
|
||||
while true do
|
||||
-- u = rand(e[R]-1)
|
||||
u = 571533488 -- match FreeBASIC output
|
||||
-- u = 605163545 -- match C output
|
||||
V = pmul(e[G], u)
|
||||
c = modr(V[X])
|
||||
if c!=0 then exit end if
|
||||
end while
|
||||
|
||||
<span style="color: #000000;">u1</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">exgcd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">u</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">e</span><span style="color: #0000FF;">[</span><span style="color: #000000;">R</span><span style="color: #0000FF;">])</span>
|
||||
<span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">modr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">u1</span><span style="color: #0000FF;">*(</span><span style="color: #000000;">f</span><span style="color: #0000FF;">+</span><span style="color: #000000;">modr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">*</span><span style="color: #000000;">c</span><span style="color: #0000FF;">)))</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"one-time u = %d\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">u</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">pprint</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"V = uG"</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">V</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">c</span><span style="color: #0000FF;">,</span><span style="color: #000000;">d</span><span style="color: #0000FF;">}</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
|
||||
u1 = exgcd(u, e[R])
|
||||
d = modr(u1*(f+modr(s*c)))
|
||||
if d!=0 then exit end if
|
||||
end while
|
||||
printf(1,"one-time u = %d\n",u)
|
||||
pprint("V = uG", V)
|
||||
return {c,d}
|
||||
end function
|
||||
|
||||
<span style="color: #008080;">function</span> <span style="color: #000000;">verify</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">W</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">sg</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000080;font-style:italic;">-- verification primitive</span>
|
||||
<span style="color: #004080;">atom</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">sg</span><span style="color: #0000FF;">[</span><span style="color: #000000;">A</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">sg</span><span style="color: #0000FF;">[</span><span style="color: #000000;">B</span><span style="color: #0000FF;">],</span>
|
||||
<span style="color: #000000;">t</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">c1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">h1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">h2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">h</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">V</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">V2</span>
|
||||
function verify(sequence W, atom f, sequence sg)
|
||||
-- verification primitive
|
||||
atom c = sg[A], d = sg[B],
|
||||
t, c1, h1, h2, h
|
||||
sequence V, V2
|
||||
|
||||
<span style="color: #000080;font-style:italic;">--domain check</span>
|
||||
<span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">c</span><span style="color: #0000FF;">></span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">and</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">c</span><span style="color: #0000FF;"><</span><span style="color: #000000;">e</span><span style="color: #0000FF;">[</span><span style="color: #000000;">R</span><span style="color: #0000FF;">])</span>
|
||||
<span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">t</span> <span style="color: #008080;">and</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">d</span><span style="color: #0000FF;">></span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">and</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">d</span><span style="color: #0000FF;"><</span><span style="color: #000000;">e</span><span style="color: #0000FF;">[</span><span style="color: #000000;">R</span><span style="color: #0000FF;">])</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #000000;">t</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
--domain check
|
||||
t = (c>0) and (c<e[R])
|
||||
t = t and (d>0) and (d<e[R])
|
||||
if not t then return 0 end if
|
||||
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\nsignature verification\n"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">h</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">exgcd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">d</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">e</span><span style="color: #0000FF;">[</span><span style="color: #000000;">R</span><span style="color: #0000FF;">])</span>
|
||||
<span style="color: #000000;">h1</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">modr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f</span><span style="color: #0000FF;">*</span><span style="color: #000000;">h</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">h2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">modr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">c</span><span style="color: #0000FF;">*</span><span style="color: #000000;">h</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"h1,h2 = %d,%d\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">h1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">h2</span><span style="color: #0000FF;">})</span>
|
||||
<span style="color: #000000;">V</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">pmul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">e</span><span style="color: #0000FF;">[</span><span style="color: #000000;">G</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">h1</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">V2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">pmul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">W</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">h2</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">pprint</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"h1G"</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">V</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">pprint</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"h2W"</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">V2</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">V</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">padd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">V</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">V2</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">pprint</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"+ ="</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">V</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">isO</span><span style="color: #0000FF;">(</span><span style="color: #000000;">V</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #000000;">c1</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">modr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">V</span><span style="color: #0000FF;">[</span><span style="color: #000000;">X</span><span style="color: #0000FF;">])</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"c' = %d\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c1</span><span style="color: #0000FF;">)</span>
|
||||
printf(1,"\nsignature verification\n")
|
||||
h = exgcd(d, e[R])
|
||||
h1 = modr(f*h)
|
||||
h2 = modr(c*h)
|
||||
printf(1,"h1,h2 = %d,%d\n",{h1,h2})
|
||||
V = pmul(e[G], h1)
|
||||
V2 = pmul(W, h2)
|
||||
pprint("h1G", V)
|
||||
pprint("h2W", V2)
|
||||
V = padd(V, V2)
|
||||
pprint("+ =", V)
|
||||
if isO(V) then return 0 end if
|
||||
c1 = modr(V[X])
|
||||
printf(1,"c' = %d\n",c1)
|
||||
|
||||
<span style="color: #008080;">return</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">c1</span><span style="color: #0000FF;">=</span><span style="color: #000000;">c</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
|
||||
return (c1=c)
|
||||
end function
|
||||
|
||||
<span style="color: #008080;">procedure</span> <span style="color: #000000;">errmsg</span><span style="color: #0000FF;">()</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"invalid parameter set\n"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"_____________________\n"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
|
||||
procedure errmsg()
|
||||
printf(1,"invalid parameter set\n")
|
||||
printf(1,"_____________________\n")
|
||||
end procedure
|
||||
|
||||
<span style="color: #008080;">procedure</span> <span style="color: #000000;">ec_dsa</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000080;font-style:italic;">-- digital signature on message hash f, error bit d</span>
|
||||
<span style="color: #004080;">atom</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">sg</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">W</span>
|
||||
procedure ec_dsa(atom f, d)
|
||||
-- digital signature on message hash f, error bit d
|
||||
atom i, s, t
|
||||
sequence sg, W
|
||||
|
||||
<span style="color: #000080;font-style:italic;">--parameter check</span>
|
||||
<span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">disc</span><span style="color: #0000FF;">()=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">t</span> <span style="color: #008080;">or</span> <span style="color: #000000;">isO</span><span style="color: #0000FF;">(</span><span style="color: #000000;">e</span><span style="color: #0000FF;">[</span><span style="color: #000000;">G</span><span style="color: #0000FF;">])</span>
|
||||
<span style="color: #000000;">W</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">pmul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">e</span><span style="color: #0000FF;">[</span><span style="color: #000000;">G</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">e</span><span style="color: #0000FF;">[</span><span style="color: #000000;">R</span><span style="color: #0000FF;">])</span>
|
||||
<span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">t</span> <span style="color: #008080;">or</span> <span style="color: #008080;">not</span> <span style="color: #000000;">isO</span><span style="color: #0000FF;">(</span><span style="color: #000000;">W</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">t</span> <span style="color: #008080;">or</span> <span style="color: #008080;">not</span> <span style="color: #000000;">ison</span><span style="color: #0000FF;">(</span><span style="color: #000000;">e</span><span style="color: #0000FF;">[</span><span style="color: #000000;">G</span><span style="color: #0000FF;">])</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">t</span> <span style="color: #008080;">then</span> <span style="color: #000000;">errmsg</span><span style="color: #0000FF;">()</span> <span style="color: #008080;">return</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
--parameter check
|
||||
t = (disc()=0)
|
||||
t = t or isO(e[G])
|
||||
W = pmul(e[G], e[R])
|
||||
t = t or not isO(W)
|
||||
t = t or not ison(e[G])
|
||||
if t then errmsg() return end if
|
||||
|
||||
<span style="color: #7060A8;">puts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\nkey generation\n"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000080;font-style:italic;">-- s = rand(e[R] - 1)</span>
|
||||
<span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">509100772</span> <span style="color: #000080;font-style:italic;">-- match FreeBASIC output
|
||||
-- s = 1343570 -- match C output</span>
|
||||
<span style="color: #000000;">W</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">pmul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">e</span><span style="color: #0000FF;">[</span><span style="color: #000000;">G</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"private key s = %d\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">s</span><span style="color: #0000FF;">})</span>
|
||||
<span style="color: #000000;">pprint</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"public key W = sG"</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">W</span><span style="color: #0000FF;">)</span>
|
||||
puts(1,"\nkey generation\n")
|
||||
-- s = rand(e[R] - 1)
|
||||
s = 509100772 -- match FreeBASIC output
|
||||
-- s = 1343570 -- match C output
|
||||
W = pmul(e[G], s)
|
||||
printf(1,"private key s = %d\n",{s})
|
||||
pprint("public key W = sG", W)
|
||||
|
||||
<span style="color: #000080;font-style:italic;">--next highest power of 2 - 1</span>
|
||||
<span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">e</span><span style="color: #0000FF;">[</span><span style="color: #000000;">R</span><span style="color: #0000FF;">]</span>
|
||||
<span style="color: #000000;">i</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
|
||||
<span style="color: #008080;">while</span> <span style="color: #000000;">i</span><span style="color: #0000FF;"><</span><span style="color: #000000;">32</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">or_bits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">/</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)))</span>
|
||||
<span style="color: #000000;">i</span> <span style="color: #0000FF;">*=</span> <span style="color: #000000;">2</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
|
||||
<span style="color: #008080;">while</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">></span><span style="color: #000000;">t</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #000000;">f</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\naligned hash %x\n\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">f</span><span style="color: #0000FF;">})</span>
|
||||
--next highest power of 2 - 1
|
||||
t = e[R]
|
||||
i = 1
|
||||
while i<32 do
|
||||
t = or_bits(t,floor(t/power(2,i)))
|
||||
i *= 2
|
||||
end while
|
||||
while f>t do
|
||||
f = floor(f/2)
|
||||
end while
|
||||
printf(1,"\naligned hash %x\n\n",{f})
|
||||
|
||||
<span style="color: #000000;">sg</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">signature</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">inverr</span> <span style="color: #008080;">then</span> <span style="color: #000000;">errmsg</span><span style="color: #0000FF;">()</span> <span style="color: #008080;">return</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"signature c,d = %d,%d\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sg</span><span style="color: #0000FF;">)</span>
|
||||
sg = signature(s, f)
|
||||
if inverr then errmsg() return end if
|
||||
printf(1,"signature c,d = %d,%d\n",sg)
|
||||
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">></span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #008080;">while</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">></span><span style="color: #000000;">t</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">d</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
|
||||
<span style="color: #000000;">f</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">xor_bits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f</span><span style="color: #0000FF;">,</span><span style="color: #000000;">d</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"corrupted hash %x\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">f</span><span style="color: #0000FF;">})</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
if d>0 then
|
||||
while d>t do
|
||||
d = floor(d/2)
|
||||
end while
|
||||
f = xor_bits(f,d)
|
||||
printf(1,"corrupted hash %x\n",{f})
|
||||
end if
|
||||
|
||||
<span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">verify</span><span style="color: #0000FF;">(</span><span style="color: #000000;">W</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">sg</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">inverr</span> <span style="color: #008080;">then</span> <span style="color: #000000;">errmsg</span><span style="color: #0000FF;">()</span> <span style="color: #008080;">return</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">t</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Valid\n_____\n"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">else</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"invalid\n_______\n"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
|
||||
t = verify(W, f, sg)
|
||||
if inverr then errmsg() return end if
|
||||
if t then
|
||||
printf(1,"Valid\n_____\n")
|
||||
else
|
||||
printf(1,"invalid\n_______\n")
|
||||
end if
|
||||
end procedure
|
||||
|
||||
<span style="color: #000080;font-style:italic;">--Test vectors: elliptic curve domain parameters,
|
||||
--short Weierstrass model y^2 = x^3 + ax + b (mod N)</span>
|
||||
--Test vectors: elliptic curve domain parameters,
|
||||
--short Weierstrass model y^2 = x^3 + ax + b (mod N)
|
||||
|
||||
<span style="color: #008080;">constant</span> <span style="color: #000000;">tests</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span>
|
||||
<span style="color: #000080;font-style:italic;">-- a, b, modulus N, base point G, order(G, E), cofactor</span>
|
||||
<span style="color: #0000FF;">{</span><span style="color: #000000;">355</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">671</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1073741789</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">13693</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">10088</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1073807281</span><span style="color: #0000FF;">},</span>
|
||||
<span style="color: #0000FF;">{</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">7</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">67096021</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">6580</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">779</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">16769911</span><span style="color: #0000FF;">},</span> <span style="color: #000080;font-style:italic;">-- 4</span>
|
||||
<span style="color: #0000FF;">{</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">877073</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">878159</span><span style="color: #0000FF;">},</span>
|
||||
<span style="color: #0000FF;">{</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">14</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">22651</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">63</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">30</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">151</span><span style="color: #0000FF;">},</span> <span style="color: #000080;font-style:italic;">-- 151</span>
|
||||
<span style="color: #0000FF;">{</span> <span style="color: #000000;">3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5</span><span style="color: #0000FF;">},</span>
|
||||
constant tests = {
|
||||
-- a, b, modulus N, base point G, order(G, E), cofactor
|
||||
{355, 671, 1073741789, 13693, 10088, 1073807281},
|
||||
{ 0, 7, 67096021, 6580, 779, 16769911}, -- 4
|
||||
{ -3, 1, 877073, 0, 1, 878159},
|
||||
{ 0, 14, 22651, 63, 30, 151}, -- 151
|
||||
{ 3, 2, 5, 2, 1, 5},
|
||||
|
||||
<span style="color: #000080;font-style:italic;">--ecdsa may fail if...
|
||||
--the base point is of composite order</span>
|
||||
<span style="color: #0000FF;">{</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">7</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">67096021</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2402</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">6067</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">33539822</span><span style="color: #0000FF;">},</span> <span style="color: #000080;font-style:italic;">-- 2
|
||||
--the given order is a multiple of the true order</span>
|
||||
<span style="color: #0000FF;">{</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">7</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">67096021</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">6580</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">779</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">67079644</span><span style="color: #0000FF;">},</span> <span style="color: #000080;font-style:italic;">-- 1
|
||||
--the modulus is not prime (deceptive example)</span>
|
||||
<span style="color: #0000FF;">{</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">7</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">877069</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">97123</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">877069</span><span style="color: #0000FF;">},</span>
|
||||
<span style="color: #000080;font-style:italic;">--fails if the modulus divides the discriminant</span>
|
||||
<span style="color: #0000FF;">{</span> <span style="color: #000000;">39</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">387</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">22651</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">95</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">27</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">22651</span><span style="color: #0000FF;">}}</span>
|
||||
--ecdsa may fail if...
|
||||
--the base point is of composite order
|
||||
{ 0, 7, 67096021, 2402, 6067, 33539822}, -- 2
|
||||
--the given order is a multiple of the true order
|
||||
{ 0, 7, 67096021, 6580, 779, 67079644}, -- 1
|
||||
--the modulus is not prime (deceptive example)
|
||||
{ 0, 7, 877069, 3, 97123, 877069},
|
||||
--fails if the modulus divides the discriminant
|
||||
{ 39, 387, 22651, 95, 27, 22651}}
|
||||
|
||||
<span style="color: #000080;font-style:italic;">--Digital signature on message hash f,
|
||||
--set d > 0 to simulate corrupted data</span>
|
||||
<span style="color: #004080;">atom</span> <span style="color: #000000;">f</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">#789ABCDE</span><span style="color: #0000FF;">,</span>
|
||||
<span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
|
||||
--Digital signature on message hash f,
|
||||
--set d > 0 to simulate corrupted data
|
||||
atom f = #789ABCDE,
|
||||
d = 0
|
||||
|
||||
<span style="color: #000080;font-style:italic;">--for i=1 to length(tests) do</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #000000;">ellinit</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tests</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #000000;">ec_dsa</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<!--
|
||||
--for i=1 to length(tests) do
|
||||
for i=1 to 1 do
|
||||
if not ellinit(tests[i]) then exit end if
|
||||
ec_dsa(f, d)
|
||||
end for
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue