Data update
This commit is contained in:
Ingy döt Net
parent
5150844a7d
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4bb20c9b71
7735 changed files with 38060 additions and 199180 deletions
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@ -1,26 +0,0 @@
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with Ada.Text_IO, Ada.Command_Line, Crypto.Types.Big_Numbers;
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procedure Mod_Exp is
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A: String :=
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"2988348162058574136915891421498819466320163312926952423791023078876139";
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B: String :=
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"2351399303373464486466122544523690094744975233415544072992656881240319";
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D: constant Positive := Positive'Max(Positive'Max(A'Length, B'Length), 40);
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-- the number of decimals to store A, B, and result
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Bits: constant Positive := (34*D)/10;
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-- (slightly more than) the number of bits to store A, B, and result
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package LN is new Crypto.Types.Big_Numbers (Bits + (32 - Bits mod 32));
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-- the actual number of bits has to be a multiple of 32
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use type LN.Big_Unsigned;
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function "+"(S: String) return LN.Big_Unsigned
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renames LN.Utils.To_Big_Unsigned;
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M: LN.Big_Unsigned := (+"10") ** (+"40");
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begin
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Ada.Text_IO.Put("A**B (mod 10**40) = ");
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Ada.Text_IO.Put_Line(LN.Utils.To_String(LN.Mod_Utils.Pow((+A), (+B), M)));
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end Mod_Exp;
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@ -1,5 +0,0 @@
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(let ((a "2988348162058574136915891421498819466320163312926952423791023078876139")
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(b "2351399303373464486466122544523690094744975233415544072992656881240319"))
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;; "$ ^ $$ mod (10 ^ 40)" performs modular exponentiation.
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;; "unpack(-5, x)_1" unpacks the integer from the modulo form.
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(message "%s" (calc-eval "unpack(-5, $ ^ $$ mod (10 ^ 40))_1" nil a b)))
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@ -1,18 +1,19 @@
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import bigints
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proc powmod(b, e, m: BigInt): BigInt =
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assert e >= 0
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assert e >= 0'bi
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var e = e
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var b = b
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let t = 2'bi
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result = initBigInt(1)
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while e > 0:
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if e mod 2 == 1:
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while e > 0'bi:
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if e mod t == 1'bi:
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result = (result * b) mod m
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e = e div 2
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e = e div t
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b = (b.pow 2) mod m
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var
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a = initBigInt("2988348162058574136915891421498819466320163312926952423791023078876139")
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b = initBigInt("2351399303373464486466122544523690094744975233415544072992656881240319")
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echo powmod(a, b, 10.pow 40)
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echo powmod(a, b, 10'bi.pow 40)
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@ -1,35 +1,33 @@
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(phixonline)-->
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<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
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<span style="color: #008080;">include</span> <span style="color: #004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
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<span style="color: #008080;">procedure</span> <span style="color: #000000;">mpz_mod_exp</span><span style="color: #0000FF;">(</span><span style="color: #004080;">mpz</span> <span style="color: #000000;">base</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">exponent</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">modulus</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">result</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">if</span> <span style="color: #7060A8;">mpz_cmp_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">exponent</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
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<span style="color: #7060A8;">mpz_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">result</span><span style="color: #0000FF;">,</span><span style="color: #000000;">base</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">else</span>
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<span style="color: #004080;">mpz</span> <span style="color: #000000;">_exp</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">exponent</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (use a copy)</span>
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<span style="color: #004080;">bool</span> <span style="color: #000000;">odd</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_odd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">_exp</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">if</span> <span style="color: #000000;">odd</span> <span style="color: #008080;">then</span>
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<span style="color: #7060A8;">mpz_sub_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">_exp</span><span style="color: #0000FF;">,</span><span style="color: #000000;">_exp</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</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: #7060A8;">mpz_fdiv_q_2exp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">_exp</span><span style="color: #0000FF;">,</span><span style="color: #000000;">_exp</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
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<span style="color: #000000;">mpz_mod_exp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">base</span><span style="color: #0000FF;">,</span><span style="color: #000000;">_exp</span><span style="color: #0000FF;">,</span><span style="color: #000000;">modulus</span><span style="color: #0000FF;">,</span><span style="color: #000000;">result</span><span style="color: #0000FF;">)</span>
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<span style="color: #000000;">_exp</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_free</span><span style="color: #0000FF;">(</span><span style="color: #000000;">_exp</span><span style="color: #0000FF;">)</span>
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<span style="color: #7060A8;">mpz_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">result</span><span style="color: #0000FF;">,</span><span style="color: #000000;">result</span><span style="color: #0000FF;">,</span><span style="color: #000000;">result</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">if</span> <span style="color: #000000;">odd</span> <span style="color: #008080;">then</span>
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<span style="color: #7060A8;">mpz_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">result</span><span style="color: #0000FF;">,</span><span style="color: #000000;">result</span><span style="color: #0000FF;">,</span><span style="color: #000000;">base</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;">if</span>
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<span style="color: #7060A8;">mpz_mod</span><span style="color: #0000FF;">(</span><span style="color: #000000;">result</span><span style="color: #0000FF;">,</span><span style="color: #000000;">result</span><span style="color: #0000FF;">,</span><span style="color: #000000;">modulus</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
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with javascript_semantics
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include mpfr.e
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procedure mpz_mod_exp(mpz base, exponent, modulus, result)
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if mpz_cmp_si(exponent,1)=0 then
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mpz_set(result,base)
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else
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mpz exp_copy = mpz_init_set(exponent)
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bool bOdd = mpz_odd(exp_copy)
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if bOdd then
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mpz_sub_ui(exp_copy,exp_copy,1)
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end if
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mpz_fdiv_q_2exp(exp_copy,exp_copy,1)
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mpz_mod_exp(base,exp_copy,modulus,result)
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exp_copy = mpz_free(exp_copy)
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mpz_mul(result,result,result)
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if bOdd then
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mpz_mul(result,result,base)
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end if
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end if
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mpz_mod(result,result,modulus)
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end procedure
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<span style="color: #004080;">mpz</span> <span style="color: #000000;">base</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"2988348162058574136915891421498819466320163312926952423791023078876139"</span><span style="color: #0000FF;">),</span>
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<span style="color: #000000;">exponent</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"2351399303373464486466122544523690094744975233415544072992656881240319"</span><span style="color: #0000FF;">),</span>
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<span style="color: #000000;">modulus</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"1"</span><span style="color: #0000FF;">&</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #008000;">'0'</span><span style="color: #0000FF;">,</span><span style="color: #000000;">40</span><span style="color: #0000FF;">)),</span>
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<span style="color: #000000;">result</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">()</span>
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mpz base = mpz_init("2988348162058574136915891421498819466320163312926952423791023078876139"),
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exponent = mpz_init("2351399303373464486466122544523690094744975233415544072992656881240319"),
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modulus = mpz_init("1e40"),
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result = mpz_init()
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<span style="color: #000000;">mpz_mod_exp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">base</span><span style="color: #0000FF;">,</span><span style="color: #000000;">exponent</span><span style="color: #0000FF;">,</span><span style="color: #000000;">modulus</span><span style="color: #0000FF;">,</span><span style="color: #000000;">result</span><span style="color: #0000FF;">)</span>
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<span style="color: #0000FF;">?</span><span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">result</span><span style="color: #0000FF;">)</span>
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mpz_mod_exp(base,exponent,modulus,result)
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?mpz_get_str(result)
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<span style="color: #000080;font-style:italic;">-- check against the builtin:</span>
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<span style="color: #7060A8;">mpz_powm</span><span style="color: #0000FF;">(</span><span style="color: #000000;">result</span><span style="color: #0000FF;">,</span><span style="color: #000000;">base</span><span style="color: #0000FF;">,</span><span style="color: #000000;">exponent</span><span style="color: #0000FF;">,</span><span style="color: #000000;">modulus</span><span style="color: #0000FF;">)</span>
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<span style="color: #0000FF;">?</span><span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">result</span><span style="color: #0000FF;">)</span>
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<!--
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-- check against the builtin:
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mpz_powm(result,base,exponent,modulus)
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?mpz_get_str(result)
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@ -1,18 +0,0 @@
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Function Invoke-ModuloExponentiation ([BigInt]$Base, [BigInt]$Exponent, $Modulo) {
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$Result = 1
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$Base = $Base % $Modulo
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If ($Base -eq 0) {return 0}
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While ($Exponent -gt 0) {
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If (($Exponent -band 1) -eq 1) {$Result = ($Result * $Base) % $Modulo}
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$Exponent = $Exponent -shr 1
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$Base = ($Base * $Base) % $Modulo
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}
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return ($Result % $Modulo)
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}
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$a = [BigInt]::Parse('2988348162058574136915891421498819466320163312926952423791023078876139')
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$b = [BigInt]::Parse('2351399303373464486466122544523690094744975233415544072992656881240319')
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$m = [BigInt]::Pow(10, 40)
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Invoke-ModuloExponentiation -Base $a -Exponent $b -Modulo $m
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