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Initial data commit

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Ingy döt Net 2023-07-01 11:58:00 -04:00
parent 72d218235f
commit f23f22d71c
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19
Task/Tonelli-Shanks-algorithm/Zkl/tonelli-shanks-algorithm-1.zkl Normal file
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var BN=Import("zklBigNum");
fcn modEq(a,b,p) { (a-b)%p==0 }
fcn legendre(a,p){ a.powm((p - 1)/2,p) }
fcn tonelli(n,p){ //(BigInt,Int|BigInt)
_assert_(legendre(n,p)==1, "not a square (mod p)"+vm.arglist);
q,s:=p-1,0;
while(q.isEven){ q/=2; s+=1; }
if(s==1) return(n.powm((p+1)/4,p));
z:=[BN(2)..p].filter1('wrap(z){ legendre(z,p)==(p-1) });
c,r,t,m,t2:=z.powm(q,p), n.powm((q+1)/2,p), n.powm(q,p), s, 0;
while(not modEq(t,1,p)){
t2=(t*t)%p;
i:=1; while(not modEq(t2,1,p)){ i+=1; t2=(t2*t2)%p; } // assert(i<m)
b:=c.powm(BN(1).shiftLeft(m-i-1), p);
r,c,t,m = (r*b)%p, (b*b)%p, (t*c)%p, i;
}
r
}

10
Task/Tonelli-Shanks-algorithm/Zkl/tonelli-shanks-algorithm-2.zkl Normal file
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ttest:=T(T(10,13), T(56,101), T(1030,10009), T(44402,100049),
T(665820697,1000000009), T(881398088036,1000000000039),
T("41660815127637347468140745042827704103445750172002", BN(10).pow(50) + 577),
T(1032,10009) );
foreach n,p in (ttest){ n=BN(n);
r:=tonelli(n,p);
assert((r*r-n)%p == 0,"(r*r-n)%p == 0 : %s,%s,%s-->%s".fmt(r,n,p,(r*r-n)%p));
println("n=%d p=%d".fmt(n,p));
println(" roots: %d %d".fmt(r, p-r));
}