50 lines
828 B
Plaintext
50 lines
828 B
Plaintext
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# negate r when n > (p-1)/2
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decaf_neg(p, n, r) {
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mod(p) m = -r;
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r = n > (p-1)>>1 ? m : r;
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}
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# field F_p
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# curve a*x**2+y**2==1+d*x**2*y**2
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# input X,Y,Z,T (extended coordinates)
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decaf_encode(p,a,d, X,Y,Z,T, s) mod(p) {
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r = misqrt((a-d)*(Z+Y)*(Z-Y), p);
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u = (a-d)*r;
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decaf_neg(p, -2*u*Z, r);
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s = u*(r*(a*Z*X-d*Y*T)+Y)/a;
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decaf_neg(p, s, s);
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}
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# field F_p
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# curve a*x**2+y**2==1+d*x**2*y**2
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# input s
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# output in extended coordinates
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decaf_decode(p,a,d, s, ok,X,Y,Z,T) {
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if(s > (p-1)>>1){
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ok = 0;
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} else mod(p) {
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ss = s^2;
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Z = 1+a*ss;
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u = Z^2 - 4*d*ss;
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v = u*ss;
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if(v == 0)
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ok = 1;
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else {
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ok = msqrt(v, p);
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if(ok != 0){
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v = 1/ok;
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ok = 1;
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}
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}
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if(ok != 0) {
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decaf_neg(p, u*v, v);
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w = v * s * (2-Z);
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if(s == 0)
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w = w + 1;
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X = 2*s;
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Y = w * Z;
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T = w * X;
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}
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}
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}
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