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make sqrt_Fp2 work for subfield elements #53

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make sqrt_Fp2 work for subfield elements #53

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b4654f7
make sqrt_Fp2 work for subfield elements
yyyyx4 Apr 23, 2022
aab495a
Merge branch 'microsoft:master' into fix_fp2_sqrt
yyyyx4 Mar 3, 2023
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32 changes: 31 additions & 1 deletion src/fpx.c
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Original file line number Diff line number Diff line change
Expand Up @@ -996,9 +996,39 @@ static bool is_zero(digit_t* a, unsigned int nwords)
void sqrt_Fp2(const f2elm_t u, f2elm_t y)
{ // Computes square roots of elements in (Fp2)^2 using Hamburg's trick.
felm_t t0, t1, t2, t3;
digit_t *a = (digit_t*)u[0], *b = (digit_t*)u[1];
const digit_t *a = u[0], *b = u[1];
unsigned int i;

// non-square elements of Fp require special treatment
fpcopy(b, t3);
fpcorrection(t3);
if (is_zero(t3, NWORDS_FIELD)) {

fpcopy(a, t1);
for (i = 0; i < OALICE_BITS - 2; i++) {
fpsqr_mont(t1, t1);
}
for (i = 0; i < OBOB_EXPON; i++) {
fpsqr_mont(t1, t0);
fpmul_mont(t1, t0, t1);
}
// t1 = a^((p+1)/4)

fpsqr_mont(t1, t0);

fpsub(t0, a, t3);
fpcorrection(t3);
if (is_zero(t3, NWORDS_FIELD)) { // t1^2 = a
fpcopy(t1, y[0]);
fpzero(y[1]);
}
else { // t1^2 = -a
fpzero(y[0]);
fpcopy(t1, y[1]);
}
return;
}

fpsqr_mont(a, t0); // t0 = a^2
fpsqr_mont(b, t1); // t1 = b^2
fpadd(t0, t1, t0); // t0 = t0+t1
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