diff options
Diffstat (limited to 'crypto/bn/bn_sqrt.c')
| -rw-r--r-- | crypto/bn/bn_sqrt.c | 52 |
1 files changed, 26 insertions, 26 deletions
diff --git a/crypto/bn/bn_sqrt.c b/crypto/bn/bn_sqrt.c index 1b259f31c6..232af99a21 100644 --- a/crypto/bn/bn_sqrt.c +++ b/crypto/bn/bn_sqrt.c @@ -152,32 +152,32 @@ BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx) } if (e == 2) { - /*- - * |p| == 5 (mod 8) - * - * In this case 2 is always a non-square since - * Legendre(2,p) = (-1)^((p^2-1)/8) for any odd prime. - * So if a really is a square, then 2*a is a non-square. - * Thus for - * b := (2*a)^((|p|-5)/8), - * i := (2*a)*b^2 - * we have - * i^2 = (2*a)^((1 + (|p|-5)/4)*2) - * = (2*a)^((p-1)/2) - * = -1; - * so if we set - * x := a*b*(i-1), - * then - * x^2 = a^2 * b^2 * (i^2 - 2*i + 1) - * = a^2 * b^2 * (-2*i) - * = a*(-i)*(2*a*b^2) - * = a*(-i)*i - * = a. - * - * (This is due to A.O.L. Atkin, - * <URL: http://listserv.nodak.edu/scripts/wa.exe?A2=ind9211&L=nmbrthry&O=T&P=562>, - * November 1992.) - */ + /*- + * |p| == 5 (mod 8) + * + * In this case 2 is always a non-square since + * Legendre(2,p) = (-1)^((p^2-1)/8) for any odd prime. + * So if a really is a square, then 2*a is a non-square. + * Thus for + * b := (2*a)^((|p|-5)/8), + * i := (2*a)*b^2 + * we have + * i^2 = (2*a)^((1 + (|p|-5)/4)*2) + * = (2*a)^((p-1)/2) + * = -1; + * so if we set + * x := a*b*(i-1), + * then + * x^2 = a^2 * b^2 * (i^2 - 2*i + 1) + * = a^2 * b^2 * (-2*i) + * = a*(-i)*(2*a*b^2) + * = a*(-i)*i + * = a. + * + * (This is due to A.O.L. Atkin, + * <URL: http://listserv.nodak.edu/scripts/wa.exe?A2=ind9211&L=nmbrthry&O=T&P=562>, + * November 1992.) + */ /* t := 2*a */ if (!BN_mod_lshift1_quick(t, A, p)) |