Commit 19cda700 authored by Bodo Möller's avatar Bodo Möller
Browse files

Corrections to the comments in BN_mod_inverse.

parent 4751717c

crypto/bn/bn_gcd.c

+7 −7
Original line number Diff line number Diff line
@@ -240,7 +240,7 @@ BIGNUM *BN_mod_inverse(BIGNUM *in, 
	/* From  B = a mod |n|,  A = |n|  it follows that

	 *

	 *      0 <= B < A,

	 *           X*a  ==  B   (mod |n|),

	 *      sign*X*a  ==  B   (mod |n|),

	 *     -sign*Y*a  ==  A   (mod |n|).

	 */
@@ -250,7 +250,7 @@ BIGNUM *BN_mod_inverse(BIGNUM *in, 


		/*

		 *      0 < B < A,

		 * (*)       X*a  ==  B   (mod |n|),

		 * (*)  sign*X*a  ==  B   (mod |n|),

		 *     -sign*Y*a  ==  A   (mod |n|)

		 */
@@ -314,15 +314,15 @@ BIGNUM *BN_mod_inverse(BIGNUM *in, 
		 * i.e.

		 *      -sign*Y*a - D*A  ==  B    (mod |n|).

		 * Similarly, (*) translates into

		 *      X*a  ==  A          (mod |n|).

		 *       sign*X*a  ==  A          (mod |n|).

		 *

		 * Thus,

		 *      -sign*Y*a - D*X*a  ==  B  (mod |n|),

		 *  -sign*Y*a - D*sign*X*a  ==  B  (mod |n|),

		 * i.e.

		 *       -sign*(Y + D*X)*a  ==  B  (mod |n|).

		 *

		 * So if we set  (X, Y, sign) := (Y + D*X, X, -sign),  we arrive back at

		 *            X*a  ==  B   (mod |n|),

		 *       sign*X*a  ==  B   (mod |n|),

		 *      -sign*Y*a  ==  A   (mod |n|).

		 * Note that  X  and  Y  stay non-negative all the time.

		 */
@@ -361,7 +361,7 @@ BIGNUM *BN_mod_inverse(BIGNUM *in, 
		}



	/*

	 * The while loop ends when

	 * The while loop (Euclid's algorithm) ends when

	 *      A == gcd(a,n);

	 * we have

	 *      -sign*Y*a  ==  A  (mod |n|),