+ /* general inversion algorithm */
+
+ while (!BN_is_zero(B))
+ {
+ BIGNUM *tmp;
+
+ /*
+ * 0 < B < A,
+ * (*) -sign*X*a == B (mod |n|),
+ * sign*Y*a == A (mod |n|)
+ */
+
+ /* (D, M) := (A/B, A%B) ... */
+ if (BN_num_bits(A) == BN_num_bits(B))
+ {
+ if (!BN_one(D)) goto err;
+ if (!BN_sub(M,A,B)) goto err;
+ }
+ else if (BN_num_bits(A) == BN_num_bits(B) + 1)
+ {
+ /* A/B is 1, 2, or 3 */
+ if (!BN_lshift1(T,B)) goto err;
+ if (BN_ucmp(A,T) < 0)
+ {
+ /* A < 2*B, so D=1 */
+ if (!BN_one(D)) goto err;
+ if (!BN_sub(M,A,B)) goto err;
+ }
+ else
+ {
+ /* A >= 2*B, so D=2 or D=3 */
+ if (!BN_sub(M,A,T)) goto err;
+ if (!BN_add(D,T,B)) goto err; /* use D (:= 3*B) as temp */
+ if (BN_ucmp(A,D) < 0)
+ {
+ /* A < 3*B, so D=2 */
+ if (!BN_set_word(D,2)) goto err;
+ /* M (= A - 2*B) already has the correct value */
+ }
+ else
+ {
+ /* only D=3 remains */
+ if (!BN_set_word(D,3)) goto err;
+ /* currently M = A - 2*B, but we need M = A - 3*B */
+ if (!BN_sub(M,M,B)) goto err;
+ }
+ }
+ }
+ else
+ {
+ if (!BN_div(D,M,A,B,ctx)) goto err;
+ }
+
+ /* Now
+ * A = D*B + M;
+ * thus we have
+ * (**) sign*Y*a == D*B + M (mod |n|).
+ */
+
+ tmp=A; /* keep the BIGNUM object, the value does not matter */
+
+ /* (A, B) := (B, A mod B) ... */
+ A=B;
+ B=M;
+ /* ... so we have 0 <= B < A again */
+
+ /* Since the former M is now B and the former B is now A,
+ * (**) translates into
+ * sign*Y*a == D*A + B (mod |n|),
+ * i.e.
+ * sign*Y*a - D*A == B (mod |n|).
+ * Similarly, (*) translates into
+ * -sign*X*a == A (mod |n|).
+ *
+ * Thus,
+ * 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
+ * -sign*X*a == B (mod |n|),
+ * sign*Y*a == A (mod |n|).
+ * Note that X and Y stay non-negative all the time.
+ */
+
+ /* most of the time D is very small, so we can optimize tmp := D*X+Y */
+ if (BN_is_one(D))
+ {
+ if (!BN_add(tmp,X,Y)) goto err;
+ }
+ else
+ {
+ if (BN_is_word(D,2))
+ {
+ if (!BN_lshift1(tmp,X)) goto err;
+ }
+ else if (BN_is_word(D,4))
+ {
+ if (!BN_lshift(tmp,X,2)) goto err;
+ }
+ else if (D->top == 1)
+ {
+ if (!BN_copy(tmp,X)) goto err;
+ if (!BN_mul_word(tmp,D->d[0])) goto err;
+ }
+ else
+ {
+ if (!BN_mul(tmp,D,X,ctx)) goto err;
+ }
+ if (!BN_add(tmp,tmp,Y)) goto err;
+ }
+
+ M=Y; /* keep the BIGNUM object, the value does not matter */
+ Y=X;
+ X=tmp;
+ sign = -sign;
+ }