- {
- BIGNUM *a,*b[2],*c,*d,*e;
- int i, j, ret = 0;
- int p0[] = {163,7,6,3,0,-1};
- int p1[] = {193,15,0,-1};
-
- a=BN_new();
- b[0]=BN_new();
- b[1]=BN_new();
- c=BN_new();
- d=BN_new();
- e=BN_new();
-
- BN_GF2m_arr2poly(p0, b[0]);
- BN_GF2m_arr2poly(p1, b[1]);
-
- for (i=0; i<num0; i++)
- {
- BN_bntest_rand(a, 1024, 0, 0);
- for (j=0; j < 2; j++)
- {
- BN_GF2m_mod(c, a, b[j]);
-#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
- if (bp != NULL)
- {
- if (!results)
- {
- BN_print(bp,a);
- BIO_puts(bp," % ");
- BN_print(bp,b[j]);
- BIO_puts(bp," - ");
- BN_print(bp,c);
- BIO_puts(bp,"\n");
- }
- }
-#endif
- BN_GF2m_add(d, a, c);
- BN_GF2m_mod(e, d, b[j]);
- /* Test that a + (a mod p) mod p == 0. */
- if(!BN_is_zero(e))
- {
- fprintf(stderr,"GF(2^m) modulo test failed!\n");
- goto err;
- }
- }
- }
- ret = 1;
- err:
- BN_free(a);
- BN_free(b[0]);
- BN_free(b[1]);
- BN_free(c);
- BN_free(d);
- BN_free(e);
- return ret;
- }
-
-int test_gf2m_mod_mul(BIO *bp,BN_CTX *ctx)
- {
- BIGNUM *a,*b[2],*c,*d,*e,*f,*g,*h;
- int i, j, ret = 0;
- int p0[] = {163,7,6,3,0,-1};
- int p1[] = {193,15,0,-1};
-
- a=BN_new();
- b[0]=BN_new();
- b[1]=BN_new();
- c=BN_new();
- d=BN_new();
- e=BN_new();
- f=BN_new();
- g=BN_new();
- h=BN_new();
-
- BN_GF2m_arr2poly(p0, b[0]);
- BN_GF2m_arr2poly(p1, b[1]);
-
- for (i=0; i<num0; i++)
- {
- BN_bntest_rand(a, 1024, 0, 0);
- BN_bntest_rand(c, 1024, 0, 0);
- BN_bntest_rand(d, 1024, 0, 0);
- for (j=0; j < 2; j++)
- {
- BN_GF2m_mod_mul(e, a, c, b[j], ctx);
-#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
- if (bp != NULL)
- {
- if (!results)
- {
- BN_print(bp,a);
- BIO_puts(bp," * ");
- BN_print(bp,c);
- BIO_puts(bp," % ");
- BN_print(bp,b[j]);
- BIO_puts(bp," - ");
- BN_print(bp,e);
- BIO_puts(bp,"\n");
- }
- }
-#endif
- BN_GF2m_add(f, a, d);
- BN_GF2m_mod_mul(g, f, c, b[j], ctx);
- BN_GF2m_mod_mul(h, d, c, b[j], ctx);
- BN_GF2m_add(f, e, g);
- BN_GF2m_add(f, f, h);
- /* Test that (a+d)*c = a*c + d*c. */
- if(!BN_is_zero(f))
- {
- fprintf(stderr,"GF(2^m) modular multiplication test failed!\n");
- goto err;
- }
- }
- }
- ret = 1;
- err:
- BN_free(a);
- BN_free(b[0]);
- BN_free(b[1]);
- BN_free(c);
- BN_free(d);
- BN_free(e);
- BN_free(f);
- BN_free(g);
- BN_free(h);
- return ret;
- }
-
-int test_gf2m_mod_sqr(BIO *bp,BN_CTX *ctx)
- {
- BIGNUM *a,*b[2],*c,*d;
- int i, j, ret = 0;
- int p0[] = {163,7,6,3,0,-1};
- int p1[] = {193,15,0,-1};
-
- a=BN_new();
- b[0]=BN_new();
- b[1]=BN_new();
- c=BN_new();
- d=BN_new();
-
- BN_GF2m_arr2poly(p0, b[0]);
- BN_GF2m_arr2poly(p1, b[1]);
-
- for (i=0; i<num0; i++)
- {
- BN_bntest_rand(a, 1024, 0, 0);
- for (j=0; j < 2; j++)
- {
- BN_GF2m_mod_sqr(c, a, b[j], ctx);
- BN_copy(d, a);
- BN_GF2m_mod_mul(d, a, d, b[j], ctx);
-#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
- if (bp != NULL)
- {
- if (!results)
- {
- BN_print(bp,a);
- BIO_puts(bp," ^ 2 % ");
- BN_print(bp,b[j]);
- BIO_puts(bp, " = ");
- BN_print(bp,c);
- BIO_puts(bp,"; a * a = ");
- BN_print(bp,d);
- BIO_puts(bp,"\n");
- }
- }
-#endif
- BN_GF2m_add(d, c, d);
- /* Test that a*a = a^2. */
- if(!BN_is_zero(d))
- {
- fprintf(stderr,"GF(2^m) modular squaring test failed!\n");
- goto err;
- }
- }
- }
- ret = 1;
- err:
- BN_free(a);
- BN_free(b[0]);
- BN_free(b[1]);
- BN_free(c);
- BN_free(d);
- return ret;
- }
-
-int test_gf2m_mod_inv(BIO *bp,BN_CTX *ctx)
- {
- BIGNUM *a,*b[2],*c,*d;
- int i, j, ret = 0;
- int p0[] = {163,7,6,3,0,-1};
- int p1[] = {193,15,0,-1};
-
- a=BN_new();
- b[0]=BN_new();
- b[1]=BN_new();
- c=BN_new();
- d=BN_new();
-
- BN_GF2m_arr2poly(p0, b[0]);
- BN_GF2m_arr2poly(p1, b[1]);
-
- for (i=0; i<num0; i++)
- {
- BN_bntest_rand(a, 512, 0, 0);
- for (j=0; j < 2; j++)
- {
- BN_GF2m_mod_inv(c, a, b[j], ctx);
- BN_GF2m_mod_mul(d, a, c, b[j], ctx);
-#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
- if (bp != NULL)
- {
- if (!results)
- {
- BN_print(bp,a);
- BIO_puts(bp, " * ");
- BN_print(bp,c);
- BIO_puts(bp," - 1 % ");
- BN_print(bp,b[j]);
- BIO_puts(bp,"\n");
- }
- }
-#endif
- /* Test that ((1/a)*a) = 1. */
- if(!BN_is_one(d))
- {
- fprintf(stderr,"GF(2^m) modular inversion test failed!\n");
- goto err;
- }
- }
- }
- ret = 1;
- err:
- BN_free(a);
- BN_free(b[0]);
- BN_free(b[1]);
- BN_free(c);
- BN_free(d);
- return ret;
- }
-
-int test_gf2m_mod_div(BIO *bp,BN_CTX *ctx)
- {
- BIGNUM *a,*b[2],*c,*d,*e,*f;
- int i, j, ret = 0;
- int p0[] = {163,7,6,3,0,-1};
- int p1[] = {193,15,0,-1};
-
- a=BN_new();
- b[0]=BN_new();
- b[1]=BN_new();
- c=BN_new();
- d=BN_new();
- e=BN_new();
- f=BN_new();
-
- BN_GF2m_arr2poly(p0, b[0]);
- BN_GF2m_arr2poly(p1, b[1]);
-
- for (i=0; i<num0; i++)
- {
- BN_bntest_rand(a, 512, 0, 0);
- BN_bntest_rand(c, 512, 0, 0);
- for (j=0; j < 2; j++)
- {
- BN_GF2m_mod_div(d, a, c, b[j], ctx);
- BN_GF2m_mod_mul(e, d, c, b[j], ctx);
- BN_GF2m_mod_div(f, a, e, b[j], ctx);
-#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
- if (bp != NULL)
- {
- if (!results)
- {
- BN_print(bp,a);
- BIO_puts(bp, " = ");
- BN_print(bp,c);
- BIO_puts(bp," * ");
- BN_print(bp,d);
- BIO_puts(bp, " % ");
- BN_print(bp,b[j]);
- BIO_puts(bp,"\n");
- }
- }
-#endif
- /* Test that ((a/c)*c)/a = 1. */
- if(!BN_is_one(f))
- {
- fprintf(stderr,"GF(2^m) modular division test failed!\n");
- goto err;
- }
- }
- }
- ret = 1;
- err:
- BN_free(a);
- BN_free(b[0]);
- BN_free(b[1]);
- BN_free(c);
- BN_free(d);
- BN_free(e);
- BN_free(f);
- return ret;
- }
-
-int test_gf2m_mod_exp(BIO *bp,BN_CTX *ctx)
- {
- BIGNUM *a,*b[2],*c,*d,*e,*f;
- int i, j, ret = 0;
- int p0[] = {163,7,6,3,0,-1};
- int p1[] = {193,15,0,-1};
-
- a=BN_new();
- b[0]=BN_new();
- b[1]=BN_new();
- c=BN_new();
- d=BN_new();
- e=BN_new();
- f=BN_new();
-
- BN_GF2m_arr2poly(p0, b[0]);
- BN_GF2m_arr2poly(p1, b[1]);
-
- for (i=0; i<num0; i++)
- {
- BN_bntest_rand(a, 512, 0, 0);
- BN_bntest_rand(c, 512, 0, 0);
- BN_bntest_rand(d, 512, 0, 0);
- for (j=0; j < 2; j++)
- {
- BN_GF2m_mod_exp(e, a, c, b[j], ctx);
- BN_GF2m_mod_exp(f, a, d, b[j], ctx);
- BN_GF2m_mod_mul(e, e, f, b[j], ctx);
- BN_add(f, c, d);
- BN_GF2m_mod_exp(f, a, f, b[j], ctx);
-#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
- if (bp != NULL)
- {
- if (!results)
- {
- BN_print(bp,a);
- BIO_puts(bp, " ^ (");
- BN_print(bp,c);
- BIO_puts(bp," + ");
- BN_print(bp,d);
- BIO_puts(bp, ") = ");
- BN_print(bp,e);
- BIO_puts(bp, "; - ");
- BN_print(bp,f);
- BIO_puts(bp, " % ");
- BN_print(bp,b[j]);
- BIO_puts(bp,"\n");
- }
- }
-#endif
- BN_GF2m_add(f, e, f);
- /* Test that a^(c+d)=a^c*a^d. */
- if(!BN_is_zero(f))
- {
- fprintf(stderr,"GF(2^m) modular exponentiation test failed!\n");
- goto err;
- }
- }
- }
- ret = 1;
- err:
- BN_free(a);
- BN_free(b[0]);
- BN_free(b[1]);
- BN_free(c);
- BN_free(d);
- BN_free(e);
- BN_free(f);
- return ret;
- }
-
-int test_gf2m_mod_sqrt(BIO *bp,BN_CTX *ctx)
- {
- BIGNUM *a,*b[2],*c,*d,*e,*f;
- int i, j, ret = 0;
- int p0[] = {163,7,6,3,0,-1};
- int p1[] = {193,15,0,-1};
-
- a=BN_new();
- b[0]=BN_new();
- b[1]=BN_new();
- c=BN_new();
- d=BN_new();
- e=BN_new();
- f=BN_new();
-
- BN_GF2m_arr2poly(p0, b[0]);
- BN_GF2m_arr2poly(p1, b[1]);
-
- for (i=0; i<num0; i++)
- {
- BN_bntest_rand(a, 512, 0, 0);
- for (j=0; j < 2; j++)
- {
- BN_GF2m_mod(c, a, b[j]);
- BN_GF2m_mod_sqrt(d, a, b[j], ctx);
- BN_GF2m_mod_sqr(e, d, b[j], ctx);
-#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
- if (bp != NULL)
- {
- if (!results)
- {
- BN_print(bp,d);
- BIO_puts(bp, " ^ 2 - ");
- BN_print(bp,a);
- BIO_puts(bp,"\n");
- }
- }
-#endif
- BN_GF2m_add(f, c, e);
- /* Test that d^2 = a, where d = sqrt(a). */
- if(!BN_is_zero(f))
- {
- fprintf(stderr,"GF(2^m) modular square root test failed!\n");
- goto err;
- }
- }
- }
- ret = 1;
- err:
- BN_free(a);
- BN_free(b[0]);
- BN_free(b[1]);
- BN_free(c);
- BN_free(d);
- BN_free(e);
- BN_free(f);
- return ret;
- }
-
-int test_gf2m_mod_solve_quad(BIO *bp,BN_CTX *ctx)
- {
- BIGNUM *a,*b[2],*c,*d,*e;
- int i, j, s = 0, t, ret = 0;
- int p0[] = {163,7,6,3,0,-1};
- int p1[] = {193,15,0,-1};
-
- a=BN_new();
- b[0]=BN_new();
- b[1]=BN_new();
- c=BN_new();
- d=BN_new();
- e=BN_new();
-
- BN_GF2m_arr2poly(p0, b[0]);
- BN_GF2m_arr2poly(p1, b[1]);
-
- for (i=0; i<num0; i++)
- {
- BN_bntest_rand(a, 512, 0, 0);
- for (j=0; j < 2; j++)
- {
- t = BN_GF2m_mod_solve_quad(c, a, b[j], ctx);
- if (t)
- {
- s++;
- BN_GF2m_mod_sqr(d, c, b[j], ctx);
- BN_GF2m_add(d, c, d);
- BN_GF2m_mod(e, a, b[j]);
-#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
- if (bp != NULL)
- {
- if (!results)
- {
- BN_print(bp,c);
- BIO_puts(bp, " is root of z^2 + z = ");
- BN_print(bp,a);
- BIO_puts(bp, " % ");
- BN_print(bp,b[j]);
- BIO_puts(bp, "\n");
- }
- }
-#endif
- BN_GF2m_add(e, e, d);
- /* Test that solution of quadratic c satisfies c^2 + c = a. */
- if(!BN_is_zero(e))
- {
- fprintf(stderr,"GF(2^m) modular solve quadratic test failed!\n");
- goto err;
- }
-
- }
- else
- {
-#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
- if (bp != NULL)
- {
- if (!results)
- {
- BIO_puts(bp, "There are no roots of z^2 + z = ");
- BN_print(bp,a);
- BIO_puts(bp, " % ");
- BN_print(bp,b[j]);
- BIO_puts(bp, "\n");
- }
- }
-#endif
- }
- }
- }
- if (s == 0)
- {
- fprintf(stderr,"All %i tests of GF(2^m) modular solve quadratic resulted in no roots;\n", num0);
- fprintf(stderr,"this is very unlikely and probably indicates an error.\n");
- goto err;
- }
- ret = 1;
- err:
- BN_free(a);
- BN_free(b[0]);
- BN_free(b[1]);
- BN_free(c);
- BN_free(d);
- BN_free(e);
- return ret;
- }
+{
+ BIGNUM *a, *b[2], *c, *d, *e;
+ int i, j, ret = 0;
+ int p0[] = { 163, 7, 6, 3, 0, -1 };
+ int p1[] = { 193, 15, 0, -1 };
+
+ a = BN_new();
+ b[0] = BN_new();
+ b[1] = BN_new();
+ c = BN_new();
+ d = BN_new();
+ e = BN_new();
+
+ BN_GF2m_arr2poly(p0, b[0]);
+ BN_GF2m_arr2poly(p1, b[1]);
+
+ for (i = 0; i < num0; i++) {
+ BN_bntest_rand(a, 1024, 0, 0);
+ for (j = 0; j < 2; j++) {
+ BN_GF2m_mod(c, a, b[j]);
+ BN_GF2m_add(d, a, c);
+ BN_GF2m_mod(e, d, b[j]);
+ /* Test that a + (a mod p) mod p == 0. */
+ if (!BN_is_zero(e)) {
+ fprintf(stderr, "GF(2^m) modulo test failed!\n");
+ goto err;
+ }
+ }
+ }
+ ret = 1;
+ err:
+ BN_free(a);
+ BN_free(b[0]);
+ BN_free(b[1]);
+ BN_free(c);
+ BN_free(d);
+ BN_free(e);
+ return ret;
+}
+
+int test_gf2m_mod_mul(BIO *bp, BN_CTX *ctx)
+{
+ BIGNUM *a, *b[2], *c, *d, *e, *f, *g, *h;
+ int i, j, ret = 0;
+ int p0[] = { 163, 7, 6, 3, 0, -1 };
+ int p1[] = { 193, 15, 0, -1 };
+
+ a = BN_new();
+ b[0] = BN_new();
+ b[1] = BN_new();
+ c = BN_new();
+ d = BN_new();
+ e = BN_new();
+ f = BN_new();
+ g = BN_new();
+ h = BN_new();
+
+ BN_GF2m_arr2poly(p0, b[0]);
+ BN_GF2m_arr2poly(p1, b[1]);
+
+ for (i = 0; i < num0; i++) {
+ BN_bntest_rand(a, 1024, 0, 0);
+ BN_bntest_rand(c, 1024, 0, 0);
+ BN_bntest_rand(d, 1024, 0, 0);
+ for (j = 0; j < 2; j++) {
+ BN_GF2m_mod_mul(e, a, c, b[j], ctx);
+ BN_GF2m_add(f, a, d);
+ BN_GF2m_mod_mul(g, f, c, b[j], ctx);
+ BN_GF2m_mod_mul(h, d, c, b[j], ctx);
+ BN_GF2m_add(f, e, g);
+ BN_GF2m_add(f, f, h);
+ /* Test that (a+d)*c = a*c + d*c. */
+ if (!BN_is_zero(f)) {
+ fprintf(stderr,
+ "GF(2^m) modular multiplication test failed!\n");
+ goto err;
+ }
+ }
+ }
+ ret = 1;
+ err:
+ BN_free(a);
+ BN_free(b[0]);
+ BN_free(b[1]);
+ BN_free(c);
+ BN_free(d);
+ BN_free(e);
+ BN_free(f);
+ BN_free(g);
+ BN_free(h);
+ return ret;
+}
+
+int test_gf2m_mod_sqr(BIO *bp, BN_CTX *ctx)
+{
+ BIGNUM *a, *b[2], *c, *d;
+ int i, j, ret = 0;
+ int p0[] = { 163, 7, 6, 3, 0, -1 };
+ int p1[] = { 193, 15, 0, -1 };
+
+ a = BN_new();
+ b[0] = BN_new();
+ b[1] = BN_new();
+ c = BN_new();
+ d = BN_new();
+
+ BN_GF2m_arr2poly(p0, b[0]);
+ BN_GF2m_arr2poly(p1, b[1]);
+
+ for (i = 0; i < num0; i++) {
+ BN_bntest_rand(a, 1024, 0, 0);
+ for (j = 0; j < 2; j++) {
+ BN_GF2m_mod_sqr(c, a, b[j], ctx);
+ BN_copy(d, a);
+ BN_GF2m_mod_mul(d, a, d, b[j], ctx);
+ BN_GF2m_add(d, c, d);
+ /* Test that a*a = a^2. */
+ if (!BN_is_zero(d)) {
+ fprintf(stderr, "GF(2^m) modular squaring test failed!\n");
+ goto err;
+ }
+ }
+ }
+ ret = 1;
+ err:
+ BN_free(a);
+ BN_free(b[0]);
+ BN_free(b[1]);
+ BN_free(c);
+ BN_free(d);
+ return ret;
+}
+
+int test_gf2m_mod_inv(BIO *bp, BN_CTX *ctx)
+{
+ BIGNUM *a, *b[2], *c, *d;
+ int i, j, ret = 0;
+ int p0[] = { 163, 7, 6, 3, 0, -1 };
+ int p1[] = { 193, 15, 0, -1 };
+
+ a = BN_new();
+ b[0] = BN_new();
+ b[1] = BN_new();
+ c = BN_new();
+ d = BN_new();
+
+ BN_GF2m_arr2poly(p0, b[0]);
+ BN_GF2m_arr2poly(p1, b[1]);
+
+ for (i = 0; i < num0; i++) {
+ BN_bntest_rand(a, 512, 0, 0);
+ for (j = 0; j < 2; j++) {
+ BN_GF2m_mod_inv(c, a, b[j], ctx);
+ BN_GF2m_mod_mul(d, a, c, b[j], ctx);
+ /* Test that ((1/a)*a) = 1. */
+ if (!BN_is_one(d)) {
+ fprintf(stderr, "GF(2^m) modular inversion test failed!\n");
+ goto err;
+ }
+ }
+ }
+ ret = 1;
+ err:
+ BN_free(a);
+ BN_free(b[0]);
+ BN_free(b[1]);
+ BN_free(c);
+ BN_free(d);
+ return ret;
+}
+
+int test_gf2m_mod_div(BIO *bp, BN_CTX *ctx)
+{
+ BIGNUM *a, *b[2], *c, *d, *e, *f;
+ int i, j, ret = 0;
+ int p0[] = { 163, 7, 6, 3, 0, -1 };
+ int p1[] = { 193, 15, 0, -1 };
+
+ a = BN_new();
+ b[0] = BN_new();
+ b[1] = BN_new();
+ c = BN_new();
+ d = BN_new();
+ e = BN_new();
+ f = BN_new();
+
+ BN_GF2m_arr2poly(p0, b[0]);
+ BN_GF2m_arr2poly(p1, b[1]);
+
+ for (i = 0; i < num0; i++) {
+ BN_bntest_rand(a, 512, 0, 0);
+ BN_bntest_rand(c, 512, 0, 0);
+ for (j = 0; j < 2; j++) {
+ BN_GF2m_mod_div(d, a, c, b[j], ctx);
+ BN_GF2m_mod_mul(e, d, c, b[j], ctx);
+ BN_GF2m_mod_div(f, a, e, b[j], ctx);
+ /* Test that ((a/c)*c)/a = 1. */
+ if (!BN_is_one(f)) {
+ fprintf(stderr, "GF(2^m) modular division test failed!\n");
+ goto err;
+ }
+ }
+ }
+ ret = 1;
+ err:
+ BN_free(a);
+ BN_free(b[0]);
+ BN_free(b[1]);
+ BN_free(c);
+ BN_free(d);
+ BN_free(e);
+ BN_free(f);
+ return ret;
+}
+
+int test_gf2m_mod_exp(BIO *bp, BN_CTX *ctx)
+{
+ BIGNUM *a, *b[2], *c, *d, *e, *f;
+ int i, j, ret = 0;
+ int p0[] = { 163, 7, 6, 3, 0, -1 };
+ int p1[] = { 193, 15, 0, -1 };
+
+ a = BN_new();
+ b[0] = BN_new();
+ b[1] = BN_new();
+ c = BN_new();
+ d = BN_new();
+ e = BN_new();
+ f = BN_new();
+
+ BN_GF2m_arr2poly(p0, b[0]);
+ BN_GF2m_arr2poly(p1, b[1]);
+
+ for (i = 0; i < num0; i++) {
+ BN_bntest_rand(a, 512, 0, 0);
+ BN_bntest_rand(c, 512, 0, 0);
+ BN_bntest_rand(d, 512, 0, 0);
+ for (j = 0; j < 2; j++) {
+ BN_GF2m_mod_exp(e, a, c, b[j], ctx);
+ BN_GF2m_mod_exp(f, a, d, b[j], ctx);
+ BN_GF2m_mod_mul(e, e, f, b[j], ctx);
+ BN_add(f, c, d);
+ BN_GF2m_mod_exp(f, a, f, b[j], ctx);
+ BN_GF2m_add(f, e, f);
+ /* Test that a^(c+d)=a^c*a^d. */
+ if (!BN_is_zero(f)) {
+ fprintf(stderr,
+ "GF(2^m) modular exponentiation test failed!\n");
+ goto err;
+ }
+ }
+ }
+ ret = 1;
+ err:
+ BN_free(a);
+ BN_free(b[0]);
+ BN_free(b[1]);
+ BN_free(c);
+ BN_free(d);
+ BN_free(e);
+ BN_free(f);
+ return ret;
+}
+
+int test_gf2m_mod_sqrt(BIO *bp, BN_CTX *ctx)
+{
+ BIGNUM *a, *b[2], *c, *d, *e, *f;
+ int i, j, ret = 0;
+ int p0[] = { 163, 7, 6, 3, 0, -1 };
+ int p1[] = { 193, 15, 0, -1 };
+
+ a = BN_new();
+ b[0] = BN_new();
+ b[1] = BN_new();
+ c = BN_new();
+ d = BN_new();
+ e = BN_new();
+ f = BN_new();
+
+ BN_GF2m_arr2poly(p0, b[0]);
+ BN_GF2m_arr2poly(p1, b[1]);
+
+ for (i = 0; i < num0; i++) {
+ BN_bntest_rand(a, 512, 0, 0);
+ for (j = 0; j < 2; j++) {
+ BN_GF2m_mod(c, a, b[j]);
+ BN_GF2m_mod_sqrt(d, a, b[j], ctx);
+ BN_GF2m_mod_sqr(e, d, b[j], ctx);
+ BN_GF2m_add(f, c, e);
+ /* Test that d^2 = a, where d = sqrt(a). */
+ if (!BN_is_zero(f)) {
+ fprintf(stderr, "GF(2^m) modular square root test failed!\n");
+ goto err;
+ }
+ }
+ }
+ ret = 1;
+ err:
+ BN_free(a);
+ BN_free(b[0]);
+ BN_free(b[1]);
+ BN_free(c);
+ BN_free(d);
+ BN_free(e);
+ BN_free(f);
+ return ret;
+}
+
+int test_gf2m_mod_solve_quad(BIO *bp, BN_CTX *ctx)
+{
+ BIGNUM *a, *b[2], *c, *d, *e;
+ int i, j, s = 0, t, ret = 0;
+ int p0[] = { 163, 7, 6, 3, 0, -1 };
+ int p1[] = { 193, 15, 0, -1 };
+
+ a = BN_new();
+ b[0] = BN_new();
+ b[1] = BN_new();
+ c = BN_new();
+ d = BN_new();
+ e = BN_new();
+
+ BN_GF2m_arr2poly(p0, b[0]);
+ BN_GF2m_arr2poly(p1, b[1]);
+
+ for (i = 0; i < num0; i++) {
+ BN_bntest_rand(a, 512, 0, 0);
+ for (j = 0; j < 2; j++) {
+ t = BN_GF2m_mod_solve_quad(c, a, b[j], ctx);
+ if (t) {
+ s++;
+ BN_GF2m_mod_sqr(d, c, b[j], ctx);
+ BN_GF2m_add(d, c, d);
+ BN_GF2m_mod(e, a, b[j]);
+ BN_GF2m_add(e, e, d);
+ /*
+ * Test that solution of quadratic c satisfies c^2 + c = a.
+ */
+ if (!BN_is_zero(e)) {
+ fprintf(stderr,
+ "GF(2^m) modular solve quadratic test failed!\n");
+ goto err;
+ }
+
+ }
+ }
+ }
+ if (s == 0) {
+ fprintf(stderr,
+ "All %i tests of GF(2^m) modular solve quadratic resulted in no roots;\n",
+ num0);
+ fprintf(stderr,
+ "this is very unlikely and probably indicates an error.\n");
+ goto err;
+ }
+ ret = 1;
+ err:
+ BN_free(a);
+ BN_free(b[0]);
+ BN_free(b[1]);
+ BN_free(c);
+ BN_free(d);
+ BN_free(e);
+ return ret;
+}