Binary field arithmetic contributed by Sun Microsystems.

The 'OPENSSL_NO_SUN_DIV' default is still subject to change,
so I didn't bother to finish the CHANGES entry yet.

Submitted by: Douglas Stebila <douglas.stebila@sun.com>, Sheueling Chang <sheueling.chang@sun.com>
(CHANGES entry by Bodo Moeller)

1 files changed, 646 insertions, 0 deletions

diff --git a/crypto/bn/bntest.c b/crypto/bn/bntest.c
index 8158a67374..377b5ba590 100644
--- a/crypto/bn/bntest.c
+++ b/crypto/bn/bntest.c
@@ -55,6 +55,32 @@
  * copied and put under another distribution licence
  * [including the GNU Public Licence.]
  */
+/* ====================================================================
+ * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
+ *
+ * Portions of the attached software ("Contribution") are developed by 
+ * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
+ *
+ * The Contribution is licensed pursuant to the Eric Young open source
+ * license provided above.
+ *
+ * In addition, Sun covenants to all licensees who provide a reciprocal
+ * covenant with respect to their own patents if any, not to sue under
+ * current and future patent claims necessarily infringed by the making,
+ * using, practicing, selling, offering for sale and/or otherwise
+ * disposing of the Contribution as delivered hereunder 
+ * (or portions thereof), provided that such covenant shall not apply:
+ *  1) for code that a licensee deletes from the Contribution;
+ *  2) separates from the Contribution; or
+ *  3) for infringements caused by:
+ *       i) the modification of the Contribution or
+ *      ii) the combination of the Contribution with other software or
+ *          devices where such combination causes the infringement.
+ *
+ * The binary polynomial arithmetic software is originally written by 
+ * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
+ *
+ */
 
 #include <stdio.h>
 #include <stdlib.h>
@@ -91,6 +117,15 @@ int test_mod(BIO *bp,BN_CTX *ctx);
 int test_mod_mul(BIO *bp,BN_CTX *ctx);
 int test_mod_exp(BIO *bp,BN_CTX *ctx);
 int test_exp(BIO *bp,BN_CTX *ctx);
+int test_gf2m_add(BIO *bp);
+int test_gf2m_mod(BIO *bp);
+int test_gf2m_mod_mul(BIO *bp,BN_CTX *ctx);
+int test_gf2m_mod_sqr(BIO *bp,BN_CTX *ctx);
+int test_gf2m_mod_inv(BIO *bp,BN_CTX *ctx);
+int test_gf2m_mod_div(BIO *bp,BN_CTX *ctx);
+int test_gf2m_mod_exp(BIO *bp,BN_CTX *ctx);
+int test_gf2m_mod_sqrt(BIO *bp,BN_CTX *ctx);
+int test_gf2m_mod_solve_quad(BIO *bp,BN_CTX *ctx);
 int test_kron(BIO *bp,BN_CTX *ctx);
 int test_sqrt(BIO *bp,BN_CTX *ctx);
 int rand_neg(void);
@@ -226,6 +261,42 @@ int main(int argc, char *argv[])
 	if (!test_exp(out,ctx)) goto err;
 	BIO_flush(out);
 
+	message(out,"BN_GF2m_add");
+	if (!test_gf2m_add(out)) goto err;
+	BIO_flush(out);
+
+	message(out,"BN_GF2m_mod");
+	if (!test_gf2m_mod(out)) goto err;
+	BIO_flush(out);
+
+	message(out,"BN_GF2m_mod_mul");
+	if (!test_gf2m_mod_mul(out,ctx)) goto err;
+	BIO_flush(out);
+
+	message(out,"BN_GF2m_mod_sqr");
+	if (!test_gf2m_mod_sqr(out,ctx)) goto err;
+	BIO_flush(out);
+
+	message(out,"BN_GF2m_mod_inv");
+	if (!test_gf2m_mod_inv(out,ctx)) goto err;
+	BIO_flush(out);
+
+	message(out,"BN_GF2m_mod_div");
+	if (!test_gf2m_mod_div(out,ctx)) goto err;
+	BIO_flush(out);
+
+	message(out,"BN_GF2m_mod_exp");
+	if (!test_gf2m_mod_exp(out,ctx)) goto err;
+	BIO_flush(out);
+
+	message(out,"BN_GF2m_mod_sqrt");
+	if (!test_gf2m_mod_sqrt(out,ctx)) goto err;
+	BIO_flush(out);
+
+	message(out,"BN_GF2m_mod_solve_quad");
+	if (!test_gf2m_mod_solve_quad(out,ctx)) goto err;
+	BIO_flush(out);
+
 	message(out,"BN_kronecker");
 	if (!test_kron(out,ctx)) goto err;
 	BIO_flush(out);
@@ -872,6 +943,581 @@ int test_exp(BIO *bp, BN_CTX *ctx)
 	return(1);
 	}
 
+int test_gf2m_add(BIO *bp)
+	{
+	BIGNUM a,b,c;
+	int i, ret = 0;
+
+	BN_init(&a);
+	BN_init(&b);
+	BN_init(&c);
+
+	for (i=0; i<num0; i++)
+		{
+		BN_rand(&a,512,0,0);
+		BN_copy(&b, BN_value_one());
+		a.neg=rand_neg();
+		b.neg=rand_neg();
+		BN_GF2m_add(&c,&a,&b);
+#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);
+				BIO_puts(bp," = ");
+				}
+			BN_print(bp,&c);
+			BIO_puts(bp,"\n");
+			}
+#endif
+		/* Test that two added values have the correct parity. */
+		if((BN_is_odd(&a) && BN_is_odd(&c)) || (!BN_is_odd(&a) && !BN_is_odd(&c)))
+			{
+		    fprintf(stderr,"GF(2^m) addition test (a) failed!\n");
+			goto err;
+			}
+		BN_GF2m_add(&c,&c,&c);
+		/* Test that c + c = 0. */
+		if(!BN_is_zero(&c))
+		    {
+		    fprintf(stderr,"GF(2^m) addition test (b) failed!\n");
+			goto err;
+		    }
+		}
+	ret = 1;
+  err:
+	BN_free(&a);
+	BN_free(&b);
+	BN_free(&c);
+	return ret;
+	}
+
+int test_gf2m_mod(BIO *bp)
+	{
+	BIGNUM *a,*b[2],*c,*d,*e;
+	int i, j, ret = 0;
+	unsigned int p0[] = {163,7,6,3,0};
+	unsigned int p1[] = {193,15,0};
+
+	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;
+	unsigned int p0[] = {163,7,6,3,0};
+	unsigned int p1[] = {193,15,0};
+
+	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;
+	unsigned int p0[] = {163,7,6,3,0};
+	unsigned int p1[] = {193,15,0};
+
+	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;
+	unsigned int p0[] = {163,7,6,3,0};
+	unsigned int p1[] = {193,15,0};
+
+	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;
+	unsigned int p0[] = {163,7,6,3,0};
+	unsigned int p1[] = {193,15,0};
+
+	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;
+	unsigned int p0[] = {163,7,6,3,0};
+	unsigned int p1[] = {193,15,0};
+
+	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;
+	unsigned int p0[] = {163,7,6,3,0};
+	unsigned int p1[] = {193,15,0};
+
+	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;
+	unsigned int p0[] = {163,7,6,3,0};
+	unsigned int p1[] = {193,15,0};
+
+	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;
+	}
+
 static void genprime_cb(int p, int n, void *arg)
 	{
 	char c='*';