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+/* crypto/bn/bn_exp.c */
+/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
+ * All rights reserved.
+ *
+ * This package is an SSL implementation written
+ * by Eric Young (eay@cryptsoft.com).
+ * The implementation was written so as to conform with Netscapes SSL.
+ *
+ * This library is free for commercial and non-commercial use as long as
+ * the following conditions are aheared to. The following conditions
+ * apply to all code found in this distribution, be it the RC4, RSA,
+ * lhash, DES, etc., code; not just the SSL code. The SSL documentation
+ * included with this distribution is covered by the same copyright terms
+ * except that the holder is Tim Hudson (tjh@cryptsoft.com).
+ *
+ * Copyright remains Eric Young's, and as such any Copyright notices in
+ * the code are not to be removed.
+ * If this package is used in a product, Eric Young should be given attribution
+ * as the author of the parts of the library used.
+ * This can be in the form of a textual message at program startup or
+ * in documentation (online or textual) provided with the package.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the copyright
+ * notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ * notice, this list of conditions and the following disclaimer in the
+ * documentation and/or other materials provided with the distribution.
+ * 3. All advertising materials mentioning features or use of this software
+ * must display the following acknowledgement:
+ * "This product includes cryptographic software written by
+ * Eric Young (eay@cryptsoft.com)"
+ * The word 'cryptographic' can be left out if the rouines from the library
+ * being used are not cryptographic related :-).
+ * 4. If you include any Windows specific code (or a derivative thereof) from
+ * the apps directory (application code) you must include an acknowledgement:
+ * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
+ *
+ * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ *
+ * The licence and distribution terms for any publically available version or
+ * derivative of this code cannot be changed. i.e. this code cannot simply be
+ * copied and put under another distribution licence
+ * [including the GNU Public Licence.]
+ */
+/* ====================================================================
+ * Copyright (c) 1998-2000 The OpenSSL Project. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ * notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ * notice, this list of conditions and the following disclaimer in
+ * the documentation and/or other materials provided with the
+ * distribution.
+ *
+ * 3. All advertising materials mentioning features or use of this
+ * software must display the following acknowledgment:
+ * "This product includes software developed by the OpenSSL Project
+ * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
+ *
+ * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
+ * endorse or promote products derived from this software without
+ * prior written permission. For written permission, please contact
+ * openssl-core@openssl.org.
+ *
+ * 5. Products derived from this software may not be called "OpenSSL"
+ * nor may "OpenSSL" appear in their names without prior written
+ * permission of the OpenSSL Project.
+ *
+ * 6. Redistributions of any form whatsoever must retain the following
+ * acknowledgment:
+ * "This product includes software developed by the OpenSSL Project
+ * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
+ * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
+ * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
+ * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+ * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
+ * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+ * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
+ * OF THE POSSIBILITY OF SUCH DAMAGE.
+ * ====================================================================
+ *
+ * This product includes cryptographic software written by Eric Young
+ * (eay@cryptsoft.com). This product includes software written by Tim
+ * Hudson (tjh@cryptsoft.com).
+ *
+ */
+
+
+#include <stdio.h>
+#include "bn_lcl.h"
+
+#define TABLE_SIZE 32
+
+/* slow but works */
+int BN_mod_mul(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m, BN_CTX *ctx)
+ {
+ BIGNUM *t;
+ int r=0;
+
+ bn_check_top(a);
+ bn_check_top(b);
+ bn_check_top(m);
+
+ BN_CTX_start(ctx);
+ if ((t = BN_CTX_get(ctx)) == NULL) goto err;
+ if (a == b)
+ { if (!BN_sqr(t,a,ctx)) goto err; }
+ else
+ { if (!BN_mul(t,a,b,ctx)) goto err; }
+ if (!BN_mod(ret,t,m,ctx)) goto err;
+ r=1;
+err:
+ BN_CTX_end(ctx);
+ return(r);
+ }
+
+int BN_mod_exp(BIGNUM *r, BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
+ BN_CTX *ctx)
+ {
+ int ret;
+
+ bn_check_top(a);
+ bn_check_top(p);
+ bn_check_top(m);
+
+#ifdef MONT_MUL_MOD
+ /* I have finally been able to take out this pre-condition of
+ * the top bit being set. It was caused by an error in BN_div
+ * with negatives. There was also another problem when for a^b%m
+ * a >= m. eay 07-May-97 */
+/* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */
+
+ if (BN_is_odd(m))
+ {
+ if (a->top == 1)
+ {
+ BN_ULONG A = a->d[0];
+ ret=BN_mod_exp_mont_word(r,A,p,m,ctx,NULL);
+ }
+ else
+ ret=BN_mod_exp_mont(r,a,p,m,ctx,NULL);
+ }
+ else
+#endif
+#ifdef RECP_MUL_MOD
+ { ret=BN_mod_exp_recp(r,a,p,m,ctx); }
+#else
+ { ret=BN_mod_exp_simple(r,a,p,m,ctx); }
+#endif
+
+ return(ret);
+ }
+
+
+#ifdef RECP_MUL_MOD
+int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
+ const BIGNUM *m, BN_CTX *ctx)
+ {
+ int i,j,bits,ret=0,wstart,wend,window,wvalue;
+ int start=1,ts=0;
+ BIGNUM *aa;
+ BIGNUM val[TABLE_SIZE];
+ BN_RECP_CTX recp;
+
+ bits=BN_num_bits(p);
+
+ if (bits == 0)
+ {
+ BN_one(r);
+ return(1);
+ }
+
+ BN_CTX_start(ctx);
+ if ((aa = BN_CTX_get(ctx)) == NULL) goto err;
+
+ BN_RECP_CTX_init(&recp);
+ if (BN_RECP_CTX_set(&recp,m,ctx) <= 0) goto err;
+
+ BN_init(&(val[0]));
+ ts=1;
+
+ if (!BN_mod(&(val[0]),a,m,ctx)) goto err; /* 1 */
+
+ window = BN_window_bits_for_exponent_size(bits);
+ if (window > 1)
+ {
+ if (!BN_mod_mul_reciprocal(aa,&(val[0]),&(val[0]),&recp,ctx))
+ goto err; /* 2 */
+ j=1<<(window-1);
+ for (i=1; i<j; i++)
+ {
+ BN_init(&val[i]);
+ if (!BN_mod_mul_reciprocal(&(val[i]),&(val[i-1]),aa,&recp,ctx))
+ goto err;
+ }
+ ts=i;
+ }
+
+ start=1; /* This is used to avoid multiplication etc
+ * when there is only the value '1' in the
+ * buffer. */
+ wvalue=0; /* The 'value' of the window */
+ wstart=bits-1; /* The top bit of the window */
+ wend=0; /* The bottom bit of the window */
+
+ if (!BN_one(r)) goto err;
+
+ for (;;)
+ {
+ if (BN_is_bit_set(p,wstart) == 0)
+ {
+ if (!start)
+ if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
+ goto err;
+ if (wstart == 0) break;
+ wstart--;
+ continue;
+ }
+ /* We now have wstart on a 'set' bit, we now need to work out
+ * how bit a window to do. To do this we need to scan
+ * forward until the last set bit before the end of the
+ * window */
+ j=wstart;
+ wvalue=1;
+ wend=0;
+ for (i=1; i<window; i++)
+ {
+ if (wstart-i < 0) break;
+ if (BN_is_bit_set(p,wstart-i))
+ {
+ wvalue<<=(i-wend);
+ wvalue|=1;
+ wend=i;
+ }
+ }
+
+ /* wend is the size of the current window */
+ j=wend+1;
+ /* add the 'bytes above' */
+ if (!start)
+ for (i=0; i<j; i++)
+ {
+ if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
+ goto err;
+ }
+
+ /* wvalue will be an odd number < 2^window */
+ if (!BN_mod_mul_reciprocal(r,r,&(val[wvalue>>1]),&recp,ctx))
+ goto err;
+
+ /* move the 'window' down further */
+ wstart-=wend+1;
+ wvalue=0;
+ start=0;
+ if (wstart < 0) break;
+ }
+ ret=1;
+err:
+ BN_CTX_end(ctx);
+ for (i=0; i<ts; i++)
+ BN_clear_free(&(val[i]));
+ BN_RECP_CTX_free(&recp);
+ return(ret);
+ }
+#else
+
+/* The old fallback, simple version :-) */
+int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
+ const BIGNUM *m, BN_CTX *ctx)
+ {
+ int i,j,bits,ret=0,wstart,wend,window,wvalue,ts=0;
+ int start=1;
+ BIGNUM *d;
+ BIGNUM val[TABLE_SIZE];
+
+ bits=BN_num_bits(p);
+
+ if (bits == 0)
+ {
+ BN_one(r);
+ return(1);
+ }
+
+ BN_CTX_start(ctx);
+ if ((d = BN_CTX_get(ctx)) == NULL) goto err;
+
+ BN_init(&(val[0]));
+ ts=1;
+ if (!BN_mod(&(val[0]),a,m,ctx)) goto err; /* 1 */
+
+ window = BN_window_bits_for_exponent_size(bits);
+ if (window > 1)
+ {
+ if (!BN_mod_mul(d,&(val[0]),&(val[0]),m,ctx))
+ goto err; /* 2 */
+ j=1<<(window-1);
+ for (i=1; i<j; i++)
+ {
+ BN_init(&(val[i]));
+ if (!BN_mod_mul(&(val[i]),&(val[i-1]),d,m,ctx))
+ goto err;
+ }
+ ts=i;
+ }
+
+ start=1; /* This is used to avoid multiplication etc
+ * when there is only the value '1' in the
+ * buffer. */
+ wvalue=0; /* The 'value' of the window */
+ wstart=bits-1; /* The top bit of the window */
+ wend=0; /* The bottom bit of the window */
+
+ if (!BN_one(r)) goto err;
+
+ for (;;)
+ {
+ if (BN_is_bit_set(p,wstart) == 0)
+ {
+ if (!start)
+ if (!BN_mod_mul(r,r,r,m,ctx))
+ goto err;
+ if (wstart == 0) break;
+ wstart--;
+ continue;
+ }
+ /* We now have wstart on a 'set' bit, we now need to work out
+ * how bit a window to do. To do this we need to scan
+ * forward until the last set bit before the end of the
+ * window */
+ j=wstart;
+ wvalue=1;
+ wend=0;
+ for (i=1; i<window; i++)
+ {
+ if (wstart-i < 0) break;
+ if (BN_is_bit_set(p,wstart-i))
+ {
+ wvalue<<=(i-wend);
+ wvalue|=1;
+ wend=i;
+ }
+ }
+
+ /* wend is the size of the current window */
+ j=wend+1;
+ /* add the 'bytes above' */
+ if (!start)
+ for (i=0; i<j; i++)
+ {
+ if (!BN_mod_mul(r,r,r,m,ctx))
+ goto err;
+ }
+
+ /* wvalue will be an odd number < 2^window */
+ if (!BN_mod_mul(r,r,&(val[wvalue>>1]),m,ctx))
+ goto err;
+
+ /* move the 'window' down further */
+ wstart-=wend+1;
+ wvalue=0;
+ start=0;
+ if (wstart < 0) break;
+ }
+ ret=1;
+err:
+ BN_CTX_end(ctx);
+ for (i=0; i<ts; i++)
+ BN_clear_free(&(val[i]));
+ return(ret);
+ }
+#endif