| /* |
| * Copyright 1995-2016 The OpenSSL Project Authors. All Rights Reserved. |
| * |
| * Licensed under the Apache License 2.0 (the "License"). You may not use |
| * this file except in compliance with the License. You can obtain a copy |
| * in the file LICENSE in the source distribution or at |
| * https://www.openssl.org/source/license.html |
| */ |
| |
| #include <assert.h> |
| #include <openssl/crypto.h> |
| #include "internal/cryptlib.h" |
| #include "bn_local.h" |
| |
| #if defined(BN_LLONG) || defined(BN_UMULT_HIGH) |
| |
| BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num, |
| BN_ULONG w) |
| { |
| BN_ULONG c1 = 0; |
| |
| assert(num >= 0); |
| if (num <= 0) |
| return c1; |
| |
| # ifndef OPENSSL_SMALL_FOOTPRINT |
| while (num & ~3) { |
| mul_add(rp[0], ap[0], w, c1); |
| mul_add(rp[1], ap[1], w, c1); |
| mul_add(rp[2], ap[2], w, c1); |
| mul_add(rp[3], ap[3], w, c1); |
| ap += 4; |
| rp += 4; |
| num -= 4; |
| } |
| # endif |
| while (num) { |
| mul_add(rp[0], ap[0], w, c1); |
| ap++; |
| rp++; |
| num--; |
| } |
| |
| return c1; |
| } |
| |
| BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w) |
| { |
| BN_ULONG c1 = 0; |
| |
| assert(num >= 0); |
| if (num <= 0) |
| return c1; |
| |
| # ifndef OPENSSL_SMALL_FOOTPRINT |
| while (num & ~3) { |
| mul(rp[0], ap[0], w, c1); |
| mul(rp[1], ap[1], w, c1); |
| mul(rp[2], ap[2], w, c1); |
| mul(rp[3], ap[3], w, c1); |
| ap += 4; |
| rp += 4; |
| num -= 4; |
| } |
| # endif |
| while (num) { |
| mul(rp[0], ap[0], w, c1); |
| ap++; |
| rp++; |
| num--; |
| } |
| return c1; |
| } |
| |
| void bn_sqr_words(BN_ULONG *r, const BN_ULONG *a, int n) |
| { |
| assert(n >= 0); |
| if (n <= 0) |
| return; |
| |
| # ifndef OPENSSL_SMALL_FOOTPRINT |
| while (n & ~3) { |
| sqr(r[0], r[1], a[0]); |
| sqr(r[2], r[3], a[1]); |
| sqr(r[4], r[5], a[2]); |
| sqr(r[6], r[7], a[3]); |
| a += 4; |
| r += 8; |
| n -= 4; |
| } |
| # endif |
| while (n) { |
| sqr(r[0], r[1], a[0]); |
| a++; |
| r += 2; |
| n--; |
| } |
| } |
| |
| #else /* !(defined(BN_LLONG) || |
| * defined(BN_UMULT_HIGH)) */ |
| |
| BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num, |
| BN_ULONG w) |
| { |
| BN_ULONG c = 0; |
| BN_ULONG bl, bh; |
| |
| assert(num >= 0); |
| if (num <= 0) |
| return (BN_ULONG)0; |
| |
| bl = LBITS(w); |
| bh = HBITS(w); |
| |
| # ifndef OPENSSL_SMALL_FOOTPRINT |
| while (num & ~3) { |
| mul_add(rp[0], ap[0], bl, bh, c); |
| mul_add(rp[1], ap[1], bl, bh, c); |
| mul_add(rp[2], ap[2], bl, bh, c); |
| mul_add(rp[3], ap[3], bl, bh, c); |
| ap += 4; |
| rp += 4; |
| num -= 4; |
| } |
| # endif |
| while (num) { |
| mul_add(rp[0], ap[0], bl, bh, c); |
| ap++; |
| rp++; |
| num--; |
| } |
| return c; |
| } |
| |
| BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w) |
| { |
| BN_ULONG carry = 0; |
| BN_ULONG bl, bh; |
| |
| assert(num >= 0); |
| if (num <= 0) |
| return (BN_ULONG)0; |
| |
| bl = LBITS(w); |
| bh = HBITS(w); |
| |
| # ifndef OPENSSL_SMALL_FOOTPRINT |
| while (num & ~3) { |
| mul(rp[0], ap[0], bl, bh, carry); |
| mul(rp[1], ap[1], bl, bh, carry); |
| mul(rp[2], ap[2], bl, bh, carry); |
| mul(rp[3], ap[3], bl, bh, carry); |
| ap += 4; |
| rp += 4; |
| num -= 4; |
| } |
| # endif |
| while (num) { |
| mul(rp[0], ap[0], bl, bh, carry); |
| ap++; |
| rp++; |
| num--; |
| } |
| return carry; |
| } |
| |
| void bn_sqr_words(BN_ULONG *r, const BN_ULONG *a, int n) |
| { |
| assert(n >= 0); |
| if (n <= 0) |
| return; |
| |
| # ifndef OPENSSL_SMALL_FOOTPRINT |
| while (n & ~3) { |
| sqr64(r[0], r[1], a[0]); |
| sqr64(r[2], r[3], a[1]); |
| sqr64(r[4], r[5], a[2]); |
| sqr64(r[6], r[7], a[3]); |
| a += 4; |
| r += 8; |
| n -= 4; |
| } |
| # endif |
| while (n) { |
| sqr64(r[0], r[1], a[0]); |
| a++; |
| r += 2; |
| n--; |
| } |
| } |
| |
| #endif /* !(defined(BN_LLONG) || |
| * defined(BN_UMULT_HIGH)) */ |
| |
| #if defined(BN_LLONG) && defined(BN_DIV2W) |
| |
| BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d) |
| { |
| return ((BN_ULONG)(((((BN_ULLONG) h) << BN_BITS2) | l) / (BN_ULLONG) d)); |
| } |
| |
| #else |
| |
| /* Divide h,l by d and return the result. */ |
| /* I need to test this some more :-( */ |
| BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d) |
| { |
| BN_ULONG dh, dl, q, ret = 0, th, tl, t; |
| int i, count = 2; |
| |
| if (d == 0) |
| return BN_MASK2; |
| |
| i = BN_num_bits_word(d); |
| assert((i == BN_BITS2) || (h <= (BN_ULONG)1 << i)); |
| |
| i = BN_BITS2 - i; |
| if (h >= d) |
| h -= d; |
| |
| if (i) { |
| d <<= i; |
| h = (h << i) | (l >> (BN_BITS2 - i)); |
| l <<= i; |
| } |
| dh = (d & BN_MASK2h) >> BN_BITS4; |
| dl = (d & BN_MASK2l); |
| for (;;) { |
| if ((h >> BN_BITS4) == dh) |
| q = BN_MASK2l; |
| else |
| q = h / dh; |
| |
| th = q * dh; |
| tl = dl * q; |
| for (;;) { |
| t = h - th; |
| if ((t & BN_MASK2h) || |
| ((tl) <= ((t << BN_BITS4) | ((l & BN_MASK2h) >> BN_BITS4)))) |
| break; |
| q--; |
| th -= dh; |
| tl -= dl; |
| } |
| t = (tl >> BN_BITS4); |
| tl = (tl << BN_BITS4) & BN_MASK2h; |
| th += t; |
| |
| if (l < tl) |
| th++; |
| l -= tl; |
| if (h < th) { |
| h += d; |
| q--; |
| } |
| h -= th; |
| |
| if (--count == 0) |
| break; |
| |
| ret = q << BN_BITS4; |
| h = ((h << BN_BITS4) | (l >> BN_BITS4)) & BN_MASK2; |
| l = (l & BN_MASK2l) << BN_BITS4; |
| } |
| ret |= q; |
| return ret; |
| } |
| #endif /* !defined(BN_LLONG) && defined(BN_DIV2W) */ |
| |
| #ifdef BN_LLONG |
| BN_ULONG bn_add_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, |
| int n) |
| { |
| BN_ULLONG ll = 0; |
| |
| assert(n >= 0); |
| if (n <= 0) |
| return (BN_ULONG)0; |
| |
| # ifndef OPENSSL_SMALL_FOOTPRINT |
| while (n & ~3) { |
| ll += (BN_ULLONG) a[0] + b[0]; |
| r[0] = (BN_ULONG)ll & BN_MASK2; |
| ll >>= BN_BITS2; |
| ll += (BN_ULLONG) a[1] + b[1]; |
| r[1] = (BN_ULONG)ll & BN_MASK2; |
| ll >>= BN_BITS2; |
| ll += (BN_ULLONG) a[2] + b[2]; |
| r[2] = (BN_ULONG)ll & BN_MASK2; |
| ll >>= BN_BITS2; |
| ll += (BN_ULLONG) a[3] + b[3]; |
| r[3] = (BN_ULONG)ll & BN_MASK2; |
| ll >>= BN_BITS2; |
| a += 4; |
| b += 4; |
| r += 4; |
| n -= 4; |
| } |
| # endif |
| while (n) { |
| ll += (BN_ULLONG) a[0] + b[0]; |
| r[0] = (BN_ULONG)ll & BN_MASK2; |
| ll >>= BN_BITS2; |
| a++; |
| b++; |
| r++; |
| n--; |
| } |
| return (BN_ULONG)ll; |
| } |
| #else /* !BN_LLONG */ |
| BN_ULONG bn_add_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, |
| int n) |
| { |
| BN_ULONG c, l, t; |
| |
| assert(n >= 0); |
| if (n <= 0) |
| return (BN_ULONG)0; |
| |
| c = 0; |
| # ifndef OPENSSL_SMALL_FOOTPRINT |
| while (n & ~3) { |
| t = a[0]; |
| t = (t + c) & BN_MASK2; |
| c = (t < c); |
| l = (t + b[0]) & BN_MASK2; |
| c += (l < t); |
| r[0] = l; |
| t = a[1]; |
| t = (t + c) & BN_MASK2; |
| c = (t < c); |
| l = (t + b[1]) & BN_MASK2; |
| c += (l < t); |
| r[1] = l; |
| t = a[2]; |
| t = (t + c) & BN_MASK2; |
| c = (t < c); |
| l = (t + b[2]) & BN_MASK2; |
| c += (l < t); |
| r[2] = l; |
| t = a[3]; |
| t = (t + c) & BN_MASK2; |
| c = (t < c); |
| l = (t + b[3]) & BN_MASK2; |
| c += (l < t); |
| r[3] = l; |
| a += 4; |
| b += 4; |
| r += 4; |
| n -= 4; |
| } |
| # endif |
| while (n) { |
| t = a[0]; |
| t = (t + c) & BN_MASK2; |
| c = (t < c); |
| l = (t + b[0]) & BN_MASK2; |
| c += (l < t); |
| r[0] = l; |
| a++; |
| b++; |
| r++; |
| n--; |
| } |
| return (BN_ULONG)c; |
| } |
| #endif /* !BN_LLONG */ |
| |
| BN_ULONG bn_sub_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, |
| int n) |
| { |
| BN_ULONG t1, t2; |
| int c = 0; |
| |
| assert(n >= 0); |
| if (n <= 0) |
| return (BN_ULONG)0; |
| |
| #ifndef OPENSSL_SMALL_FOOTPRINT |
| while (n & ~3) { |
| t1 = a[0]; |
| t2 = b[0]; |
| r[0] = (t1 - t2 - c) & BN_MASK2; |
| if (t1 != t2) |
| c = (t1 < t2); |
| t1 = a[1]; |
| t2 = b[1]; |
| r[1] = (t1 - t2 - c) & BN_MASK2; |
| if (t1 != t2) |
| c = (t1 < t2); |
| t1 = a[2]; |
| t2 = b[2]; |
| r[2] = (t1 - t2 - c) & BN_MASK2; |
| if (t1 != t2) |
| c = (t1 < t2); |
| t1 = a[3]; |
| t2 = b[3]; |
| r[3] = (t1 - t2 - c) & BN_MASK2; |
| if (t1 != t2) |
| c = (t1 < t2); |
| a += 4; |
| b += 4; |
| r += 4; |
| n -= 4; |
| } |
| #endif |
| while (n) { |
| t1 = a[0]; |
| t2 = b[0]; |
| r[0] = (t1 - t2 - c) & BN_MASK2; |
| if (t1 != t2) |
| c = (t1 < t2); |
| a++; |
| b++; |
| r++; |
| n--; |
| } |
| return c; |
| } |
| |
| #if defined(BN_MUL_COMBA) && !defined(OPENSSL_SMALL_FOOTPRINT) |
| |
| /* mul_add_c(a,b,c0,c1,c2) -- c+=a*b for three word number c=(c2,c1,c0) */ |
| /* mul_add_c2(a,b,c0,c1,c2) -- c+=2*a*b for three word number c=(c2,c1,c0) */ |
| /* sqr_add_c(a,i,c0,c1,c2) -- c+=a[i]^2 for three word number c=(c2,c1,c0) */ |
| /* |
| * sqr_add_c2(a,i,c0,c1,c2) -- c+=2*a[i]*a[j] for three word number |
| * c=(c2,c1,c0) |
| */ |
| |
| # ifdef BN_LLONG |
| /* |
| * Keep in mind that additions to multiplication result can not |
| * overflow, because its high half cannot be all-ones. |
| */ |
| # define mul_add_c(a,b,c0,c1,c2) do { \ |
| BN_ULONG hi; \ |
| BN_ULLONG t = (BN_ULLONG)(a)*(b); \ |
| t += c0; /* no carry */ \ |
| c0 = (BN_ULONG)Lw(t); \ |
| hi = (BN_ULONG)Hw(t); \ |
| c1 = (c1+hi)&BN_MASK2; if (c1<hi) c2++; \ |
| } while(0) |
| |
| # define mul_add_c2(a,b,c0,c1,c2) do { \ |
| BN_ULONG hi; \ |
| BN_ULLONG t = (BN_ULLONG)(a)*(b); \ |
| BN_ULLONG tt = t+c0; /* no carry */ \ |
| c0 = (BN_ULONG)Lw(tt); \ |
| hi = (BN_ULONG)Hw(tt); \ |
| c1 = (c1+hi)&BN_MASK2; if (c1<hi) c2++; \ |
| t += c0; /* no carry */ \ |
| c0 = (BN_ULONG)Lw(t); \ |
| hi = (BN_ULONG)Hw(t); \ |
| c1 = (c1+hi)&BN_MASK2; if (c1<hi) c2++; \ |
| } while(0) |
| |
| # define sqr_add_c(a,i,c0,c1,c2) do { \ |
| BN_ULONG hi; \ |
| BN_ULLONG t = (BN_ULLONG)a[i]*a[i]; \ |
| t += c0; /* no carry */ \ |
| c0 = (BN_ULONG)Lw(t); \ |
| hi = (BN_ULONG)Hw(t); \ |
| c1 = (c1+hi)&BN_MASK2; if (c1<hi) c2++; \ |
| } while(0) |
| |
| # define sqr_add_c2(a,i,j,c0,c1,c2) \ |
| mul_add_c2((a)[i],(a)[j],c0,c1,c2) |
| |
| # elif defined(BN_UMULT_LOHI) |
| /* |
| * Keep in mind that additions to hi can not overflow, because |
| * the high word of a multiplication result cannot be all-ones. |
| */ |
| # define mul_add_c(a,b,c0,c1,c2) do { \ |
| BN_ULONG ta = (a), tb = (b); \ |
| BN_ULONG lo, hi; \ |
| BN_UMULT_LOHI(lo,hi,ta,tb); \ |
| c0 += lo; hi += (c0<lo)?1:0; \ |
| c1 += hi; c2 += (c1<hi)?1:0; \ |
| } while(0) |
| |
| # define mul_add_c2(a,b,c0,c1,c2) do { \ |
| BN_ULONG ta = (a), tb = (b); \ |
| BN_ULONG lo, hi, tt; \ |
| BN_UMULT_LOHI(lo,hi,ta,tb); \ |
| c0 += lo; tt = hi+((c0<lo)?1:0); \ |
| c1 += tt; c2 += (c1<tt)?1:0; \ |
| c0 += lo; hi += (c0<lo)?1:0; \ |
| c1 += hi; c2 += (c1<hi)?1:0; \ |
| } while(0) |
| |
| # define sqr_add_c(a,i,c0,c1,c2) do { \ |
| BN_ULONG ta = (a)[i]; \ |
| BN_ULONG lo, hi; \ |
| BN_UMULT_LOHI(lo,hi,ta,ta); \ |
| c0 += lo; hi += (c0<lo)?1:0; \ |
| c1 += hi; c2 += (c1<hi)?1:0; \ |
| } while(0) |
| |
| # define sqr_add_c2(a,i,j,c0,c1,c2) \ |
| mul_add_c2((a)[i],(a)[j],c0,c1,c2) |
| |
| # elif defined(BN_UMULT_HIGH) |
| /* |
| * Keep in mind that additions to hi can not overflow, because |
| * the high word of a multiplication result cannot be all-ones. |
| */ |
| # define mul_add_c(a,b,c0,c1,c2) do { \ |
| BN_ULONG ta = (a), tb = (b); \ |
| BN_ULONG lo = ta * tb; \ |
| BN_ULONG hi = BN_UMULT_HIGH(ta,tb); \ |
| c0 += lo; hi += (c0<lo)?1:0; \ |
| c1 += hi; c2 += (c1<hi)?1:0; \ |
| } while(0) |
| |
| # define mul_add_c2(a,b,c0,c1,c2) do { \ |
| BN_ULONG ta = (a), tb = (b), tt; \ |
| BN_ULONG lo = ta * tb; \ |
| BN_ULONG hi = BN_UMULT_HIGH(ta,tb); \ |
| c0 += lo; tt = hi + ((c0<lo)?1:0); \ |
| c1 += tt; c2 += (c1<tt)?1:0; \ |
| c0 += lo; hi += (c0<lo)?1:0; \ |
| c1 += hi; c2 += (c1<hi)?1:0; \ |
| } while(0) |
| |
| # define sqr_add_c(a,i,c0,c1,c2) do { \ |
| BN_ULONG ta = (a)[i]; \ |
| BN_ULONG lo = ta * ta; \ |
| BN_ULONG hi = BN_UMULT_HIGH(ta,ta); \ |
| c0 += lo; hi += (c0<lo)?1:0; \ |
| c1 += hi; c2 += (c1<hi)?1:0; \ |
| } while(0) |
| |
| # define sqr_add_c2(a,i,j,c0,c1,c2) \ |
| mul_add_c2((a)[i],(a)[j],c0,c1,c2) |
| |
| # else /* !BN_LLONG */ |
| /* |
| * Keep in mind that additions to hi can not overflow, because |
| * the high word of a multiplication result cannot be all-ones. |
| */ |
| # define mul_add_c(a,b,c0,c1,c2) do { \ |
| BN_ULONG lo = LBITS(a), hi = HBITS(a); \ |
| BN_ULONG bl = LBITS(b), bh = HBITS(b); \ |
| mul64(lo,hi,bl,bh); \ |
| c0 = (c0+lo)&BN_MASK2; if (c0<lo) hi++; \ |
| c1 = (c1+hi)&BN_MASK2; if (c1<hi) c2++; \ |
| } while(0) |
| |
| # define mul_add_c2(a,b,c0,c1,c2) do { \ |
| BN_ULONG tt; \ |
| BN_ULONG lo = LBITS(a), hi = HBITS(a); \ |
| BN_ULONG bl = LBITS(b), bh = HBITS(b); \ |
| mul64(lo,hi,bl,bh); \ |
| tt = hi; \ |
| c0 = (c0+lo)&BN_MASK2; if (c0<lo) tt++; \ |
| c1 = (c1+tt)&BN_MASK2; if (c1<tt) c2++; \ |
| c0 = (c0+lo)&BN_MASK2; if (c0<lo) hi++; \ |
| c1 = (c1+hi)&BN_MASK2; if (c1<hi) c2++; \ |
| } while(0) |
| |
| # define sqr_add_c(a,i,c0,c1,c2) do { \ |
| BN_ULONG lo, hi; \ |
| sqr64(lo,hi,(a)[i]); \ |
| c0 = (c0+lo)&BN_MASK2; if (c0<lo) hi++; \ |
| c1 = (c1+hi)&BN_MASK2; if (c1<hi) c2++; \ |
| } while(0) |
| |
| # define sqr_add_c2(a,i,j,c0,c1,c2) \ |
| mul_add_c2((a)[i],(a)[j],c0,c1,c2) |
| # endif /* !BN_LLONG */ |
| |
| void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b) |
| { |
| BN_ULONG c1, c2, c3; |
| |
| c1 = 0; |
| c2 = 0; |
| c3 = 0; |
| mul_add_c(a[0], b[0], c1, c2, c3); |
| r[0] = c1; |
| c1 = 0; |
| mul_add_c(a[0], b[1], c2, c3, c1); |
| mul_add_c(a[1], b[0], c2, c3, c1); |
| r[1] = c2; |
| c2 = 0; |
| mul_add_c(a[2], b[0], c3, c1, c2); |
| mul_add_c(a[1], b[1], c3, c1, c2); |
| mul_add_c(a[0], b[2], c3, c1, c2); |
| r[2] = c3; |
| c3 = 0; |
| mul_add_c(a[0], b[3], c1, c2, c3); |
| mul_add_c(a[1], b[2], c1, c2, c3); |
| mul_add_c(a[2], b[1], c1, c2, c3); |
| mul_add_c(a[3], b[0], c1, c2, c3); |
| r[3] = c1; |
| c1 = 0; |
| mul_add_c(a[4], b[0], c2, c3, c1); |
| mul_add_c(a[3], b[1], c2, c3, c1); |
| mul_add_c(a[2], b[2], c2, c3, c1); |
| mul_add_c(a[1], b[3], c2, c3, c1); |
| mul_add_c(a[0], b[4], c2, c3, c1); |
| r[4] = c2; |
| c2 = 0; |
| mul_add_c(a[0], b[5], c3, c1, c2); |
| mul_add_c(a[1], b[4], c3, c1, c2); |
| mul_add_c(a[2], b[3], c3, c1, c2); |
| mul_add_c(a[3], b[2], c3, c1, c2); |
| mul_add_c(a[4], b[1], c3, c1, c2); |
| mul_add_c(a[5], b[0], c3, c1, c2); |
| r[5] = c3; |
| c3 = 0; |
| mul_add_c(a[6], b[0], c1, c2, c3); |
| mul_add_c(a[5], b[1], c1, c2, c3); |
| mul_add_c(a[4], b[2], c1, c2, c3); |
| mul_add_c(a[3], b[3], c1, c2, c3); |
| mul_add_c(a[2], b[4], c1, c2, c3); |
| mul_add_c(a[1], b[5], c1, c2, c3); |
| mul_add_c(a[0], b[6], c1, c2, c3); |
| r[6] = c1; |
| c1 = 0; |
| mul_add_c(a[0], b[7], c2, c3, c1); |
| mul_add_c(a[1], b[6], c2, c3, c1); |
| mul_add_c(a[2], b[5], c2, c3, c1); |
| mul_add_c(a[3], b[4], c2, c3, c1); |
| mul_add_c(a[4], b[3], c2, c3, c1); |
| mul_add_c(a[5], b[2], c2, c3, c1); |
| mul_add_c(a[6], b[1], c2, c3, c1); |
| mul_add_c(a[7], b[0], c2, c3, c1); |
| r[7] = c2; |
| c2 = 0; |
| mul_add_c(a[7], b[1], c3, c1, c2); |
| mul_add_c(a[6], b[2], c3, c1, c2); |
| mul_add_c(a[5], b[3], c3, c1, c2); |
| mul_add_c(a[4], b[4], c3, c1, c2); |
| mul_add_c(a[3], b[5], c3, c1, c2); |
| mul_add_c(a[2], b[6], c3, c1, c2); |
| mul_add_c(a[1], b[7], c3, c1, c2); |
| r[8] = c3; |
| c3 = 0; |
| mul_add_c(a[2], b[7], c1, c2, c3); |
| mul_add_c(a[3], b[6], c1, c2, c3); |
| mul_add_c(a[4], b[5], c1, c2, c3); |
| mul_add_c(a[5], b[4], c1, c2, c3); |
| mul_add_c(a[6], b[3], c1, c2, c3); |
| mul_add_c(a[7], b[2], c1, c2, c3); |
| r[9] = c1; |
| c1 = 0; |
| mul_add_c(a[7], b[3], c2, c3, c1); |
| mul_add_c(a[6], b[4], c2, c3, c1); |
| mul_add_c(a[5], b[5], c2, c3, c1); |
| mul_add_c(a[4], b[6], c2, c3, c1); |
| mul_add_c(a[3], b[7], c2, c3, c1); |
| r[10] = c2; |
| c2 = 0; |
| mul_add_c(a[4], b[7], c3, c1, c2); |
| mul_add_c(a[5], b[6], c3, c1, c2); |
| mul_add_c(a[6], b[5], c3, c1, c2); |
| mul_add_c(a[7], b[4], c3, c1, c2); |
| r[11] = c3; |
| c3 = 0; |
| mul_add_c(a[7], b[5], c1, c2, c3); |
| mul_add_c(a[6], b[6], c1, c2, c3); |
| mul_add_c(a[5], b[7], c1, c2, c3); |
| r[12] = c1; |
| c1 = 0; |
| mul_add_c(a[6], b[7], c2, c3, c1); |
| mul_add_c(a[7], b[6], c2, c3, c1); |
| r[13] = c2; |
| c2 = 0; |
| mul_add_c(a[7], b[7], c3, c1, c2); |
| r[14] = c3; |
| r[15] = c1; |
| } |
| |
| void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b) |
| { |
| BN_ULONG c1, c2, c3; |
| |
| c1 = 0; |
| c2 = 0; |
| c3 = 0; |
| mul_add_c(a[0], b[0], c1, c2, c3); |
| r[0] = c1; |
| c1 = 0; |
| mul_add_c(a[0], b[1], c2, c3, c1); |
| mul_add_c(a[1], b[0], c2, c3, c1); |
| r[1] = c2; |
| c2 = 0; |
| mul_add_c(a[2], b[0], c3, c1, c2); |
| mul_add_c(a[1], b[1], c3, c1, c2); |
| mul_add_c(a[0], b[2], c3, c1, c2); |
| r[2] = c3; |
| c3 = 0; |
| mul_add_c(a[0], b[3], c1, c2, c3); |
| mul_add_c(a[1], b[2], c1, c2, c3); |
| mul_add_c(a[2], b[1], c1, c2, c3); |
| mul_add_c(a[3], b[0], c1, c2, c3); |
| r[3] = c1; |
| c1 = 0; |
| mul_add_c(a[3], b[1], c2, c3, c1); |
| mul_add_c(a[2], b[2], c2, c3, c1); |
| mul_add_c(a[1], b[3], c2, c3, c1); |
| r[4] = c2; |
| c2 = 0; |
| mul_add_c(a[2], b[3], c3, c1, c2); |
| mul_add_c(a[3], b[2], c3, c1, c2); |
| r[5] = c3; |
| c3 = 0; |
| mul_add_c(a[3], b[3], c1, c2, c3); |
| r[6] = c1; |
| r[7] = c2; |
| } |
| |
| void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a) |
| { |
| BN_ULONG c1, c2, c3; |
| |
| c1 = 0; |
| c2 = 0; |
| c3 = 0; |
| sqr_add_c(a, 0, c1, c2, c3); |
| r[0] = c1; |
| c1 = 0; |
| sqr_add_c2(a, 1, 0, c2, c3, c1); |
| r[1] = c2; |
| c2 = 0; |
| sqr_add_c(a, 1, c3, c1, c2); |
| sqr_add_c2(a, 2, 0, c3, c1, c2); |
| r[2] = c3; |
| c3 = 0; |
| sqr_add_c2(a, 3, 0, c1, c2, c3); |
| sqr_add_c2(a, 2, 1, c1, c2, c3); |
| r[3] = c1; |
| c1 = 0; |
| sqr_add_c(a, 2, c2, c3, c1); |
| sqr_add_c2(a, 3, 1, c2, c3, c1); |
| sqr_add_c2(a, 4, 0, c2, c3, c1); |
| r[4] = c2; |
| c2 = 0; |
| sqr_add_c2(a, 5, 0, c3, c1, c2); |
| sqr_add_c2(a, 4, 1, c3, c1, c2); |
| sqr_add_c2(a, 3, 2, c3, c1, c2); |
| r[5] = c3; |
| c3 = 0; |
| sqr_add_c(a, 3, c1, c2, c3); |
| sqr_add_c2(a, 4, 2, c1, c2, c3); |
| sqr_add_c2(a, 5, 1, c1, c2, c3); |
| sqr_add_c2(a, 6, 0, c1, c2, c3); |
| r[6] = c1; |
| c1 = 0; |
| sqr_add_c2(a, 7, 0, c2, c3, c1); |
| sqr_add_c2(a, 6, 1, c2, c3, c1); |
| sqr_add_c2(a, 5, 2, c2, c3, c1); |
| sqr_add_c2(a, 4, 3, c2, c3, c1); |
| r[7] = c2; |
| c2 = 0; |
| sqr_add_c(a, 4, c3, c1, c2); |
| sqr_add_c2(a, 5, 3, c3, c1, c2); |
| sqr_add_c2(a, 6, 2, c3, c1, c2); |
| sqr_add_c2(a, 7, 1, c3, c1, c2); |
| r[8] = c3; |
| c3 = 0; |
| sqr_add_c2(a, 7, 2, c1, c2, c3); |
| sqr_add_c2(a, 6, 3, c1, c2, c3); |
| sqr_add_c2(a, 5, 4, c1, c2, c3); |
| r[9] = c1; |
| c1 = 0; |
| sqr_add_c(a, 5, c2, c3, c1); |
| sqr_add_c2(a, 6, 4, c2, c3, c1); |
| sqr_add_c2(a, 7, 3, c2, c3, c1); |
| r[10] = c2; |
| c2 = 0; |
| sqr_add_c2(a, 7, 4, c3, c1, c2); |
| sqr_add_c2(a, 6, 5, c3, c1, c2); |
| r[11] = c3; |
| c3 = 0; |
| sqr_add_c(a, 6, c1, c2, c3); |
| sqr_add_c2(a, 7, 5, c1, c2, c3); |
| r[12] = c1; |
| c1 = 0; |
| sqr_add_c2(a, 7, 6, c2, c3, c1); |
| r[13] = c2; |
| c2 = 0; |
| sqr_add_c(a, 7, c3, c1, c2); |
| r[14] = c3; |
| r[15] = c1; |
| } |
| |
| void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a) |
| { |
| BN_ULONG c1, c2, c3; |
| |
| c1 = 0; |
| c2 = 0; |
| c3 = 0; |
| sqr_add_c(a, 0, c1, c2, c3); |
| r[0] = c1; |
| c1 = 0; |
| sqr_add_c2(a, 1, 0, c2, c3, c1); |
| r[1] = c2; |
| c2 = 0; |
| sqr_add_c(a, 1, c3, c1, c2); |
| sqr_add_c2(a, 2, 0, c3, c1, c2); |
| r[2] = c3; |
| c3 = 0; |
| sqr_add_c2(a, 3, 0, c1, c2, c3); |
| sqr_add_c2(a, 2, 1, c1, c2, c3); |
| r[3] = c1; |
| c1 = 0; |
| sqr_add_c(a, 2, c2, c3, c1); |
| sqr_add_c2(a, 3, 1, c2, c3, c1); |
| r[4] = c2; |
| c2 = 0; |
| sqr_add_c2(a, 3, 2, c3, c1, c2); |
| r[5] = c3; |
| c3 = 0; |
| sqr_add_c(a, 3, c1, c2, c3); |
| r[6] = c1; |
| r[7] = c2; |
| } |
| |
| # ifdef OPENSSL_NO_ASM |
| # ifdef OPENSSL_BN_ASM_MONT |
| # include <alloca.h> |
| /* |
| * This is essentially reference implementation, which may or may not |
| * result in performance improvement. E.g. on IA-32 this routine was |
| * observed to give 40% faster rsa1024 private key operations and 10% |
| * faster rsa4096 ones, while on AMD64 it improves rsa1024 sign only |
| * by 10% and *worsens* rsa4096 sign by 15%. Once again, it's a |
| * reference implementation, one to be used as starting point for |
| * platform-specific assembler. Mentioned numbers apply to compiler |
| * generated code compiled with and without -DOPENSSL_BN_ASM_MONT and |
| * can vary not only from platform to platform, but even for compiler |
| * versions. Assembler vs. assembler improvement coefficients can |
| * [and are known to] differ and are to be documented elsewhere. |
| */ |
| int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp, |
| const BN_ULONG *np, const BN_ULONG *n0p, int num) |
| { |
| BN_ULONG c0, c1, ml, *tp, n0; |
| # ifdef mul64 |
| BN_ULONG mh; |
| # endif |
| volatile BN_ULONG *vp; |
| int i = 0, j; |
| |
| # if 0 /* template for platform-specific |
| * implementation */ |
| if (ap == bp) |
| return bn_sqr_mont(rp, ap, np, n0p, num); |
| # endif |
| vp = tp = alloca((num + 2) * sizeof(BN_ULONG)); |
| |
| n0 = *n0p; |
| |
| c0 = 0; |
| ml = bp[0]; |
| # ifdef mul64 |
| mh = HBITS(ml); |
| ml = LBITS(ml); |
| for (j = 0; j < num; ++j) |
| mul(tp[j], ap[j], ml, mh, c0); |
| # else |
| for (j = 0; j < num; ++j) |
| mul(tp[j], ap[j], ml, c0); |
| # endif |
| |
| tp[num] = c0; |
| tp[num + 1] = 0; |
| goto enter; |
| |
| for (i = 0; i < num; i++) { |
| c0 = 0; |
| ml = bp[i]; |
| # ifdef mul64 |
| mh = HBITS(ml); |
| ml = LBITS(ml); |
| for (j = 0; j < num; ++j) |
| mul_add(tp[j], ap[j], ml, mh, c0); |
| # else |
| for (j = 0; j < num; ++j) |
| mul_add(tp[j], ap[j], ml, c0); |
| # endif |
| c1 = (tp[num] + c0) & BN_MASK2; |
| tp[num] = c1; |
| tp[num + 1] = (c1 < c0 ? 1 : 0); |
| enter: |
| c1 = tp[0]; |
| ml = (c1 * n0) & BN_MASK2; |
| c0 = 0; |
| # ifdef mul64 |
| mh = HBITS(ml); |
| ml = LBITS(ml); |
| mul_add(c1, np[0], ml, mh, c0); |
| # else |
| mul_add(c1, ml, np[0], c0); |
| # endif |
| for (j = 1; j < num; j++) { |
| c1 = tp[j]; |
| # ifdef mul64 |
| mul_add(c1, np[j], ml, mh, c0); |
| # else |
| mul_add(c1, ml, np[j], c0); |
| # endif |
| tp[j - 1] = c1 & BN_MASK2; |
| } |
| c1 = (tp[num] + c0) & BN_MASK2; |
| tp[num - 1] = c1; |
| tp[num] = tp[num + 1] + (c1 < c0 ? 1 : 0); |
| } |
| |
| if (tp[num] != 0 || tp[num - 1] >= np[num - 1]) { |
| c0 = bn_sub_words(rp, tp, np, num); |
| if (tp[num] != 0 || c0 == 0) { |
| for (i = 0; i < num + 2; i++) |
| vp[i] = 0; |
| return 1; |
| } |
| } |
| for (i = 0; i < num; i++) |
| rp[i] = tp[i], vp[i] = 0; |
| vp[num] = 0; |
| vp[num + 1] = 0; |
| return 1; |
| } |
| # else |
| /* |
| * Return value of 0 indicates that multiplication/convolution was not |
| * performed to signal the caller to fall down to alternative/original |
| * code-path. |
| */ |
| int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp, |
| const BN_ULONG *np, const BN_ULONG *n0, int num) |
| { |
| return 0; |
| } |
| # endif /* OPENSSL_BN_ASM_MONT */ |
| # endif |
| |
| #else /* !BN_MUL_COMBA */ |
| |
| /* hmm... is it faster just to do a multiply? */ |
| void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a) |
| { |
| BN_ULONG t[8]; |
| bn_sqr_normal(r, a, 4, t); |
| } |
| |
| void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a) |
| { |
| BN_ULONG t[16]; |
| bn_sqr_normal(r, a, 8, t); |
| } |
| |
| void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b) |
| { |
| r[4] = bn_mul_words(&(r[0]), a, 4, b[0]); |
| r[5] = bn_mul_add_words(&(r[1]), a, 4, b[1]); |
| r[6] = bn_mul_add_words(&(r[2]), a, 4, b[2]); |
| r[7] = bn_mul_add_words(&(r[3]), a, 4, b[3]); |
| } |
| |
| void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b) |
| { |
| r[8] = bn_mul_words(&(r[0]), a, 8, b[0]); |
| r[9] = bn_mul_add_words(&(r[1]), a, 8, b[1]); |
| r[10] = bn_mul_add_words(&(r[2]), a, 8, b[2]); |
| r[11] = bn_mul_add_words(&(r[3]), a, 8, b[3]); |
| r[12] = bn_mul_add_words(&(r[4]), a, 8, b[4]); |
| r[13] = bn_mul_add_words(&(r[5]), a, 8, b[5]); |
| r[14] = bn_mul_add_words(&(r[6]), a, 8, b[6]); |
| r[15] = bn_mul_add_words(&(r[7]), a, 8, b[7]); |
| } |
| |
| # ifdef OPENSSL_NO_ASM |
| # ifdef OPENSSL_BN_ASM_MONT |
| # include <alloca.h> |
| int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp, |
| const BN_ULONG *np, const BN_ULONG *n0p, int num) |
| { |
| BN_ULONG c0, c1, *tp, n0 = *n0p; |
| volatile BN_ULONG *vp; |
| int i = 0, j; |
| |
| vp = tp = alloca((num + 2) * sizeof(BN_ULONG)); |
| |
| for (i = 0; i <= num; i++) |
| tp[i] = 0; |
| |
| for (i = 0; i < num; i++) { |
| c0 = bn_mul_add_words(tp, ap, num, bp[i]); |
| c1 = (tp[num] + c0) & BN_MASK2; |
| tp[num] = c1; |
| tp[num + 1] = (c1 < c0 ? 1 : 0); |
| |
| c0 = bn_mul_add_words(tp, np, num, tp[0] * n0); |
| c1 = (tp[num] + c0) & BN_MASK2; |
| tp[num] = c1; |
| tp[num + 1] += (c1 < c0 ? 1 : 0); |
| for (j = 0; j <= num; j++) |
| tp[j] = tp[j + 1]; |
| } |
| |
| if (tp[num] != 0 || tp[num - 1] >= np[num - 1]) { |
| c0 = bn_sub_words(rp, tp, np, num); |
| if (tp[num] != 0 || c0 == 0) { |
| for (i = 0; i < num + 2; i++) |
| vp[i] = 0; |
| return 1; |
| } |
| } |
| for (i = 0; i < num; i++) |
| rp[i] = tp[i], vp[i] = 0; |
| vp[num] = 0; |
| vp[num + 1] = 0; |
| return 1; |
| } |
| # else |
| int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp, |
| const BN_ULONG *np, const BN_ULONG *n0, int num) |
| { |
| return 0; |
| } |
| # endif /* OPENSSL_BN_ASM_MONT */ |
| # endif |
| |
| #endif /* !BN_MUL_COMBA */ |
