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Diffstat (limited to 'src/crypto/fipsmodule/ec/util.c')
-rw-r--r-- | src/crypto/fipsmodule/ec/util.c | 104 |
1 files changed, 104 insertions, 0 deletions
diff --git a/src/crypto/fipsmodule/ec/util.c b/src/crypto/fipsmodule/ec/util.c new file mode 100644 index 00000000..7303a151 --- /dev/null +++ b/src/crypto/fipsmodule/ec/util.c @@ -0,0 +1,104 @@ +/* Copyright (c) 2015, Google Inc. + * + * Permission to use, copy, modify, and/or distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY + * SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION + * OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN + * CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */ + +#include <openssl/base.h> + +#include <openssl/ec.h> + +#include "internal.h" + +// This function looks at 5+1 scalar bits (5 current, 1 adjacent less +// significant bit), and recodes them into a signed digit for use in fast point +// multiplication: the use of signed rather than unsigned digits means that +// fewer points need to be precomputed, given that point inversion is easy (a +// precomputed point dP makes -dP available as well). +// +// BACKGROUND: +// +// Signed digits for multiplication were introduced by Booth ("A signed binary +// multiplication technique", Quart. Journ. Mech. and Applied Math., vol. IV, +// pt. 2 (1951), pp. 236-240), in that case for multiplication of integers. +// Booth's original encoding did not generally improve the density of nonzero +// digits over the binary representation, and was merely meant to simplify the +// handling of signed factors given in two's complement; but it has since been +// shown to be the basis of various signed-digit representations that do have +// further advantages, including the wNAF, using the following general +// approach: +// +// (1) Given a binary representation +// +// b_k ... b_2 b_1 b_0, +// +// of a nonnegative integer (b_k in {0, 1}), rewrite it in digits 0, 1, -1 +// by using bit-wise subtraction as follows: +// +// b_k b_(k-1) ... b_2 b_1 b_0 +// - b_k ... b_3 b_2 b_1 b_0 +// ------------------------------------- +// s_k b_(k-1) ... s_3 s_2 s_1 s_0 +// +// A left-shift followed by subtraction of the original value yields a new +// representation of the same value, using signed bits s_i = b_(i+1) - b_i. +// This representation from Booth's paper has since appeared in the +// literature under a variety of different names including "reversed binary +// form", "alternating greedy expansion", "mutual opposite form", and +// "sign-alternating {+-1}-representation". +// +// An interesting property is that among the nonzero bits, values 1 and -1 +// strictly alternate. +// +// (2) Various window schemes can be applied to the Booth representation of +// integers: for example, right-to-left sliding windows yield the wNAF +// (a signed-digit encoding independently discovered by various researchers +// in the 1990s), and left-to-right sliding windows yield a left-to-right +// equivalent of the wNAF (independently discovered by various researchers +// around 2004). +// +// To prevent leaking information through side channels in point multiplication, +// we need to recode the given integer into a regular pattern: sliding windows +// as in wNAFs won't do, we need their fixed-window equivalent -- which is a few +// decades older: we'll be using the so-called "modified Booth encoding" due to +// MacSorley ("High-speed arithmetic in binary computers", Proc. IRE, vol. 49 +// (1961), pp. 67-91), in a radix-2^5 setting. That is, we always combine five +// signed bits into a signed digit: +// +// s_(4j + 4) s_(4j + 3) s_(4j + 2) s_(4j + 1) s_(4j) +// +// The sign-alternating property implies that the resulting digit values are +// integers from -16 to 16. +// +// Of course, we don't actually need to compute the signed digits s_i as an +// intermediate step (that's just a nice way to see how this scheme relates +// to the wNAF): a direct computation obtains the recoded digit from the +// six bits b_(4j + 4) ... b_(4j - 1). +// +// This function takes those five bits as an integer (0 .. 63), writing the +// recoded digit to *sign (0 for positive, 1 for negative) and *digit (absolute +// value, in the range 0 .. 8). Note that this integer essentially provides the +// input bits "shifted to the left" by one position: for example, the input to +// compute the least significant recoded digit, given that there's no bit b_-1, +// has to be b_4 b_3 b_2 b_1 b_0 0. +void ec_GFp_nistp_recode_scalar_bits(uint8_t *sign, uint8_t *digit, + uint8_t in) { + uint8_t s, d; + + s = ~((in >> 5) - 1); /* sets all bits to MSB(in), 'in' seen as + * 6-bit value */ + d = (1 << 6) - in - 1; + d = (d & s) | (in & ~s); + d = (d >> 1) + (d & 1); + + *sign = s & 1; + *digit = d; +} |