--- /dev/null
+/* -*-c-*-
+ *
+ * The GCM authenticated encryption mode
+ *
+ * (c) 2017 Straylight/Edgeware
+ */
+
+/*----- Licensing notice --------------------------------------------------*
+ *
+ * This file is part of Catacomb.
+ *
+ * Catacomb is free software: you can redistribute it and/or modify it
+ * under the terms of the GNU Library General Public License as published
+ * by the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * Catacomb is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ * Library General Public License for more details.
+ *
+ * You should have received a copy of the GNU Library General Public
+ * License along with Catacomb. If not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307,
+ * USA.
+ */
+
+/*----- Header files ------------------------------------------------------*/
+
+#include "config.h"
+
+#include <stdio.h>
+
+#include <mLib/bits.h>
+
+#include "gcm.h"
+#include "gcm-def.h"
+
+/*----- Overall strategy --------------------------------------------------*
+ *
+ * GCM is pretty awful to implement in software. (This presentation is going
+ * to be somewhat different to that in the specification, but I think it
+ * makes more sense like this.)
+ *
+ * We're given a %$w$%-bit blockcipher %$E$% with a key %$K$%.
+ *
+ * The main part is arithmetic in the finite field %$k = \gf{2^w}$%, which we
+ * represent as the quotient ring %$\gf{2}[t]/(p_w(t))$% for some irreducible
+ * degree-%$w$% polynomial %$p(t)$%, whose precise value isn't very important
+ * right now. We choose a secret point %$x = E_K(0^w)$%.
+ *
+ * We choose a length size %$z$% as follows: if %$w < 96%$ then %$z = w$%;
+ * otherwise %$z = w/2$%. Format a message pair as follows:
+ *
+ * %$F(a, b) = P_w(a) \cat P_w(b) \cat [\ell(a)]_z \cat [\ell(b)]_z$%
+ *
+ * where %$P_w(x) = x \cat 0^n$% where $%0 \le n < w$% such that
+ * %$\ell(x) + n \equiv 0 \pmod{w}$%.
+ *
+ * Hash a (block-aligned) message %$u$% as follows. First, split %$u$% into
+ * %$w$%-bit blocks %$u_0$%, %$u_1$%, %%\ldots%%, %$u_{n-1}$%. Interpret
+ * these as elements of %$k$%. Then
+ *
+ * %$G_x(u) = u_0 t^n + u_1 t^{n-1} + \cdots + u_{n-1} t$%
+ *
+ * converted back to a %$w$%-bit string.
+ *
+ * We're ready to go now. Suppose we're to encrypt a message %$M$% with
+ * header %$H$% and nonce %$N$%. If %$\ell(N) + 32 = w$% then let
+ * %$N' = N$% and let %$i_0 = 1$%; otherwise, let %$U = G_t(F(\epsilon, N))$%
+ * and split this into %$N' = U[0 \bitsto w - 32]$% and
+ * %$[i_0]_{32} = U[w - 32 \bitsto w]$%.
+ *
+ * Let %$n = \lceil \ell(M)/w \rceil$%. Compute
+ *
+ * %$y_j = E_K(N' \cat [i_0 + j]_{32})$%
+ *
+ * for %$0 \le j \le n$%. Let
+ *
+ * %$s = (y_1 \cat y_2 \cat \cdots \cat y_n)[0 \bitsto \ell(M)$%
+ *
+ * Let %$C = M \xor s$% and let %$T = G_x(F(H, C)) \xor y_0$%. These are the
+ * ciphertext and tag respectively.
+ *
+ * So why is this awful?
+ *
+ * For one thing, the bits are in a completely terrible order. The bytes are
+ * arranged in little-endian order, so the unit coefficient is in the first
+ * byte, and the degree-127 coefficient is in the last byte. But within each
+ * byte, the lowest-degree coefficient is in the most significant bit. It's
+ * therefore better to think of GCM as using a big-endian byte-ordering
+ * convention, but with the bits backwards.
+ *
+ * But messing about with byte ordering is expensive, so let's not do that in
+ * the inner loop. But multiplication in %$k$% is not easy either. Some
+ * kind of precomputed table would be nice, but that will leak secrets
+ * through the cache.
+ *
+ * I choose a particularly simple table: given %$x$%, let %$X[i'] = x t^i$%.
+ * Then $%$x y = \sum_{0\le i<w} y_i X[i']$% which is just a bunch of
+ * bitmasking. But the natural order for examining bits of %$y$% is not
+ * necessarily the obvious one. We'll have already loaded %$y$% into
+ * internal form, as 32-bit words. The good order to process these is left
+ * to right, from high to low bits. But now the order of degrees depends on
+ * the endianness of our conversion of bytes to words. Oh, well.
+ *
+ * If we've adopted a big-endian convention, then we'll see the degrees in
+ * order, 0, 1, ..., all the way up to %$w - 1$% and everything is fine. If
+ * we've adopted a little-endian convention, though, we'll see an ordering
+ * like this:
+ *
+ * 24, 25, ..., 31, 16, 17, ..., 23, 8, 9, ..., 15, 0, 1, ..., 7,
+ * 56, 57, ..., 63, 48, 49, ..., 55, 40, 41, ..., 47, 32, 33, ..., 39,
+ * etc.
+ *
+ * which is the ordinary order with 0x18 = 24 XORed into the index. That is,
+ * %$i' = i$% if we've adopted a big-endian convention, and
+ * %$i' = i \xor 24$% if we've adopted a little-endian convention.
+ */
+
+/*----- Low-level utilities -----------------------------------------------*/
+
+/* --- @mult@ --- *
+ *
+ * Arguments: @const gcm_params *p@ = pointer to the parameters
+ * @uint32 *z@ = where to write the result
+ * @const uint32 *x@ = input field element
+ *
+ * Returns: ---
+ *
+ * Use: Multiply the input field element by %$t$%, and write the
+ * product to @z@. It's safe for @x@ and @z@ to be equal, but
+ * they should not otherwise overlap. Both input and output are
+ * in big-endian form, i.e., with the lowest-degree coefficients
+ * in the most significant bits.
+ */
+
+static void mult(const gcm_params *p, uint32 *z, const uint32 *x)
+{
+ uint32 m, c, t;
+ unsigned i;
+
+ t = x[p->n - 1]; m = -(t&1u); c = m&p->poly;
+ for (i = 0; i < p->n; i++) { t = x[i]; z[i] = (t >> 1) ^ c; c = t << 31; }
+}
+
+/* --- @mul@ --- *
+ *
+ * Arguments: @const gcm_params *p@ = pointer to the parameters
+ * @uint32 *z@ = where to write the result
+ * @const uint32 *x, *y@ = input field elements
+ *
+ * Returns: ---
+ *
+ * Use: Multiply the input field elements together, and write the
+ * product to @z@. It's safe for the operands to overlap. Both
+ * inputs and the output are in big-endian form, i.e., with the
+ * lowest-degree coefficients in the most significant bits.
+ */
+
+static void mul(const gcm_params *p, uint32 *z,
+ const uint32 *x, const uint32 *y)
+{
+ uint32 m, t, u[GCM_NMAX], v[GCM_NMAX];
+ unsigned i, j, k;
+
+ /* We can't do this in-place at all, so use temporary space. Make a copy
+ * of @x@ in @u@, where we can clobber it, and build the product in @v@.
+ */
+ for (i = 0; i < p->n; i++) { u[i] = x[i]; v[i] = 0; }
+
+ /* Repeatedly multiply @x@ (in @u@) by %$t$%, and add together those
+ * %$x t^i$% selected by the bits of @y@. This is basically what you get
+ * by streaming the result of @gcm_mktable@ into @gcm_mulk_...@.
+ */
+ for (i = 0; i < p->n; i++) {
+ t = y[i];
+ for (j = 0; j < 32; j++) {
+ m = -((t >> 31)&1u);
+ for (k = 0; k < p->n; k++) v[k] ^= u[k]&m;
+ mult(p, u, u); t <<= 1;
+ }
+ }
+
+ /* Write out the result now that it's ready. */
+ for (i = 0; i < p->n; i++) z[i] = v[i];
+}
+
+/*----- Table-based multiplication ----------------------------------------*/
+
+/* --- @gcm_mktable@ --- *
+ *
+ * Arguments: @const gcm_params *p@ = pointer to the parameters
+ * @uint32 *ktab@ = where to write the table; there must be
+ * space for %$32 n$% $%n$%-word entries, i.e.,
+ * %$32 n^2$% 32-bit words in total, where %$n$% is
+ * @p->n@, the block size in words
+ * @const uint32 *k@ = input field element
+ *
+ * Returns: ---
+ *
+ * Use: Construct a table for use by @gcm_mulk_...@ below, to
+ * multiply (vaguely) efficiently by @k@.
+ */
+
+void gcm_mktable(const gcm_params *p, uint32 *ktab, const uint32 *k)
+{
+ unsigned m = (p->f&GCMF_SWAP ? 0x18 : 0);
+ unsigned i, j, o = m*p->n;
+
+ /* As described above, the table stores entries %$K[i \xor m] = k t^i$%,
+ * where %$m = 0$% (big-endian cipher) or %$m = 24$% (little-endian).
+ * The first job is to store %$K[m] = k$%.
+ *
+ * We initially build the table with the entries in big-endian order, and
+ * then swap them if necessary. This makes the arithmetic functions more
+ * amenable for use by @gcm_concat@ below.
+ */
+ if (!(p->f&GCMF_SWAP)) for (i = 0; i < p->n; i++) ktab[o + i] = k[i];
+ else for (i = 0; i < p->n; i++) ktab[o + i] = ENDSWAP32(k[i]);
+
+ /* Fill in the rest of the table by repeatedly multiplying the previous
+ * entry by %$t$%.
+ */
+ for (i = 1; i < 32*p->n; i++)
+ { j = (i ^ m)*p->n; mult(p, ktab + j, ktab + o); o = j; }
+
+ /* Finally, if the cipher uses a little-endian convention, then swap all of
+ * the individual words.
+ */
+ if (p->f&GCMF_SWAP)
+ for (i = 0; i < 32*p->n*p->n; i++) ktab[i] = ENDSWAP32(ktab[i]);
+}
+
+/* --- @gcm_mulk_N@ --- *
+ *
+ * Arguments: @uint32 *a@ = accumulator to multiply
+ * @const uint32 *ktab@ = table constructed by @gcm_mktable@
+ *
+ * Returns: ---
+ *
+ * Use: Multiply @a@ by @k@ (implicitly represented in @ktab@),
+ * updating @a@ in-place. There are separate functions for each
+ * supported block size because this is the function whose
+ * performance actually matters.
+ */
+
+#define DEF_MULK(nbits) \
+void gcm_mulk_##nbits(uint32 *a, const uint32 *ktab) \
+{ \
+ uint32 m, t; \
+ uint32 z[nbits/32]; \
+ unsigned i, j, k; \
+ \
+ for (i = 0; i < nbits/32; i++) z[i] = 0; \
+ \
+ for (i = 0; i < nbits/32; i++) { \
+ t = a[i]; \
+ for (j = 0; j < 32; j++) { \
+ m = -((t >> 31)&1u); \
+ for (k = 0; k < nbits/32; k++) z[k] ^= *ktab++&m; \
+ t <<= 1; \
+ } \
+ } \
+ \
+ for (i = 0; i < nbits/32; i++) a[i] = z[i]; \
+}
+GCM_WIDTHS(DEF_MULK)
+
+/*----- Other utilities ---------------------------------------------------*/
+
+/* --- @putlen@ --- *
+ *
+ * Arguments: @octet *p@ = pointer to output buffer
+ * @unsigned w@ = size of output buffer
+ * @unsigned blksz@ = block size (assumed fairly small)
+ * @unsigned long nblocks@ = number of blocks
+ * @unsigned nbytes@ = tail size in bytes (assumed small)
+ *
+ * Returns: ---
+ *
+ * Use: Store the overall length in %$\emph{bits}$% (i.e.,
+ * @3*(nblocks*blksz + nbytes)@ in big-endian form in the
+ * buffer @p@.
+ */
+
+static void putlen(octet *p, unsigned w, unsigned blksz,
+ unsigned long nblocks, unsigned nbytes)
+{
+ unsigned long nblo = nblocks&((1ul << (ULONG_BITS/2)) - 1),
+ nbhi = nblocks >> ULONG_BITS/2;
+ unsigned long nlo = nblo*blksz + nbytes, nhi = nbhi*blksz;
+
+ /* This is fiddly. Split @nblocks@, which is the big number, into high and
+ * low halves, multiply those separately by @blksz@, propagate carries, and
+ * then multiply by eight.
+ */
+ nhi += nlo >> ULONG_BITS/2;
+ nlo &= (1ul << (ULONG_BITS/2)) - 1;
+ nlo <<= 3;
+
+ /* Now write out the size, feeding bits in from @nhi@ as necessary. */
+ p += w;
+ while (w--) {
+ *--p = U8(nlo);
+ nlo = (nlo >> 8) | ((nhi&0xff) << (ULONG_BITS/2 - 5));
+ nhi >>= 8;
+ }
+}
+
+/* --- @mix@ --- *
+ *
+ * Arguments: @const gcm_params *p@ = pointer to the parameters
+ * @uint32 *a@ = GHASH accumulator
+ * @const octet *q@ = pointer to an input block
+ * @const uint32 *ktab@ = multiplication table, built by
+ * @gcm_mktable@
+ *
+ * Returns: ---
+ *
+ * Use: Fold the block @q@ into the GHASH accumulator. The
+ * calculation is %$a' = k (a + q)$%.
+ */
+
+static void mix(const gcm_params *p, uint32 *a,
+ const octet *q, const uint32 *ktab)
+{
+ unsigned i;
+
+ /* Convert the block from bytes into words, using the appropriate
+ * convention.
+ */
+ if (p->f&GCMF_SWAP)
+ for (i = 0; i < p->n; i++) { a[i] ^= LOAD32_L(q); q += 4; }
+ else
+ for (i = 0; i < p->n; i++) { a[i] ^= LOAD32_B(q); q += 4; }
+
+ /* Dispatch to the correct multiply-by-%$k$% function. */
+ switch (p->n) {
+#define CASE(nbits) case nbits/32: gcm_mulk_##nbits(a, ktab); break;
+ GCM_WIDTHS(CASE)
+#undef CASE
+ default: abort();
+ }
+}
+
+/* --- @gcm_ghashdone@ --- *
+ *
+ * Arguments: @const gcm_params *p@ = pointer to the parameters
+ * @uint32 *a@ = GHASH accumulator
+ * @const uint32 *ktab@ = multiplication table, built by
+ * @gcm_mktable@
+ * @unsigned long xblocks, yblocks@ = number of whole blocks in
+ * the two inputs
+ * @unsigned xbytes, ybytes@ = number of trailing bytes in the
+ * two inputs
+ *
+ * Returns: ---
+ *
+ * Use: Finishes a GHASH operation by appending the appropriately
+ * encoded lengths of the two constituent messages.
+ */
+
+void gcm_ghashdone(const gcm_params *p, uint32 *a, const uint32 *ktab,
+ unsigned long xblocks, unsigned xbytes,
+ unsigned long yblocks, unsigned ybytes)
+{
+ octet b[4*GCM_NMAX];
+ unsigned w = p->n < 3 ? 4*p->n : 2*p->n;
+
+ /* Construct the encoded lengths. Note that smaller-block versions of GCM
+ * encode the lengths in separate blocks. GCM is only officially defined
+ * for 64- and 128-bit blocks; I've placed the cutoff somewhat arbitrarily
+ * at 96 bits.
+ */
+ putlen(b, w, 4*p->n, xblocks, xbytes);
+ putlen(b + w, w, 4*p->n, yblocks, ybytes);
+
+ /* Feed the lengths into the accumulator. */
+ mix(p, a, b, ktab);
+ if (p->n < 3) mix(p, a, b + w, ktab);
+}
+
+/* --- @gcm_concat@ --- *
+ *
+ * Arguments: @const gcm_params *p@ = pointer to the parameters
+ * @uint32 *z@ = GHASH accumulator for suffix, updated
+ * @const uint32 *x@ = GHASH accumulator for prefix
+ * @const uint32 *ktab@ = multiplication table, built by
+ * @gcm_mktable@
+ * @unsigned long n@ = length of suffix in whole blocks
+ *
+ * Returns: ---
+ *
+ * Use: On entry, @x@ and @z@ are the results of hashing two strings
+ * %$a$% and %$b$%, each a whole number of blocks long; in
+ * particular, %$b$% is @n@ blocks long. On exit, @z@ is
+ * updated to be the hash of %$a \cat b$%.
+ */
+
+void gcm_concat(const gcm_params *p, uint32 *z, const uint32 *x,
+ const uint32 *ktab, unsigned long n)
+{
+ uint32 t[GCM_NMAX], u[GCM_NMAX];
+ unsigned i, j;
+
+ if (!n) {
+ /* If @n@ is zero, then there's not much to do. The mathematics
+ * (explained below) still works, but the code takes a shortcut which
+ * doesn't handle this case: so set %$z' = z + x k^n = z + x$%.
+ */
+
+ for (j = 0; j < p->n; j++) z[j] ^= x[j];
+ } else {
+ /* We have %$x = a_0 t^m + \cdots + a_{m-2} t^2 + a_{m-1} t$% and
+ * %$z = b_0 t^n + \cdots + b_{n-2} t^2 + b_{n-1} t$%. What we'd like is
+ * the hash of %$a \cat b$%, which is %$z + x k^n$%.
+ *
+ * The first job, then, is to calculate %$k^n$%, and for this we use a
+ * simple left-to-right square-and-multiply algorithm. There's no need
+ * to keep %$n$% secret here.
+ */
+
+ /* Start by retrieving %$k$% from the table, and convert it to big-endian
+ * form.
+ */
+ if (!(p->f&GCMF_SWAP)) for (j = 0; j < p->n; j++) u[j] = ktab[j];
+ else for (j = 0; j < p->n; j++) u[j] = ENDSWAP32(ktab[24*p->n + j]);
+
+ /* Now calculate %$k^n$%. */
+ i = ULONG_BITS;
+#define BIT (1ul << (ULONG_BITS - 1))
+ while (!(n&BIT)) { n <<= 1; i--; }
+ n <<= 1; i--; for (j = 0; j < p->n; j++) t[j] = u[j];
+ while (i--) { mul(p, t, t, t); if (n&BIT) mul(p, t, t, u); n <<= 1; }
+#undef BIT
+
+ /* Next, calculate %$x k^n$%. If we're using a little-endian convention
+ * then we must convert %$x$%; otherwise we can just use it in place.
+ */
+ if (!(p->f&GCMF_SWAP))
+ mul(p, t, t, x);
+ else {
+ for (j = 0; j < p->n; j++) u[j] = ENDSWAP32(x[j]);
+ mul(p, t, t, u);
+ }
+
+ /* Finally, add %$x k^n$% onto %$z$%, converting back to little-endian if
+ * necessary.
+ */
+ if (!(p->f&GCMF_SWAP)) for (j = 0; j < p->n; j++) z[j] ^= t[j];
+ else for (j = 0; j < p->n; j++) z[j] ^= ENDSWAP32(t[j]);
+ }
+}
+
+/*----- That's all, folks -------------------------------------------------*/
~mdw / catacomb / blobdiff