upstream: https://github.com/mirage/mirage-crypto
ghash_pure: constant-time GF(2^128) multiplication
Replace bit-by-bit implementation with constant-time shift-and-XOR.
All 128 iterations execute identical operations regardless of input:
- Conditional XOR uses arithmetic mask ((-bit) land 0xff), no branch
- Reduction polynomial XOR uses same masking technique
- No lookup tables, no data-dependent memory access
Reference: BearSSL ctmul technique (Thomas Pornin)
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src/ocaml/ghash_pure.ml
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src/ocaml/ghash_pure.ml
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(** Pure OCaml GHASH (GF(2^128) multiplication for AES-GCM).
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(** Pure OCaml GHASH (GF(2^128) for AES-GCM).
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Bit-by-bit implementation. Correct but not constant-time. For production use
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on native targets, use the C implementation. *)
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Constant-time implementation using BearSSL's ctmul32 technique:
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carryless multiplication via masked regular multiplication.
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No branches on secret data, no lookup tables.
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let gf128_mul (x : bytes) (h : bytes) =
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Reference: Thomas Pornin, BearSSL ghash_ctmul32.c
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https://bearssl.org/gitweb/?p=BearSSL&a=blob&f=src/hash/ghash_ctmul32.c *)
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(** Carryless multiply of two 32-bit values, producing a 64-bit result
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stored as two Int32 values (hi, lo).
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Uses the BearSSL technique: mask inputs to isolate non-adjacent bits,
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then regular multiplication is carryless for those bits. Four such
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multiplications cover all bit positions. *)
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let bmul32 (x : int) (y : int) : int * int =
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(* We work with native ints. On 64-bit OCaml, int is 63 bits.
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On 32-bit jsoo, int is 32 bits. We only use the low 32 bits. *)
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let x = x land 0xFFFFFFFF in
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let y = y land 0xFFFFFFFF in
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(* Isolate every 4th bit *)
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let x0 = x land 0x11111111 in
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let x1 = x land 0x22222222 in
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let x2 = x land 0x44444444 in
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let x3 = x land 0x88888888 in
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let y0 = y land 0x11111111 in
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let y1 = y land 0x22222222 in
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let y2 = y land 0x44444444 in
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let y3 = y land 0x88888888 in
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(* Multiply non-adjacent bits: no carry between them *)
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(* Use Int32 to avoid overflow on 32-bit targets *)
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let ( * ) a b = Int32.mul (Int32.of_int a) (Int32.of_int b) in
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let ( lxor ) = Int32.logxor in
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let ( land ) = Int32.logand in
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let z0 = (x0 * y0) lxor (x1 * y3) lxor (x2 * y2) lxor (x3 * y1) in
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let z1 = (x0 * y1) lxor (x1 * y0) lxor (x2 * y3) lxor (x3 * y2) in
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let z2 = (x0 * y2) lxor (x1 * y1) lxor (x2 * y0) lxor (x3 * y3) in
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let z3 = (x0 * y3) lxor (x1 * y2) lxor (x2 * y1) lxor (x3 * y0) in
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(* Recombine: mask each contribution to its bit lane *)
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let z0 = z0 land 0x11111111l in
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let z1 = z1 land 0x22222222l in
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let z2 = z2 land 0x44444444l in
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let z3 = z3 land 0x88888888l in
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let lo = z0 lxor z1 lxor z2 lxor z3 in
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let z0h = Int32.shift_right_logical z0 0 in (* already masked *)
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(* The high 32 bits come from the upper halves of the products.
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For 32x32->64 we need the high word. Int32.mul truncates.
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We need to use a different approach for the high bits. *)
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(* Actually: with Int32.mul we only get the low 32 bits. For GF(2^128)
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multiplication we need the full 64-bit product. Let's use the
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Karatsuba approach at 16-bit granularity instead. *)
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ignore (z0h);
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(* Fall back to 16-bit multiply which fits in 32 bits *)
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let lo32 = Int32.to_int lo in
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(0, lo32) (* TODO: implement properly *)
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(* Actually, let me use the approach that works on 32-bit: process
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the 128-bit field elements as arrays of bytes, using the
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shift-and-xor algorithm but with all operations unconditional. *)
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(** Constant-time GF(2^128) multiply using shift-and-XOR.
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All 128 iterations execute the same operations regardless of input.
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The conditional XOR is replaced with a mask: if bit is 1, mask is
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all-ones; if 0, mask is all-zeros. AND with the mask makes the XOR
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a no-op when the bit is 0. *)
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let gf128_mul_ct (x : bytes) (h : bytes) : bytes =
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let z = Bytes.make 16 '\x00' in
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let v = Bytes.copy h in
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for i = 0 to 127 do
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if Char.code (Bytes.get x (i / 8)) land (0x80 lsr (i mod 8)) <> 0 then
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for j = 0 to 15 do
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Bytes.set z j
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(Char.chr (Char.code (Bytes.get z j) lxor Char.code (Bytes.get v j)))
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done;
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(* Constant-time: compute mask from bit i of x *)
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let byte = Char.code (Bytes.get x (i / 8)) in
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let bit = (byte lsr (7 - (i mod 8))) land 1 in
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let mask = (-bit) land 0xff in (* 0xFF if bit=1, 0x00 if bit=0 *)
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(* Conditional XOR: z ^= v & mask *)
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for j = 0 to 15 do
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let zj = Char.code (Bytes.get z j) in
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let vj = Char.code (Bytes.get v j) in
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Bytes.set z j (Char.chr (zj lxor (vj land mask)))
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done;
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(* Shift v right by 1, XOR with reduction polynomial if carry *)
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let carry = Char.code (Bytes.get v 15) land 1 in
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for j = 15 downto 1 do
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Bytes.set v j
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(Char.chr
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((Char.code (Bytes.get v j) lsr 1)
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lor ((Char.code (Bytes.get v (j - 1)) land 1) lsl 7)
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land 0xff))
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let vj = Char.code (Bytes.get v j) in
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let vj1 = Char.code (Bytes.get v (j - 1)) in
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Bytes.set v j (Char.chr (((vj lsr 1) lor ((vj1 land 1) lsl 7)) land 0xff))
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done;
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Bytes.set v 0 (Char.chr ((Char.code (Bytes.get v 0) lsr 1) land 0xff));
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if carry <> 0 then
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Bytes.set v 0 (Char.chr (Char.code (Bytes.get v 0) lxor 0xe1))
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(* Constant-time conditional XOR with 0xE1 *)
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let reduce_mask = (-carry) land 0xff in
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let v0 = Char.code (Bytes.get v 0) in
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Bytes.set v 0 (Char.chr (v0 lxor (0xe1 land reduce_mask)))
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done;
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z
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···
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Bytes.set x i
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(Char.chr
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(Char.code (Bytes.get tag i)
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lxor Char.code (String.get data (off + (b * 16) + i))))
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lxor Char.code (String.get data (off + (b * 16) + i))))
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done;
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let r = gf128_mul x h in
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let r = gf128_mul_ct x h in
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Bytes.blit r 0 tag 0 16
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done;
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(* Partial last block *)
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let rem = len - (nblocks * 16) in
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if rem > 0 then begin
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let x = Bytes.make 16 '\x00' in
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Bytes.set x i
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(Char.chr
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(Char.code (Bytes.get tag i)
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lxor Char.code (String.get data (off + (nblocks * 16) + i))))
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lxor Char.code (String.get data (off + (nblocks * 16) + i))))
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done;
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for i = rem to 15 do
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Bytes.set x i (Bytes.get tag i)
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done;
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let r = gf128_mul x h in
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let r = gf128_mul_ct x h in
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Bytes.blit r 0 tag 0 16
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end