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- /* SPDX-License-Identifier: GPL-2.0 */
- /*
- * Copyright 2021 Google LLC
- */
- /*
- * This is an efficient implementation of POLYVAL using intel PCLMULQDQ-NI
- * instructions. It works on 8 blocks at a time, by precomputing the first 8
- * keys powers h^8, ..., h^1 in the POLYVAL finite field. This precomputation
- * allows us to split finite field multiplication into two steps.
- *
- * In the first step, we consider h^i, m_i as normal polynomials of degree less
- * than 128. We then compute p(x) = h^8m_0 + ... + h^1m_7 where multiplication
- * is simply polynomial multiplication.
- *
- * In the second step, we compute the reduction of p(x) modulo the finite field
- * modulus g(x) = x^128 + x^127 + x^126 + x^121 + 1.
- *
- * This two step process is equivalent to computing h^8m_0 + ... + h^1m_7 where
- * multiplication is finite field multiplication. The advantage is that the
- * two-step process only requires 1 finite field reduction for every 8
- * polynomial multiplications. Further parallelism is gained by interleaving the
- * multiplications and polynomial reductions.
- */
- #include <linux/linkage.h>
- #include <asm/frame.h>
- #define STRIDE_BLOCKS 8
- #define GSTAR %xmm7
- #define PL %xmm8
- #define PH %xmm9
- #define TMP_XMM %xmm11
- #define LO %xmm12
- #define HI %xmm13
- #define MI %xmm14
- #define SUM %xmm15
- #define KEY_POWERS %rdi
- #define MSG %rsi
- #define BLOCKS_LEFT %rdx
- #define ACCUMULATOR %rcx
- #define TMP %rax
- .section .rodata.cst16.gstar, "aM", @progbits, 16
- .align 16
- .Lgstar:
- .quad 0xc200000000000000, 0xc200000000000000
- .text
- /*
- * Performs schoolbook1_iteration on two lists of 128-bit polynomials of length
- * count pointed to by MSG and KEY_POWERS.
- */
- .macro schoolbook1 count
- .set i, 0
- .rept (\count)
- schoolbook1_iteration i 0
- .set i, (i +1)
- .endr
- .endm
- /*
- * Computes the product of two 128-bit polynomials at the memory locations
- * specified by (MSG + 16*i) and (KEY_POWERS + 16*i) and XORs the components of
- * the 256-bit product into LO, MI, HI.
- *
- * Given:
- * X = [X_1 : X_0]
- * Y = [Y_1 : Y_0]
- *
- * We compute:
- * LO += X_0 * Y_0
- * MI += X_0 * Y_1 + X_1 * Y_0
- * HI += X_1 * Y_1
- *
- * Later, the 256-bit result can be extracted as:
- * [HI_1 : HI_0 + MI_1 : LO_1 + MI_0 : LO_0]
- * This step is done when computing the polynomial reduction for efficiency
- * reasons.
- *
- * If xor_sum == 1, then also XOR the value of SUM into m_0. This avoids an
- * extra multiplication of SUM and h^8.
- */
- .macro schoolbook1_iteration i xor_sum
- movups (16*\i)(MSG), %xmm0
- .if (\i == 0 && \xor_sum == 1)
- pxor SUM, %xmm0
- .endif
- vpclmulqdq $0x01, (16*\i)(KEY_POWERS), %xmm0, %xmm2
- vpclmulqdq $0x00, (16*\i)(KEY_POWERS), %xmm0, %xmm1
- vpclmulqdq $0x10, (16*\i)(KEY_POWERS), %xmm0, %xmm3
- vpclmulqdq $0x11, (16*\i)(KEY_POWERS), %xmm0, %xmm4
- vpxor %xmm2, MI, MI
- vpxor %xmm1, LO, LO
- vpxor %xmm4, HI, HI
- vpxor %xmm3, MI, MI
- .endm
- /*
- * Performs the same computation as schoolbook1_iteration, except we expect the
- * arguments to already be loaded into xmm0 and xmm1 and we set the result
- * registers LO, MI, and HI directly rather than XOR'ing into them.
- */
- .macro schoolbook1_noload
- vpclmulqdq $0x01, %xmm0, %xmm1, MI
- vpclmulqdq $0x10, %xmm0, %xmm1, %xmm2
- vpclmulqdq $0x00, %xmm0, %xmm1, LO
- vpclmulqdq $0x11, %xmm0, %xmm1, HI
- vpxor %xmm2, MI, MI
- .endm
- /*
- * Computes the 256-bit polynomial represented by LO, HI, MI. Stores
- * the result in PL, PH.
- * [PH : PL] = [HI_1 : HI_0 + MI_1 : LO_1 + MI_0 : LO_0]
- */
- .macro schoolbook2
- vpslldq $8, MI, PL
- vpsrldq $8, MI, PH
- pxor LO, PL
- pxor HI, PH
- .endm
- /*
- * Computes the 128-bit reduction of PH : PL. Stores the result in dest.
- *
- * This macro computes p(x) mod g(x) where p(x) is in montgomery form and g(x) =
- * x^128 + x^127 + x^126 + x^121 + 1.
- *
- * We have a 256-bit polynomial PH : PL = P_3 : P_2 : P_1 : P_0 that is the
- * product of two 128-bit polynomials in Montgomery form. We need to reduce it
- * mod g(x). Also, since polynomials in Montgomery form have an "extra" factor
- * of x^128, this product has two extra factors of x^128. To get it back into
- * Montgomery form, we need to remove one of these factors by dividing by x^128.
- *
- * To accomplish both of these goals, we add multiples of g(x) that cancel out
- * the low 128 bits P_1 : P_0, leaving just the high 128 bits. Since the low
- * bits are zero, the polynomial division by x^128 can be done by right shifting.
- *
- * Since the only nonzero term in the low 64 bits of g(x) is the constant term,
- * the multiple of g(x) needed to cancel out P_0 is P_0 * g(x). The CPU can
- * only do 64x64 bit multiplications, so split P_0 * g(x) into x^128 * P_0 +
- * x^64 * g*(x) * P_0 + P_0, where g*(x) is bits 64-127 of g(x). Adding this to
- * the original polynomial gives P_3 : P_2 + P_0 + T_1 : P_1 + T_0 : 0, where T
- * = T_1 : T_0 = g*(x) * P_0. Thus, bits 0-63 got "folded" into bits 64-191.
- *
- * Repeating this same process on the next 64 bits "folds" bits 64-127 into bits
- * 128-255, giving the answer in bits 128-255. This time, we need to cancel P_1
- * + T_0 in bits 64-127. The multiple of g(x) required is (P_1 + T_0) * g(x) *
- * x^64. Adding this to our previous computation gives P_3 + P_1 + T_0 + V_1 :
- * P_2 + P_0 + T_1 + V_0 : 0 : 0, where V = V_1 : V_0 = g*(x) * (P_1 + T_0).
- *
- * So our final computation is:
- * T = T_1 : T_0 = g*(x) * P_0
- * V = V_1 : V_0 = g*(x) * (P_1 + T_0)
- * p(x) / x^{128} mod g(x) = P_3 + P_1 + T_0 + V_1 : P_2 + P_0 + T_1 + V_0
- *
- * The implementation below saves a XOR instruction by computing P_1 + T_0 : P_0
- * + T_1 and XORing into dest, rather than separately XORing P_1 : P_0 and T_0 :
- * T_1 into dest. This allows us to reuse P_1 + T_0 when computing V.
- */
- .macro montgomery_reduction dest
- vpclmulqdq $0x00, PL, GSTAR, TMP_XMM # TMP_XMM = T_1 : T_0 = P_0 * g*(x)
- pshufd $0b01001110, TMP_XMM, TMP_XMM # TMP_XMM = T_0 : T_1
- pxor PL, TMP_XMM # TMP_XMM = P_1 + T_0 : P_0 + T_1
- pxor TMP_XMM, PH # PH = P_3 + P_1 + T_0 : P_2 + P_0 + T_1
- pclmulqdq $0x11, GSTAR, TMP_XMM # TMP_XMM = V_1 : V_0 = V = [(P_1 + T_0) * g*(x)]
- vpxor TMP_XMM, PH, \dest
- .endm
- /*
- * Compute schoolbook multiplication for 8 blocks
- * m_0h^8 + ... + m_7h^1
- *
- * If reduce is set, also computes the montgomery reduction of the
- * previous full_stride call and XORs with the first message block.
- * (m_0 + REDUCE(PL, PH))h^8 + ... + m_7h^1.
- * I.e., the first multiplication uses m_0 + REDUCE(PL, PH) instead of m_0.
- */
- .macro full_stride reduce
- pxor LO, LO
- pxor HI, HI
- pxor MI, MI
- schoolbook1_iteration 7 0
- .if \reduce
- vpclmulqdq $0x00, PL, GSTAR, TMP_XMM
- .endif
- schoolbook1_iteration 6 0
- .if \reduce
- pshufd $0b01001110, TMP_XMM, TMP_XMM
- .endif
- schoolbook1_iteration 5 0
- .if \reduce
- pxor PL, TMP_XMM
- .endif
- schoolbook1_iteration 4 0
- .if \reduce
- pxor TMP_XMM, PH
- .endif
- schoolbook1_iteration 3 0
- .if \reduce
- pclmulqdq $0x11, GSTAR, TMP_XMM
- .endif
- schoolbook1_iteration 2 0
- .if \reduce
- vpxor TMP_XMM, PH, SUM
- .endif
- schoolbook1_iteration 1 0
- schoolbook1_iteration 0 1
- addq $(8*16), MSG
- schoolbook2
- .endm
- /*
- * Process BLOCKS_LEFT blocks, where 0 < BLOCKS_LEFT < STRIDE_BLOCKS
- */
- .macro partial_stride
- mov BLOCKS_LEFT, TMP
- shlq $4, TMP
- addq $(16*STRIDE_BLOCKS), KEY_POWERS
- subq TMP, KEY_POWERS
- movups (MSG), %xmm0
- pxor SUM, %xmm0
- movaps (KEY_POWERS), %xmm1
- schoolbook1_noload
- dec BLOCKS_LEFT
- addq $16, MSG
- addq $16, KEY_POWERS
- test $4, BLOCKS_LEFT
- jz .Lpartial4BlocksDone
- schoolbook1 4
- addq $(4*16), MSG
- addq $(4*16), KEY_POWERS
- .Lpartial4BlocksDone:
- test $2, BLOCKS_LEFT
- jz .Lpartial2BlocksDone
- schoolbook1 2
- addq $(2*16), MSG
- addq $(2*16), KEY_POWERS
- .Lpartial2BlocksDone:
- test $1, BLOCKS_LEFT
- jz .LpartialDone
- schoolbook1 1
- .LpartialDone:
- schoolbook2
- montgomery_reduction SUM
- .endm
- /*
- * Perform montgomery multiplication in GF(2^128) and store result in op1.
- *
- * Computes op1*op2*x^{-128} mod x^128 + x^127 + x^126 + x^121 + 1
- * If op1, op2 are in montgomery form, this computes the montgomery
- * form of op1*op2.
- *
- * void clmul_polyval_mul(u8 *op1, const u8 *op2);
- */
- SYM_FUNC_START(clmul_polyval_mul)
- FRAME_BEGIN
- vmovdqa .Lgstar(%rip), GSTAR
- movups (%rdi), %xmm0
- movups (%rsi), %xmm1
- schoolbook1_noload
- schoolbook2
- montgomery_reduction SUM
- movups SUM, (%rdi)
- FRAME_END
- RET
- SYM_FUNC_END(clmul_polyval_mul)
- /*
- * Perform polynomial evaluation as specified by POLYVAL. This computes:
- * h^n * accumulator + h^n * m_0 + ... + h^1 * m_{n-1}
- * where n=nblocks, h is the hash key, and m_i are the message blocks.
- *
- * rdi - pointer to precomputed key powers h^8 ... h^1
- * rsi - pointer to message blocks
- * rdx - number of blocks to hash
- * rcx - pointer to the accumulator
- *
- * void clmul_polyval_update(const struct polyval_tfm_ctx *keys,
- * const u8 *in, size_t nblocks, u8 *accumulator);
- */
- SYM_FUNC_START(clmul_polyval_update)
- FRAME_BEGIN
- vmovdqa .Lgstar(%rip), GSTAR
- movups (ACCUMULATOR), SUM
- subq $STRIDE_BLOCKS, BLOCKS_LEFT
- js .LstrideLoopExit
- full_stride 0
- subq $STRIDE_BLOCKS, BLOCKS_LEFT
- js .LstrideLoopExitReduce
- .LstrideLoop:
- full_stride 1
- subq $STRIDE_BLOCKS, BLOCKS_LEFT
- jns .LstrideLoop
- .LstrideLoopExitReduce:
- montgomery_reduction SUM
- .LstrideLoopExit:
- add $STRIDE_BLOCKS, BLOCKS_LEFT
- jz .LskipPartial
- partial_stride
- .LskipPartial:
- movups SUM, (ACCUMULATOR)
- FRAME_END
- RET
- SYM_FUNC_END(clmul_polyval_update)
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