/* 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)
