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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)