Add hardware accelerated version of POLYVAL for ARM64 CPUs with Crypto Extensions support. This implementation is accelerated using PMULL instructions to perform the finite field computations. For added efficiency, 8 blocks of the message are processed simultaneously by precomputing the first 8 powers of the key. Karatsuba multiplication is used instead of Schoolbook multiplication because it was found to be slightly faster on ARM64 CPUs. Montgomery reduction must be used instead of Barrett reduction due to the difference in modulus between POLYVAL's field and other finite fields. More information on POLYVAL can be found in the HCTR2 paper: "Length-preserving encryption with HCTR2": https://eprint.iacr.org/2021/1441.pdf Signed-off-by: Nathan Huckleberry <nhuck@xxxxxxxxxx> Reviewed-by: Ard Biesheuvel <ardb@xxxxxxxxxx> Reviewed-by: Eric Biggers <ebiggers@xxxxxxxxxx> --- arch/arm64/crypto/Kconfig | 5 + arch/arm64/crypto/Makefile | 3 + arch/arm64/crypto/polyval-ce-core.S | 361 ++++++++++++++++++++++++++++ arch/arm64/crypto/polyval-ce-glue.c | 193 +++++++++++++++ 4 files changed, 562 insertions(+) create mode 100644 arch/arm64/crypto/polyval-ce-core.S create mode 100644 arch/arm64/crypto/polyval-ce-glue.c diff --git a/arch/arm64/crypto/Kconfig b/arch/arm64/crypto/Kconfig index 897f9a4b5b67..06431d298a92 100644 --- a/arch/arm64/crypto/Kconfig +++ b/arch/arm64/crypto/Kconfig @@ -60,6 +60,11 @@ config CRYPTO_GHASH_ARM64_CE select CRYPTO_GF128MUL select CRYPTO_LIB_AES +config CRYPTO_POLYVAL_ARM64_CE + tristate "POLYVAL using ARMv8 Crypto Extensions (for HCTR2)" + depends on KERNEL_MODE_NEON + select CRYPTO_POLYVAL + config CRYPTO_CRCT10DIF_ARM64_CE tristate "CRCT10DIF digest algorithm using PMULL instructions" depends on KERNEL_MODE_NEON && CRC_T10DIF diff --git a/arch/arm64/crypto/Makefile b/arch/arm64/crypto/Makefile index 09a805cc32d7..53f9af962b86 100644 --- a/arch/arm64/crypto/Makefile +++ b/arch/arm64/crypto/Makefile @@ -26,6 +26,9 @@ sm4-ce-y := sm4-ce-glue.o sm4-ce-core.o obj-$(CONFIG_CRYPTO_GHASH_ARM64_CE) += ghash-ce.o ghash-ce-y := ghash-ce-glue.o ghash-ce-core.o +obj-$(CONFIG_CRYPTO_POLYVAL_ARM64_CE) += polyval-ce.o +polyval-ce-y := polyval-ce-glue.o polyval-ce-core.o + obj-$(CONFIG_CRYPTO_CRCT10DIF_ARM64_CE) += crct10dif-ce.o crct10dif-ce-y := crct10dif-ce-core.o crct10dif-ce-glue.o diff --git a/arch/arm64/crypto/polyval-ce-core.S b/arch/arm64/crypto/polyval-ce-core.S new file mode 100644 index 000000000000..b5326540d2e3 --- /dev/null +++ b/arch/arm64/crypto/polyval-ce-core.S @@ -0,0 +1,361 @@ +/* SPDX-License-Identifier: GPL-2.0 */ +/* + * Implementation of POLYVAL using ARMv8 Crypto Extensions. + * + * Copyright 2021 Google LLC + */ +/* + * This is an efficient implementation of POLYVAL using ARMv8 Crypto Extensions + * 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> +#define STRIDE_BLOCKS 8 + +KEY_POWERS .req x0 +MSG .req x1 +BLOCKS_LEFT .req x2 +ACCUMULATOR .req x3 +KEY_START .req x10 +EXTRA_BYTES .req x11 +TMP .req x13 + +M0 .req v0 +M1 .req v1 +M2 .req v2 +M3 .req v3 +M4 .req v4 +M5 .req v5 +M6 .req v6 +M7 .req v7 +KEY8 .req v8 +KEY7 .req v9 +KEY6 .req v10 +KEY5 .req v11 +KEY4 .req v12 +KEY3 .req v13 +KEY2 .req v14 +KEY1 .req v15 +PL .req v16 +PH .req v17 +TMP_V .req v18 +LO .req v20 +MI .req v21 +HI .req v22 +SUM .req v23 +GSTAR .req v24 + + .text + + .arch armv8-a+crypto + .align 4 + +.Lgstar: + .quad 0xc200000000000000, 0xc200000000000000 + +/* + * Computes the product of two 128-bit polynomials in X and Y 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 + X_1) * (Y_0 + Y_1) + * HI += X_1 * Y_1 + * + * Later, the 256-bit result can be extracted as: + * [HI_1 : HI_0 + HI_1 + MI_1 + LO_1 : LO_1 + HI_0 + MI_0 + LO_0 : LO_0] + * This step is done when computing the polynomial reduction for efficiency + * reasons. + * + * Karatsuba multiplication is used instead of Schoolbook multiplication because + * it was found to be slightly faster on ARM64 CPUs. + * + */ +.macro karatsuba1 X Y + X .req \X + Y .req \Y + ext v25.16b, X.16b, X.16b, #8 + ext v26.16b, Y.16b, Y.16b, #8 + eor v25.16b, v25.16b, X.16b + eor v26.16b, v26.16b, Y.16b + pmull2 v28.1q, X.2d, Y.2d + pmull v29.1q, X.1d, Y.1d + pmull v27.1q, v25.1d, v26.1d + eor HI.16b, HI.16b, v28.16b + eor LO.16b, LO.16b, v29.16b + eor MI.16b, MI.16b, v27.16b + .unreq X + .unreq Y +.endm + +/* + * Same as karatsuba1, except overwrites HI, LO, MI rather than XORing into + * them. + */ +.macro karatsuba1_store X Y + X .req \X + Y .req \Y + ext v25.16b, X.16b, X.16b, #8 + ext v26.16b, Y.16b, Y.16b, #8 + eor v25.16b, v25.16b, X.16b + eor v26.16b, v26.16b, Y.16b + pmull2 HI.1q, X.2d, Y.2d + pmull LO.1q, X.1d, Y.1d + pmull MI.1q, v25.1d, v26.1d + .unreq X + .unreq Y +.endm + +/* + * Computes the 256-bit polynomial represented by LO, HI, MI. Stores + * the result in PL, PH. + * [PH : PL] = + * [HI_1 : HI_1 + HI_0 + MI_1 + LO_1 : HI_0 + MI_0 + LO_1 + LO_0 : LO_0] + */ +.macro karatsuba2 + // v4 = [HI_1 + MI_1 : HI_0 + MI_0] + eor v4.16b, HI.16b, MI.16b + // v4 = [HI_1 + MI_1 + LO_1 : HI_0 + MI_0 + LO_0] + eor v4.16b, v4.16b, LO.16b + // v5 = [HI_0 : LO_1] + ext v5.16b, LO.16b, HI.16b, #8 + // v4 = [HI_1 + HI_0 + MI_1 + LO_1 : HI_0 + MI_0 + LO_1 + LO_0] + eor v4.16b, v4.16b, v5.16b + // HI = [HI_0 : HI_1] + ext HI.16b, HI.16b, HI.16b, #8 + // LO = [LO_0 : LO_1] + ext LO.16b, LO.16b, LO.16b, #8 + // PH = [HI_1 : HI_1 + HI_0 + MI_1 + LO_1] + ext PH.16b, v4.16b, HI.16b, #8 + // PL = [HI_0 + MI_0 + LO_1 + LO_0 : LO_0] + ext PL.16b, LO.16b, v4.16b, #8 +.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 + DEST .req \dest + // TMP_V = T_1 : T_0 = P_0 * g*(x) + pmull TMP_V.1q, PL.1d, GSTAR.1d + // TMP_V = T_0 : T_1 + ext TMP_V.16b, TMP_V.16b, TMP_V.16b, #8 + // TMP_V = P_1 + T_0 : P_0 + T_1 + eor TMP_V.16b, PL.16b, TMP_V.16b + // PH = P_3 + P_1 + T_0 : P_2 + P_0 + T_1 + eor PH.16b, PH.16b, TMP_V.16b + // TMP_V = V_1 : V_0 = (P_1 + T_0) * g*(x) + pmull2 TMP_V.1q, TMP_V.2d, GSTAR.2d + eor DEST.16b, PH.16b, TMP_V.16b + .unreq DEST +.endm + +/* + * Compute Polyval on 8 blocks. + * + * 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. + * + * Sets PL, PH. + */ +.macro full_stride reduce + eor LO.16b, LO.16b, LO.16b + eor MI.16b, MI.16b, MI.16b + eor HI.16b, HI.16b, HI.16b + + ld1 {M0.16b, M1.16b, M2.16b, M3.16b}, [MSG], #64 + ld1 {M4.16b, M5.16b, M6.16b, M7.16b}, [MSG], #64 + + karatsuba1 M7 KEY1 + .if \reduce + pmull TMP_V.1q, PL.1d, GSTAR.1d + .endif + + karatsuba1 M6 KEY2 + .if \reduce + ext TMP_V.16b, TMP_V.16b, TMP_V.16b, #8 + .endif + + karatsuba1 M5 KEY3 + .if \reduce + eor TMP_V.16b, PL.16b, TMP_V.16b + .endif + + karatsuba1 M4 KEY4 + .if \reduce + eor PH.16b, PH.16b, TMP_V.16b + .endif + + karatsuba1 M3 KEY5 + .if \reduce + pmull2 TMP_V.1q, TMP_V.2d, GSTAR.2d + .endif + + karatsuba1 M2 KEY6 + .if \reduce + eor SUM.16b, PH.16b, TMP_V.16b + .endif + + karatsuba1 M1 KEY7 + eor M0.16b, M0.16b, SUM.16b + + karatsuba1 M0 KEY8 + karatsuba2 +.endm + +/* + * Handle any extra blocks after full_stride loop. + */ +.macro partial_stride + add KEY_POWERS, KEY_START, #(STRIDE_BLOCKS << 4) + sub KEY_POWERS, KEY_POWERS, BLOCKS_LEFT, lsl #4 + ld1 {KEY1.16b}, [KEY_POWERS], #16 + + ld1 {TMP_V.16b}, [MSG], #16 + eor SUM.16b, SUM.16b, TMP_V.16b + karatsuba1_store KEY1 SUM + sub BLOCKS_LEFT, BLOCKS_LEFT, #1 + + tst BLOCKS_LEFT, #4 + beq .Lpartial4BlocksDone + ld1 {M0.16b, M1.16b, M2.16b, M3.16b}, [MSG], #64 + ld1 {KEY8.16b, KEY7.16b, KEY6.16b, KEY5.16b}, [KEY_POWERS], #64 + karatsuba1 M0 KEY8 + karatsuba1 M1 KEY7 + karatsuba1 M2 KEY6 + karatsuba1 M3 KEY5 +.Lpartial4BlocksDone: + tst BLOCKS_LEFT, #2 + beq .Lpartial2BlocksDone + ld1 {M0.16b, M1.16b}, [MSG], #32 + ld1 {KEY8.16b, KEY7.16b}, [KEY_POWERS], #32 + karatsuba1 M0 KEY8 + karatsuba1 M1 KEY7 +.Lpartial2BlocksDone: + tst BLOCKS_LEFT, #1 + beq .LpartialDone + ld1 {M0.16b}, [MSG], #16 + ld1 {KEY8.16b}, [KEY_POWERS], #16 + karatsuba1 M0 KEY8 +.LpartialDone: + karatsuba2 + 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 pmull_polyval_mul(u8 *op1, const u8 *op2); + */ +SYM_FUNC_START(pmull_polyval_mul) + adr TMP, .Lgstar + ld1 {GSTAR.2d}, [TMP] + ld1 {v0.16b}, [x0] + ld1 {v1.16b}, [x1] + karatsuba1_store v0 v1 + karatsuba2 + montgomery_reduction SUM + st1 {SUM.16b}, [x0] + ret +SYM_FUNC_END(pmull_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. + * + * x0 - pointer to precomputed key powers h^8 ... h^1 + * x1 - pointer to message blocks + * x2 - number of blocks to hash + * x3 - pointer to accumulator + * + * void pmull_polyval_update(const struct polyval_ctx *ctx, const u8 *in, + * size_t nblocks, u8 *accumulator); + */ +SYM_FUNC_START(pmull_polyval_update) + adr TMP, .Lgstar + mov KEY_START, KEY_POWERS + ld1 {GSTAR.2d}, [TMP] + ld1 {SUM.16b}, [ACCUMULATOR] + subs BLOCKS_LEFT, BLOCKS_LEFT, #STRIDE_BLOCKS + blt .LstrideLoopExit + ld1 {KEY8.16b, KEY7.16b, KEY6.16b, KEY5.16b}, [KEY_POWERS], #64 + ld1 {KEY4.16b, KEY3.16b, KEY2.16b, KEY1.16b}, [KEY_POWERS], #64 + full_stride 0 + subs BLOCKS_LEFT, BLOCKS_LEFT, #STRIDE_BLOCKS + blt .LstrideLoopExitReduce +.LstrideLoop: + full_stride 1 + subs BLOCKS_LEFT, BLOCKS_LEFT, #STRIDE_BLOCKS + bge .LstrideLoop +.LstrideLoopExitReduce: + montgomery_reduction SUM +.LstrideLoopExit: + adds BLOCKS_LEFT, BLOCKS_LEFT, #STRIDE_BLOCKS + beq .LskipPartial + partial_stride +.LskipPartial: + st1 {SUM.16b}, [ACCUMULATOR] + ret +SYM_FUNC_END(pmull_polyval_update) diff --git a/arch/arm64/crypto/polyval-ce-glue.c b/arch/arm64/crypto/polyval-ce-glue.c new file mode 100644 index 000000000000..2a6f2500d8b3 --- /dev/null +++ b/arch/arm64/crypto/polyval-ce-glue.c @@ -0,0 +1,193 @@ +// SPDX-License-Identifier: GPL-2.0-only +/* + * Glue code for POLYVAL using ARMv8 Crypto Extensions + * + * Copyright (c) 2007 Nokia Siemens Networks - Mikko Herranen <mh1@xxxxxx> + * Copyright (c) 2009 Intel Corp. + * Author: Huang Ying <ying.huang@xxxxxxxxx> + * Copyright 2021 Google LLC + */ + +/* + * Glue code based on ghash-clmulni-intel_glue.c. + * + * This implementation of POLYVAL uses montgomery multiplication accelerated by + * ARMv8 Crypto Extensions instructions to implement the finite field operations. + */ + +#include <crypto/algapi.h> +#include <crypto/internal/hash.h> +#include <crypto/internal/simd.h> +#include <crypto/polyval.h> +#include <linux/crypto.h> +#include <linux/init.h> +#include <linux/kernel.h> +#include <linux/module.h> +#include <linux/cpufeature.h> +#include <asm/neon.h> +#include <asm/simd.h> + +#define NUM_KEY_POWERS 8 + +struct polyval_tfm_ctx { + /* + * These powers must be in the order h^8, ..., h^1. + */ + u8 key_powers[NUM_KEY_POWERS][POLYVAL_BLOCK_SIZE]; +}; + +struct polyval_desc_ctx { + u8 buffer[POLYVAL_BLOCK_SIZE]; + u32 bytes; +}; + +asmlinkage void pmull_polyval_update(const struct polyval_tfm_ctx *keys, + const u8 *in, size_t nblocks, u8 *accumulator); +asmlinkage void pmull_polyval_mul(u8 *op1, const u8 *op2); + +static void internal_polyval_update(const struct polyval_tfm_ctx *keys, + const u8 *in, size_t nblocks, u8 *accumulator) +{ + if (likely(crypto_simd_usable())) { + kernel_neon_begin(); + pmull_polyval_update(keys, in, nblocks, accumulator); + kernel_neon_end(); + } else { + polyval_update_non4k(keys->key_powers[NUM_KEY_POWERS-1], in, + nblocks, accumulator); + } +} + +static void internal_polyval_mul(u8 *op1, const u8 *op2) +{ + if (likely(crypto_simd_usable())) { + kernel_neon_begin(); + pmull_polyval_mul(op1, op2); + kernel_neon_end(); + } else { + polyval_mul_non4k(op1, op2); + } +} + +static int polyval_arm64_setkey(struct crypto_shash *tfm, + const u8 *key, unsigned int keylen) +{ + struct polyval_tfm_ctx *tctx = crypto_shash_ctx(tfm); + int i; + + if (keylen != POLYVAL_BLOCK_SIZE) + return -EINVAL; + + memcpy(tctx->key_powers[NUM_KEY_POWERS-1], key, POLYVAL_BLOCK_SIZE); + + for (i = NUM_KEY_POWERS-2; i >= 0; i--) { + memcpy(tctx->key_powers[i], key, POLYVAL_BLOCK_SIZE); + internal_polyval_mul(tctx->key_powers[i], + tctx->key_powers[i+1]); + } + + return 0; +} + +static int polyval_arm64_init(struct shash_desc *desc) +{ + struct polyval_desc_ctx *dctx = shash_desc_ctx(desc); + + memset(dctx, 0, sizeof(*dctx)); + + return 0; +} + +static int polyval_arm64_update(struct shash_desc *desc, + const u8 *src, unsigned int srclen) +{ + struct polyval_desc_ctx *dctx = shash_desc_ctx(desc); + const struct polyval_tfm_ctx *tctx = crypto_shash_ctx(desc->tfm); + u8 *pos; + unsigned int nblocks; + unsigned int n; + + if (dctx->bytes) { + n = min(srclen, dctx->bytes); + pos = dctx->buffer + POLYVAL_BLOCK_SIZE - dctx->bytes; + + dctx->bytes -= n; + srclen -= n; + + while (n--) + *pos++ ^= *src++; + + if (!dctx->bytes) + internal_polyval_mul(dctx->buffer, + tctx->key_powers[NUM_KEY_POWERS-1]); + } + + while (srclen >= POLYVAL_BLOCK_SIZE) { + /* allow rescheduling every 4K bytes */ + nblocks = min(srclen, 4096U) / POLYVAL_BLOCK_SIZE; + internal_polyval_update(tctx, src, nblocks, dctx->buffer); + srclen -= nblocks * POLYVAL_BLOCK_SIZE; + src += nblocks * POLYVAL_BLOCK_SIZE; + } + + if (srclen) { + dctx->bytes = POLYVAL_BLOCK_SIZE - srclen; + pos = dctx->buffer; + while (srclen--) + *pos++ ^= *src++; + } + + return 0; +} + +static int polyval_arm64_final(struct shash_desc *desc, u8 *dst) +{ + struct polyval_desc_ctx *dctx = shash_desc_ctx(desc); + const struct polyval_tfm_ctx *tctx = crypto_shash_ctx(desc->tfm); + + if (dctx->bytes) { + internal_polyval_mul(dctx->buffer, + tctx->key_powers[NUM_KEY_POWERS-1]); + } + + memcpy(dst, dctx->buffer, POLYVAL_BLOCK_SIZE); + + return 0; +} + +static struct shash_alg polyval_alg = { + .digestsize = POLYVAL_DIGEST_SIZE, + .init = polyval_arm64_init, + .update = polyval_arm64_update, + .final = polyval_arm64_final, + .setkey = polyval_arm64_setkey, + .descsize = sizeof(struct polyval_desc_ctx), + .base = { + .cra_name = "polyval", + .cra_driver_name = "polyval-ce", + .cra_priority = 200, + .cra_blocksize = POLYVAL_BLOCK_SIZE, + .cra_ctxsize = sizeof(struct polyval_tfm_ctx), + .cra_module = THIS_MODULE, + }, +}; + +static int __init polyval_ce_mod_init(void) +{ + return crypto_register_shash(&polyval_alg); +} + +static void __exit polyval_ce_mod_exit(void) +{ + crypto_unregister_shash(&polyval_alg); +} + +module_cpu_feature_match(PMULL, polyval_ce_mod_init) + +module_init(polyval_ce_mod_init); +module_exit(polyval_ce_mod_exit); + +MODULE_LICENSE("GPL"); +MODULE_DESCRIPTION("POLYVAL hash function accelerated by ARMv8 Crypto Extensions"); +MODULE_ALIAS_CRYPTO("polyval"); +MODULE_ALIAS_CRYPTO("polyval-ce"); -- 2.36.0.512.ge40c2bad7a-goog
