Add AArch64 ML-DSA Forward NTT HOL Light proof by dkostic · Pull Request #993 · pq-code-package/mldsa-native

dkostic · 2026-03-10T04:13:12Z

Port the ML-DSA Forward NTT implementation and its HOL Light proof of correctness from s2n-bignum to mldsa-native. The proof verifies the AArch64 NEON NTT implementation at the object-code level, showing that the output coefficients are congruent to the forward NTT of the input modulo 8380417, with bounded output coefficients. A constant-time and memory safety proof is also included.

New files:

aarch64/mldsa/mldsa_ntt.S: Assembly derived from dev/aarch64_opt/src/ntt.S
aarch64/proofs/mldsa_ntt.ml: HOL Light proof (MLDSA_NTT_CORRECT, MLDSA_NTT_SUBROUTINE_CORRECT, and MLDSA_NTT_SUBROUTINE_SAFE theorems)
aarch64/proofs/mldsa_specs.ml: Self-contained ML-DSA specifications and congruence/bounds propagation infrastructure, ported from s2n-bignum's common/mlkem_mldsa.ml with only ARM ML-DSA relevant definitions
aarch64/proofs/subroutine_signatures.ml: ML-DSA subroutine signatures for the safety proof infrastructure

Modified files:

aarch64/proofs/aarch64_utils.ml: Add MEMORY_128_FROM_32_TAC
aarch64/Makefile: Add mldsa_ntt to build targets
Resolves HOL-Light: Prove AArch64 NTT #919

dkostic · 2026-03-10T04:15:31Z

addresses #919

oqs-bot · 2026-03-10T04:34:04Z

CBMC Results (ML-DSA-44)

Full Results (176 proofs)

Proof	Status	Current	Previous	Change
`TOTAL`	✅	2097s	2039s	+2.8%
`mld_attempt_signature_generation`	✅	244s	247s	-1%
`polyvecl_pointwise_acc_montgomery_c`	✅	237s	221s	+7%
`poly_pointwise_montgomery_c`	✅	173s	161s	+7%
`rej_uniform_native`	✅	151s	151s	+0%
`sign_verify_internal`	✅	127s	132s	-4%
`mld_invntt_layer`	✅	95s	88s	+8%
`mld_ct_memcmp`	✅	84s	76s	+11%
`mld_ntt_layer`	✅	55s	56s	-2%
`keccak_squeezeblocks_x4`	✅	44s	44s	+0%
`sign_signature_internal`	✅	34s	35s	-3%
`polyvec_matrix_expand`	✅	30s	27s	+11%
`poly_chknorm_c`	✅	21s	21s	+0%
`fqmul`	✅	20s	19s	+5%
`rej_uniform`	✅	20s	22s	-9%
`mld_compute_t0_t1_tr_from_sk_components`	✅	18s	15s	+20%
`polyeta_unpack`	✅	18s	17s	+6%
`rej_uniform_c`	✅	18s	14s	+29%
`poly_uniform_eta_4x`	✅	17s	18s	-6%
`polymat_permute_bitrev_to_custom`	✅	15s	16s	-6%
`poly_uniform_4x`	✅	14s	16s	-12%
`polyt0_unpack`	✅	14s	15s	-7%
`polyvec_matrix_expand_serial`	✅	14s	11s	+27%
`polyvec_matrix_pointwise_montgomery`	✅	14s	11s	+27%
`polyveck_power2round`	✅	14s	11s	+27%
`mld_ntt_butterfly_block`	✅	13s	12s	+8%
`poly_add`	✅	13s	13s	+0%
`keccakf1600x4_permute_native`	✅	12s	14s	-14%
`polyz_unpack_c`	✅	11s	11s	+0%
`sign`	✅	11s	6s	+83%
`keccak_absorb_once_x4`	✅	10s	10s	+0%
`keccakf1600_permute_native`	✅	9s	8s	+12%
`keccakf1600_permute`	✅	8s	8s	+0%
`polyveck_use_hint`	✅	8s	7s	+14%
`sign_pk_from_sk`	✅	8s	5s	+60%
`keccak_absorb`	✅	7s	8s	-12%
`mld_check_pct`	✅	7s	7s	+0%
`mld_polyvecl_permute_bitrev_to_custom_native`	✅	7s	7s	+0%
`poly_challenge`	✅	7s	5s	+40%
`poly_uniform_eta`	✅	7s	3s	+133%
`poly_use_hint_c`	✅	7s	5s	+40%
`polyveck_chknorm`	✅	7s	6s	+17%
`polyveck_sub`	✅	7s	4s	+75%
`poly_caddq_c`	✅	6s	6s	+0%
`poly_invntt_tomont_c`	✅	6s	6s	+0%
`polyveck_add`	✅	6s	7s	-14%
`polyveck_pointwise_poly_montgomery`	✅	6s	6s	+0%
`polyveck_reduce`	✅	6s	5s	+20%
`polyveck_shiftl`	✅	6s	6s	+0%
`polyvecl_ntt`	✅	6s	3s	+100%
`unpack_hints`	✅	6s	5s	+20%
`keccak_init`	✅	5s	2s	+150%
`mld_compute_pack_z`	✅	5s	10s	-50%
`mld_ct_cmask_neg_i32`	✅	5s	2s	+150%
`mld_h`	✅	5s	3s	+67%
`poly_uniform_gamma1_4x`	✅	5s	2s	+150%
`polyveck_caddq`	✅	5s	5s	+0%
`polyveck_pack_w1`	✅	5s	4s	+25%
`polyvecl_pointwise_acc_montgomery_native`	✅	5s	3s	+67%
`sign_keypair_internal`	✅	5s	4s	+25%
`sign_signature_extmu`	✅	5s	3s	+67%
`sign_signature_pre_hash_shake256`	✅	5s	7s	-29%
`sign_verify_pre_hash_shake256`	✅	5s	4s	+25%
`unpack_sk`	✅	5s	3s	+67%
`use_hint`	✅	5s	4s	+25%
`caddq`	✅	4s	3s	+33%
`fqscale`	✅	4s	3s	+33%
`intt_native_x86_64`	✅	4s	4s	+0%
`keccak_squeeze`	✅	4s	3s	+33%
`keccakf1600x4_xor_bytes`	✅	4s	2s	+100%
`make_hint`	✅	4s	2s	+100%
`mld_sample_s1_s2`	✅	4s	6s	-33%
`pack_sk`	✅	4s	2s	+100%
`poly_caddq`	✅	4s	4s	+0%
`poly_chknorm`	✅	4s	2s	+100%
`poly_decompose_c`	✅	4s	4s	+0%
`poly_decompose_native`	✅	4s	3s	+33%
`poly_ntt_native`	✅	4s	3s	+33%
`poly_power2round`	✅	4s	4s	+0%
`poly_reduce`	✅	4s	3s	+33%
`poly_sub`	✅	4s	3s	+33%
`poly_uniform`	✅	4s	3s	+33%
`poly_use_hint_native`	✅	4s	3s	+33%
`polyveck_decompose`	✅	4s	5s	-20%
`polyveck_invntt_tomont`	✅	4s	5s	-20%
`polyveck_make_hint`	✅	4s	6s	-33%
`polyveck_ntt`	✅	4s	6s	-33%
`polyveck_unpack_t0`	✅	4s	2s	+100%
`polyvecl_chknorm`	✅	4s	5s	-20%
`polyvecl_pointwise_acc_montgomery`	✅	4s	4s	+0%
`polyvecl_uniform_gamma1`	✅	4s	4s	+0%
`polyvecl_uniform_gamma1_serial`	✅	4s	3s	+33%
`polyz_unpack`	✅	4s	3s	+33%
`polyz_unpack_native`	✅	4s	2s	+100%
`power2round`	✅	4s	3s	+33%
`shake128_release`	✅	4s	2s	+100%
`sign_open`	✅	4s	3s	+33%
`sign_verify`	✅	4s	4s	+0%
`sign_verify_extmu`	✅	4s	4s	+0%
`sys_check_capability`	✅	4s	2s	+100%
`unpack_pk`	✅	4s	3s	+33%
`decompose`	✅	3s	2s	+50%
`keccak_finalize`	✅	3s	2s	+50%
`keccakf1600x4_permute`	✅	3s	3s	+0%
`mld_ct_cmask_nonzero_u32`	✅	3s	5s	-40%
`mld_ct_get_optblocker_u32`	✅	3s	1s	+200%
`mld_ct_get_optblocker_u8`	✅	3s	2s	+50%
`mld_sample_s1_s2_serial`	✅	3s	5s	-40%
`montgomery_reduce`	✅	3s	1s	+200%
`ntt_native_aarch64`	✅	3s	-	new
`pack_sig_z`	✅	3s	3s	+0%
`poly_invntt_tomont_native`	✅	3s	4s	-25%
`poly_ntt`	✅	3s	3s	+0%
`poly_ntt_c`	✅	3s	3s	+0%
`poly_pointwise_montgomery`	✅	3s	5s	-40%
`poly_pointwise_montgomery_native`	✅	3s	3s	+0%
`poly_uniform_gamma1`	✅	3s	2s	+50%
`poly_use_hint`	✅	3s	6s	-50%
`polyeta_pack`	✅	3s	1s	+200%
`polyt0_pack`	✅	3s	3s	+0%
`polyt1_pack`	✅	3s	5s	-40%
`polyveck_pack_eta`	✅	3s	3s	+0%
`polyvecl_unpack_eta`	✅	3s	4s	-25%
`polyvecl_unpack_z`	✅	3s	4s	-25%
`polyz_pack`	✅	3s	4s	-25%
`rej_eta_c`	✅	3s	4s	-25%
`rej_eta_native`	✅	3s	4s	-25%
`shake128_absorb`	✅	3s	2s	+50%
`shake128_finalize`	✅	3s	2s	+50%
`shake128_init`	✅	3s	3s	+0%
`shake128x4_absorb_once`	✅	3s	2s	+50%
`shake256_finalize`	✅	3s	3s	+0%
`shake256x4_absorb_once`	✅	3s	3s	+0%
`shake256x4_squeezeblocks`	✅	3s	2s	+50%
`sign_signature`	✅	3s	4s	-25%
`sign_verify_pre_hash_internal`	✅	3s	5s	-40%
`unpack_sig`	✅	3s	2s	+50%
`keccakf1600_extract_bytes (big endian)`	✅	2s	2s	+0%
`keccakf1600_xor_bytes`	✅	2s	2s	+0%
`keccakf1600_xor_bytes (big endian)`	✅	2s	3s	-33%
`mld_ct_abs_i32`	✅	2s	2s	+0%
`mld_ct_cmask_nonzero_u8`	✅	2s	3s	-33%
`mld_ct_get_optblocker_i64`	✅	2s	2s	+0%
`mld_ct_sel_int32`	✅	2s	2s	+0%
`mld_keccakf1600_extract_bytes`	✅	2s	3s	-33%
`mld_prepare_domain_separation_prefix`	✅	2s	4s	-50%
`mld_value_barrier_i64`	✅	2s	3s	-33%
`mld_value_barrier_u32`	✅	2s	1s	+100%
`mld_value_barrier_u8`	✅	2s	3s	-33%
`ntt_native_x86_64`	✅	2s	3s	-33%
`pack_pk`	✅	2s	4s	-50%
`pack_sig_c_h`	✅	2s	4s	-50%
`poly_caddq_native`	✅	2s	2s	+0%
`poly_caddq_native_aarch64`	✅	2s	4s	-50%
`poly_chknorm_native`	✅	2s	5s	-60%
`poly_decompose`	✅	2s	2s	+0%
`poly_invntt_tomont`	✅	2s	3s	-33%
`poly_make_hint`	✅	2s	6s	-67%
`polyt1_unpack`	✅	2s	3s	-33%
`polyveck_pack_t0`	✅	2s	4s	-50%
`polyveck_unpack_eta`	✅	2s	4s	-50%
`polyvecl_pack_eta`	✅	2s	2s	+0%
`polyvecl_permute_bitrev_to_custom`	✅	2s	4s	-50%
`polyw1_pack`	✅	2s	3s	-33%
`reduce32`	✅	2s	2s	+0%
`shake128_squeeze`	✅	2s	2s	+0%
`shake128x4_squeezeblocks`	✅	2s	2s	+0%
`shake256`	✅	2s	2s	+0%
`shake256_absorb`	✅	2s	2s	+0%
`shake256_init`	✅	2s	5s	-60%
`shake256_release`	✅	2s	4s	-50%
`shake256_squeeze`	✅	2s	3s	-33%
`sign_keypair`	✅	2s	4s	-50%
`sign_signature_pre_hash_internal`	✅	2s	4s	-50%
`keccakf1600x4_extract_bytes`	✅	1s	4s	-75%
`poly_shiftl`	✅	1s	4s	-75%
`rej_eta`	✅	1s	2s	-50%

oqs-bot · 2026-03-10T04:34:21Z

CBMC Results (ML-DSA-65)

Full Results (176 proofs)

Proof	Status	Current	Previous	Change
`TOTAL`	✅	2581s	2521s	+2.4%
`sign_verify_internal`	✅	353s	351s	+1%
`mld_attempt_signature_generation`	✅	287s	279s	+3%
`polyvecl_pointwise_acc_montgomery_c`	✅	206s	195s	+6%
`poly_pointwise_montgomery_c`	✅	168s	165s	+2%
`rej_uniform_native`	✅	155s	149s	+4%
`polyvec_matrix_expand`	✅	132s	128s	+3%
`mld_invntt_layer`	✅	101s	97s	+4%
`mld_ct_memcmp`	✅	81s	78s	+4%
`polyvec_matrix_expand_serial`	✅	70s	70s	+0%
`mld_ntt_layer`	✅	59s	57s	+4%
`keccak_squeezeblocks_x4`	✅	45s	43s	+5%
`sign_signature_internal`	✅	38s	39s	-3%
`polymat_permute_bitrev_to_custom`	✅	31s	32s	-3%
`mld_compute_t0_t1_tr_from_sk_components`	✅	27s	26s	+4%
`rej_uniform`	✅	21s	19s	+11%
`poly_chknorm_c`	✅	20s	20s	+0%
`fqmul`	✅	18s	20s	-10%
`poly_uniform_eta_4x`	✅	18s	15s	+20%
`poly_uniform_4x`	✅	17s	15s	+13%
`polyt0_unpack`	✅	17s	14s	+21%
`rej_uniform_c`	✅	16s	16s	+0%
`mld_ntt_butterfly_block`	✅	15s	13s	+15%
`polyveck_decompose`	✅	13s	14s	-7%
`polyvecl_chknorm`	✅	13s	11s	+18%
`keccakf1600x4_permute_native`	✅	12s	13s	-8%
`polyvec_matrix_pointwise_montgomery`	✅	12s	12s	+0%
`keccak_absorb_once_x4`	✅	11s	12s	-8%
`poly_add`	✅	11s	11s	+0%
`polyveck_invntt_tomont`	✅	11s	9s	+22%
`polyveck_sub`	✅	11s	12s	-8%
`polyveck_add`	✅	10s	11s	-9%
`polyveck_ntt`	✅	10s	10s	+0%
`polyveck_power2round`	✅	10s	11s	-9%
`keccakf1600_permute_native`	✅	9s	7s	+29%
`polyveck_use_hint`	✅	9s	8s	+12%
`keccak_absorb`	✅	8s	7s	+14%
`mld_polyvecl_permute_bitrev_to_custom_native`	✅	8s	9s	-11%
`polyt0_pack`	✅	8s	6s	+33%
`polyveck_caddq`	✅	8s	7s	+14%
`polyveck_pointwise_poly_montgomery`	✅	8s	8s	+0%
`polyveck_reduce`	✅	8s	6s	+33%
`polyveck_shiftl`	✅	8s	6s	+33%
`sign`	✅	8s	7s	+14%
`sign_pk_from_sk`	✅	8s	10s	-20%
`sign_verify_extmu`	✅	8s	3s	+167%
`keccakf1600_permute`	✅	7s	7s	+0%
`keccakf1600x4_permute`	✅	7s	5s	+40%
`polyvecl_ntt`	✅	7s	7s	+0%
`intt_native_x86_64`	✅	6s	2s	+200%
`mld_check_pct`	✅	6s	7s	-14%
`poly_caddq_c`	✅	6s	5s	+20%
`poly_decompose_c`	✅	6s	7s	-14%
`poly_invntt_tomont_c`	✅	6s	8s	-25%
`poly_ntt_c`	✅	6s	4s	+50%
`poly_power2round`	✅	6s	4s	+50%
`polyeta_unpack`	✅	6s	5s	+20%
`polyveck_make_hint`	✅	6s	6s	+0%
`rej_eta_native`	✅	6s	7s	-14%
`sign_verify_pre_hash_shake256`	✅	6s	5s	+20%
`unpack_hints`	✅	6s	4s	+50%
`mld_ct_get_optblocker_u8`	✅	5s	3s	+67%
`mld_h`	✅	5s	5s	+0%
`mld_prepare_domain_separation_prefix`	✅	5s	5s	+0%
`mld_sample_s1_s2`	✅	5s	6s	-17%
`mld_sample_s1_s2_serial`	✅	5s	5s	+0%
`poly_chknorm`	✅	5s	3s	+67%
`poly_uniform_gamma1`	✅	5s	2s	+150%
`poly_uniform_gamma1_4x`	✅	5s	4s	+25%
`polyveck_chknorm`	✅	5s	7s	-29%
`polyvecl_uniform_gamma1`	✅	5s	4s	+25%
`shake128_release`	✅	5s	2s	+150%
`shake256_finalize`	✅	5s	2s	+150%
`sign_keypair_internal`	✅	5s	4s	+25%
`sign_signature_pre_hash_shake256`	✅	5s	4s	+25%
`unpack_sig`	✅	5s	2s	+150%
`unpack_sk`	✅	5s	6s	-17%
`keccak_squeeze`	✅	4s	4s	+0%
`make_hint`	✅	4s	2s	+100%
`mld_compute_pack_z`	✅	4s	6s	-33%
`mld_ct_sel_int32`	✅	4s	1s	+300%
`ntt_native_x86_64`	✅	4s	5s	-20%
`pack_sig_z`	✅	4s	2s	+100%
`poly_decompose`	✅	4s	5s	-20%
`poly_invntt_tomont_native`	✅	4s	4s	+0%
`poly_pointwise_montgomery_native`	✅	4s	5s	-20%
`poly_uniform`	✅	4s	6s	-33%
`poly_uniform_eta`	✅	4s	7s	-43%
`poly_use_hint`	✅	4s	4s	+0%
`poly_use_hint_c`	✅	4s	5s	-20%
`polyveck_pack_t0`	✅	4s	4s	+0%
`polyveck_pack_w1`	✅	4s	3s	+33%
`polyvecl_pointwise_acc_montgomery_native`	✅	4s	4s	+0%
`polyvecl_uniform_gamma1_serial`	✅	4s	3s	+33%
`polyvecl_unpack_z`	✅	4s	3s	+33%
`polyw1_pack`	✅	4s	2s	+100%
`polyz_unpack_c`	✅	4s	3s	+33%
`polyz_unpack_native`	✅	4s	4s	+0%
`rej_eta_c`	✅	4s	4s	+0%
`shake128x4_squeezeblocks`	✅	4s	1s	+300%
`shake256`	✅	4s	2s	+100%
`shake256_release`	✅	4s	1s	+300%
`shake256_squeeze`	✅	4s	2s	+100%
`sign_open`	✅	4s	8s	-50%
`sign_signature_extmu`	✅	4s	4s	+0%
`caddq`	✅	3s	4s	-25%
`decompose`	✅	3s	2s	+50%
`fqscale`	✅	3s	3s	+0%
`keccakf1600_xor_bytes`	✅	3s	3s	+0%
`keccakf1600_xor_bytes (big endian)`	✅	3s	2s	+50%
`keccakf1600x4_extract_bytes`	✅	3s	1s	+200%
`keccakf1600x4_xor_bytes`	✅	3s	2s	+50%
`mld_ct_abs_i32`	✅	3s	3s	+0%
`mld_ct_cmask_neg_i32`	✅	3s	2s	+50%
`mld_ct_cmask_nonzero_u8`	✅	3s	7s	-57%
`mld_keccakf1600_extract_bytes`	✅	3s	2s	+50%
`mld_value_barrier_u32`	✅	3s	3s	+0%
`pack_pk`	✅	3s	3s	+0%
`pack_sig_c_h`	✅	3s	5s	-40%
`pack_sk`	✅	3s	3s	+0%
`poly_caddq`	✅	3s	4s	-25%
`poly_caddq_native`	✅	3s	2s	+50%
`poly_caddq_native_aarch64`	✅	3s	4s	-25%
`poly_challenge`	✅	3s	3s	+0%
`poly_invntt_tomont`	✅	3s	3s	+0%
`poly_make_hint`	✅	3s	7s	-57%
`poly_ntt`	✅	3s	3s	+0%
`poly_pointwise_montgomery`	✅	3s	3s	+0%
`poly_use_hint_native`	✅	3s	4s	-25%
`polyt1_pack`	✅	3s	4s	-25%
`polyt1_unpack`	✅	3s	3s	+0%
`polyvecl_permute_bitrev_to_custom`	✅	3s	3s	+0%
`polyvecl_pointwise_acc_montgomery`	✅	3s	2s	+50%
`polyz_pack`	✅	3s	2s	+50%
`power2round`	✅	3s	2s	+50%
`reduce32`	✅	3s	1s	+200%
`rej_eta`	✅	3s	3s	+0%
`shake128x4_absorb_once`	✅	3s	2s	+50%
`shake256_absorb`	✅	3s	2s	+50%
`shake256_init`	✅	3s	2s	+50%
`sign_verify`	✅	3s	5s	-40%
`sign_verify_pre_hash_internal`	✅	3s	6s	-50%
`unpack_pk`	✅	3s	4s	-25%
`use_hint`	✅	3s	3s	+0%
`keccak_finalize`	✅	2s	2s	+0%
`keccak_init`	✅	2s	3s	-33%
`keccakf1600_extract_bytes (big endian)`	✅	2s	2s	+0%
`mld_ct_cmask_nonzero_u32`	✅	2s	3s	-33%
`mld_ct_get_optblocker_u32`	✅	2s	1s	+100%
`mld_value_barrier_i64`	✅	2s	2s	+0%
`mld_value_barrier_u8`	✅	2s	5s	-60%
`montgomery_reduce`	✅	2s	3s	-33%
`ntt_native_aarch64`	✅	2s	-	new
`poly_chknorm_native`	✅	2s	2s	+0%
`poly_decompose_native`	✅	2s	3s	-33%
`poly_ntt_native`	✅	2s	4s	-50%
`poly_reduce`	✅	2s	4s	-50%
`poly_shiftl`	✅	2s	2s	+0%
`poly_sub`	✅	2s	4s	-50%
`polyeta_pack`	✅	2s	4s	-50%
`polyveck_unpack_eta`	✅	2s	5s	-60%
`polyveck_unpack_t0`	✅	2s	3s	-33%
`polyvecl_pack_eta`	✅	2s	4s	-50%
`polyvecl_unpack_eta`	✅	2s	3s	-33%
`polyz_unpack`	✅	2s	2s	+0%
`shake128_absorb`	✅	2s	3s	-33%
`shake128_finalize`	✅	2s	3s	-33%
`shake128_init`	✅	2s	1s	+100%
`shake128_squeeze`	✅	2s	3s	-33%
`shake256x4_squeezeblocks`	✅	2s	3s	-33%
`sign_keypair`	✅	2s	4s	-50%
`sign_signature`	✅	2s	4s	-50%
`sign_signature_pre_hash_internal`	✅	2s	4s	-50%
`mld_ct_get_optblocker_i64`	✅	1s	2s	-50%
`polyveck_pack_eta`	✅	1s	4s	-75%
`shake256x4_absorb_once`	✅	1s	1s	+0%
`sys_check_capability`	✅	1s	4s	-75%

oqs-bot · 2026-03-10T04:36:03Z

CBMC Results (ML-DSA-87)

Full Results (176 proofs)

Proof	Status	Current	Previous	Change
`TOTAL`	✅	2659s	2658s	+0.0%
`sign_verify_internal`	✅	331s	337s	-2%
`polyvecl_pointwise_acc_montgomery_c`	✅	280s	270s	+4%
`mld_attempt_signature_generation`	✅	233s	233s	+0%
`polyvec_matrix_expand`	✅	174s	177s	-2%
`rej_uniform_native`	✅	148s	147s	+1%
`poly_pointwise_montgomery_c`	✅	147s	156s	-6%
`mld_invntt_layer`	✅	95s	91s	+4%
`polyvec_matrix_expand_serial`	✅	81s	81s	+0%
`mld_ct_memcmp`	✅	70s	79s	-11%
`polyveck_decompose`	✅	58s	55s	+5%
`sign_signature_internal`	✅	54s	51s	+6%
`mld_ntt_layer`	✅	53s	52s	+2%
`polymat_permute_bitrev_to_custom`	✅	47s	46s	+2%
`keccak_squeezeblocks_x4`	✅	41s	41s	+0%
`mld_compute_t0_t1_tr_from_sk_components`	✅	24s	26s	-8%
`rej_uniform`	✅	22s	23s	-4%
`fqmul`	✅	20s	19s	+5%
`poly_chknorm_c`	✅	18s	20s	-10%
`polyeta_unpack`	✅	17s	17s	+0%
`poly_uniform_4x`	✅	15s	18s	-17%
`poly_uniform_eta_4x`	✅	15s	15s	+0%
`polyt0_unpack`	✅	14s	13s	+8%
`rej_uniform_c`	✅	14s	16s	-12%
`keccak_absorb_once_x4`	✅	13s	10s	+30%
`mld_ntt_butterfly_block`	✅	13s	12s	+8%
`keccakf1600x4_permute_native`	✅	12s	12s	+0%
`mld_polyvecl_permute_bitrev_to_custom_native`	✅	12s	12s	+0%
`poly_add`	✅	11s	11s	+0%
`polyvec_matrix_pointwise_montgomery`	✅	11s	11s	+0%
`polyveck_use_hint`	✅	11s	11s	+0%
`poly_decompose_c`	✅	10s	9s	+11%
`polyveck_add`	✅	10s	11s	-9%
`keccakf1600_permute`	✅	9s	7s	+29%
`polyveck_ntt`	✅	9s	8s	+12%
`polyveck_pointwise_poly_montgomery`	✅	9s	9s	+0%
`polyveck_power2round`	✅	9s	8s	+12%
`polyveck_reduce`	✅	9s	10s	-10%
`polyvecl_ntt`	✅	9s	9s	+0%
`keccak_absorb`	✅	8s	9s	-11%
`keccakf1600_permute_native`	✅	8s	9s	-11%
`mld_sample_s1_s2_serial`	✅	8s	7s	+14%
`poly_invntt_tomont_c`	✅	8s	7s	+14%
`polyz_unpack_c`	✅	8s	10s	-20%
`mld_check_pct`	✅	7s	8s	-12%
`poly_uniform`	✅	7s	4s	+75%
`polyveck_invntt_tomont`	✅	7s	10s	-30%
`polyveck_shiftl`	✅	7s	7s	+0%
`polyveck_sub`	✅	7s	7s	+0%
`sign`	✅	7s	8s	-12%
`sign_pk_from_sk`	✅	7s	7s	+0%
`mld_prepare_domain_separation_prefix`	✅	6s	4s	+50%
`poly_challenge`	✅	6s	3s	+100%
`polyveck_caddq`	✅	6s	10s	-40%
`polyveck_chknorm`	✅	6s	4s	+50%
`sign_keypair_internal`	✅	6s	7s	-14%
`keccakf1600x4_permute`	✅	5s	2s	+150%
`mld_compute_pack_z`	✅	5s	9s	-44%
`mld_h`	✅	5s	5s	+0%
`mld_sample_s1_s2`	✅	5s	8s	-38%
`montgomery_reduce`	✅	5s	4s	+25%
`poly_caddq_c`	✅	5s	5s	+0%
`poly_chknorm_native`	✅	5s	3s	+67%
`poly_ntt_native`	✅	5s	4s	+25%
`poly_power2round`	✅	5s	6s	-17%
`poly_sub`	✅	5s	3s	+67%
`poly_uniform_eta`	✅	5s	7s	-29%
`poly_uniform_gamma1`	✅	5s	2s	+150%
`poly_use_hint_c`	✅	5s	3s	+67%
`polyveck_unpack_t0`	✅	5s	5s	+0%
`polyvecl_chknorm`	✅	5s	6s	-17%
`polyz_unpack_native`	✅	5s	3s	+67%
`rej_eta_native`	✅	5s	5s	+0%
`sign_signature_extmu`	✅	5s	6s	-17%
`sign_signature_pre_hash_internal`	✅	5s	4s	+25%
`sign_verify_extmu`	✅	5s	3s	+67%
`sys_check_capability`	✅	5s	3s	+67%
`unpack_hints`	✅	5s	6s	-17%
`unpack_pk`	✅	5s	2s	+150%
`decompose`	✅	4s	4s	+0%
`intt_native_x86_64`	✅	4s	3s	+33%
`keccak_finalize`	✅	4s	1s	+300%
`keccakf1600_extract_bytes (big endian)`	✅	4s	4s	+0%
`keccakf1600_xor_bytes`	✅	4s	1s	+300%
`keccakf1600_xor_bytes (big endian)`	✅	4s	2s	+100%
`mld_ct_abs_i32`	✅	4s	1s	+300%
`mld_ct_cmask_nonzero_u32`	✅	4s	3s	+33%
`mld_ct_sel_int32`	✅	4s	3s	+33%
`mld_value_barrier_u8`	✅	4s	3s	+33%
`ntt_native_aarch64`	✅	4s	-	new
`pack_pk`	✅	4s	2s	+100%
`pack_sig_z`	✅	4s	3s	+33%
`pack_sk`	✅	4s	2s	+100%
`poly_caddq_native`	✅	4s	4s	+0%
`poly_chknorm`	✅	4s	4s	+0%
`poly_decompose_native`	✅	4s	4s	+0%
`poly_invntt_tomont`	✅	4s	3s	+33%
`poly_invntt_tomont_native`	✅	4s	2s	+100%
`poly_ntt`	✅	4s	3s	+33%
`poly_pointwise_montgomery`	✅	4s	2s	+100%
`poly_shiftl`	✅	4s	4s	+0%
`poly_uniform_gamma1_4x`	✅	4s	3s	+33%
`poly_use_hint`	✅	4s	3s	+33%
`poly_use_hint_native`	✅	4s	3s	+33%
`polyeta_pack`	✅	4s	3s	+33%
`polyveck_make_hint`	✅	4s	8s	-50%
`polyvecl_uniform_gamma1`	✅	4s	5s	-20%
`polyvecl_unpack_eta`	✅	4s	4s	+0%
`polyvecl_unpack_z`	✅	4s	4s	+0%
`polyw1_pack`	✅	4s	2s	+100%
`power2round`	✅	4s	3s	+33%
`reduce32`	✅	4s	3s	+33%
`shake128_finalize`	✅	4s	3s	+33%
`sign_keypair`	✅	4s	6s	-33%
`sign_open`	✅	4s	4s	+0%
`sign_verify_pre_hash_internal`	✅	4s	3s	+33%
`sign_verify_pre_hash_shake256`	✅	4s	4s	+0%
`unpack_sk`	✅	4s	5s	-20%
`caddq`	✅	3s	5s	-40%
`fqscale`	✅	3s	2s	+50%
`keccak_init`	✅	3s	4s	-25%
`mld_ct_cmask_neg_i32`	✅	3s	3s	+0%
`mld_ct_cmask_nonzero_u8`	✅	3s	3s	+0%
`mld_ct_get_optblocker_u32`	✅	3s	2s	+50%
`ntt_native_x86_64`	✅	3s	3s	+0%
`poly_decompose`	✅	3s	2s	+50%
`poly_make_hint`	✅	3s	2s	+50%
`poly_reduce`	✅	3s	4s	-25%
`polyt1_unpack`	✅	3s	2s	+50%
`polyveck_pack_w1`	✅	3s	3s	+0%
`polyveck_unpack_eta`	✅	3s	4s	-25%
`polyvecl_permute_bitrev_to_custom`	✅	3s	3s	+0%
`polyvecl_uniform_gamma1_serial`	✅	3s	6s	-50%
`polyz_pack`	✅	3s	2s	+50%
`rej_eta`	✅	3s	2s	+50%
`rej_eta_c`	✅	3s	4s	-25%
`shake128_squeeze`	✅	3s	3s	+0%
`shake128x4_absorb_once`	✅	3s	3s	+0%
`shake256_release`	✅	3s	2s	+50%
`shake256_squeeze`	✅	3s	1s	+200%
`sign_signature_pre_hash_shake256`	✅	3s	4s	-25%
`sign_verify`	✅	3s	4s	-25%
`unpack_sig`	✅	3s	2s	+50%
`use_hint`	✅	3s	5s	-40%
`keccak_squeeze`	✅	2s	3s	-33%
`keccakf1600x4_extract_bytes`	✅	2s	2s	+0%
`make_hint`	✅	2s	5s	-60%
`mld_ct_get_optblocker_u8`	✅	2s	2s	+0%
`mld_value_barrier_i64`	✅	2s	2s	+0%
`mld_value_barrier_u32`	✅	2s	2s	+0%
`pack_sig_c_h`	✅	2s	3s	-33%
`poly_caddq`	✅	2s	4s	-50%
`poly_caddq_native_aarch64`	✅	2s	2s	+0%
`poly_ntt_c`	✅	2s	3s	-33%
`poly_pointwise_montgomery_native`	✅	2s	3s	-33%
`polyt0_pack`	✅	2s	4s	-50%
`polyt1_pack`	✅	2s	2s	+0%
`polyveck_pack_eta`	✅	2s	3s	-33%
`polyveck_pack_t0`	✅	2s	4s	-50%
`polyvecl_pack_eta`	✅	2s	4s	-50%
`polyvecl_pointwise_acc_montgomery`	✅	2s	2s	+0%
`polyvecl_pointwise_acc_montgomery_native`	✅	2s	4s	-50%
`polyz_unpack`	✅	2s	3s	-33%
`shake128_absorb`	✅	2s	3s	-33%
`shake128_init`	✅	2s	3s	-33%
`shake128_release`	✅	2s	2s	+0%
`shake128x4_squeezeblocks`	✅	2s	2s	+0%
`shake256`	✅	2s	3s	-33%
`shake256_absorb`	✅	2s	3s	-33%
`shake256_finalize`	✅	2s	3s	-33%
`shake256_init`	✅	2s	3s	-33%
`shake256x4_absorb_once`	✅	2s	2s	+0%
`shake256x4_squeezeblocks`	✅	2s	2s	+0%
`sign_signature`	✅	2s	4s	-50%
`keccakf1600x4_xor_bytes`	✅	1s	4s	-75%
`mld_ct_get_optblocker_i64`	✅	1s	3s	-67%
`mld_keccakf1600_extract_bytes`	✅	1s	2s	-50%

mkannwischer

Thanks @dkostic! I took the liberty to add the corresponding CBMC contract and proof.

The specs should still be moved into common/ to be shared with the x86 proofs. Rest looks very good to me.

proofs/hol_light/common/mldsa_specs.ml

.github/workflows/hol_light.yml

mkannwischer

Thanks @dkostic for the changes! I took the liberty to revert some of the changes you made to the hol_light workflow as they are not needed.
Rest looks good to me now.

@hanno-becker, could you take another look, please?

proofs/hol_light/aarch64/proofs/subroutine_signatures.ml

proofs/hol_light/aarch64/proofs/mldsa_ntt.ml

hanno-becker

Overall this looks excellent, thank you @dkostic!

The only minor point is the avoidance of hardcoded lengths constants in the scripts. Could you follow the pattern in mlkem-native to avoid hardcoded lengths and thereby make the proof scripts agnostic to re-running SLOTHY?

Port the ML-DSA Forward NTT implementation and its HOL Light proof of correctness from s2n-bignum to mldsa-native. The proof verifies the AArch64 NEON NTT implementation at the object-code level, showing that the output coefficients are congruent to the forward NTT of the input modulo 8380417, with bounded output coefficients. A constant-time and memory safety proof is also included. New files: - aarch64/mldsa/mldsa_ntt.S: Assembly derived from dev/aarch64_opt/src/ntt.S - aarch64/proofs/mldsa_ntt.ml: HOL Light proof (MLDSA_NTT_CORRECT, MLDSA_NTT_SUBROUTINE_CORRECT, and MLDSA_NTT_SUBROUTINE_SAFE theorems) - aarch64/proofs/mldsa_specs.ml: Self-contained ML-DSA specifications and congruence/bounds propagation infrastructure, ported from s2n-bignum's common/mlkem_mldsa.ml with only ARM ML-DSA relevant definitions - aarch64/proofs/subroutine_signatures.ml: ML-DSA subroutine signatures for the safety proof infrastructure Modified files: - aarch64/proofs/aarch64_utils.ml: Add MEMORY_128_FROM_32_TAC - aarch64/Makefile: Add mldsa_ntt to build targets Signed-off-by: dkostic <dkostic@amazon.com>

Add CBMC contract for mld_ntt_asm matching the bounds from the AArch64 NTT HOL Light proof (input: abs <= 8380416, output: abs <= 75423752). Add corresponding CBMC proof for mld_ntt_native using the contract. Signed-off-by: Matthias J. Kannwischer <matthias@kannwischer.eu>

Consolidate the shared ML-DSA specifications and congruence/bounds propagation infrastructure into a single file at proofs/hol_light/common/mldsa_specs.ml, used by both AArch64 and x86_64 proofs. The merged file contains: - Shared: bitreverse8, reorder, BITREVERSE8_CLAUSES, congruence/bounds infrastructure (CONGBOUND_WORD_*, ASM_CONGBOUND_RULE, etc.), SIMD simplification tactics - x86_64-specific: AVX2 NTT ordering, mldsa_montred/barred/montmul - AArch64-specific: arm_mldsa_forward_ntt, arm_mldsa_barmul ASM_CONGBOUND_RULE now handles both arm_mldsa_barmul and mldsa_montred/barred/montmul cases. Signed-off-by: dkostic <dkostic@amazon.com>

Signed-off-by: dkostic <dkostic@amazon.com>

hanno-becker

LGTM. Thanks a lot @dkostic!

dkostic requested a review from a team as a code owner March 10, 2026 04:13

mkannwischer requested changes Mar 10, 2026

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mkannwischer force-pushed the aarch64-ntt-hol branch from 0b391cd to 1bf5302 Compare March 15, 2026 07:47

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mkannwischer force-pushed the aarch64-ntt-hol branch 2 times, most recently from 6285a26 to 581acd0 Compare March 15, 2026 07:59

mkannwischer approved these changes Mar 15, 2026

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hanno-becker reviewed Mar 16, 2026

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dkostic force-pushed the aarch64-ntt-hol branch from 3eb9c3e to 62ee2b6 Compare March 17, 2026 21:37

dkostic and others added 4 commits March 18, 2026 04:22

Avoid hard-coded lengths in the proof

f7b4f98

Signed-off-by: dkostic <dkostic@amazon.com>

hanno-becker force-pushed the aarch64-ntt-hol branch from 62ee2b6 to f7b4f98 Compare March 18, 2026 04:22

hanno-becker approved these changes Mar 18, 2026

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dkostic mentioned this pull request Mar 18, 2026

ML-DSA aarch64 rejection sampling proof #997

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Add AArch64 ML-DSA Forward NTT HOL Light proof#993

Add AArch64 ML-DSA Forward NTT HOL Light proof#993
dkostic wants to merge 4 commits intomainfrom
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CBMC Results (ML-DSA-44)

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CBMC Results (ML-DSA-65)

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CBMC Results (ML-DSA-87)

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dkostic commented Mar 10, 2026 •

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oqs-bot commented Mar 10, 2026 •

edited

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oqs-bot commented Mar 10, 2026 •

edited

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oqs-bot commented Mar 10, 2026 •

edited

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