Robert Allan JamesandClaude Sonnet 5
2e7e957680
New freestanding, verify-only Ed25519 (RFC 8032) implementation:
include/starkernel/{sha512,fe25519,scalar25519,ed25519}.h +
src/starkernel/crypto/{sha512,fe25519,scalar25519,ed25519}.c, wired into
Makefile.starkernel. Kernel never signs or generates keys -- only
ed25519_verify() is needed; signing happens in the host-side mkcapsule
build tool via libsodium/OpenSSL.
Confirmed __int128 multiply/add/shift-by-constant compile with zero
undefined symbols on all three target toolchains (only division needs
libgcc's __udivti3, per timer.c's existing documented finding -- that
file's comment updated to narrow the claim, since it had been read as
"avoid __int128 entirely"). This enabled the standard 5-limb radix-2^51
field arithmetic representation.
An abandoned first attempt (10-limb radix-2^26, avoiding __int128 out of
premature caution) hit two real bugs, both invisible on inspection and
found only by property-based testing against Python's own bignum
arithmetic: a non-uniform-radix limb misalignment in multiplication, and
a double-counted carry. Verification chain: SHA-512 against known +
boundary vectors (7/7); field arithmetic property-tested 25,045 cases;
scalar-mod-L arithmetic 300 cases (L confirmed prime via Miller-Rabin
first); full verify() end-to-end against 110 real signatures from
Python's cryptography library, including tampered inputs and the RFC
8032 S>=L malleability attack -- all correctly accepted/rejected.
Compiles clean (zero warnings) and links on all three architectures,
confirmed via the mandatory three-arch QEMU boot. The code is linked but
not yet called from anywhere -- wiring into capsule_birth.c needs a
from-scratch X.509/DER parser first (Captain Bob chose real X.509 over a
raw-blob cert format this session), which is the next open item.
Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01HZ8kNoTuP63pbQtro4qvrm
61 lines
3.0 KiB
C
61 lines
3.0 KiB
C
/* fe25519.h -- arithmetic mod p = 2^255-19, for Ed25519.
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*
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* Five-limb representation, uniform radix 2^51 (value =
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* sum(limb[i] * 2^(51*i)), limb i in roughly [0, 2^51)) -- the standard
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* Ed25519 reference layout (matches the widely-reviewed "amd64-51"-style
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* implementations), not something invented for this codebase. 51*5=255
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* exactly, so unlike a mismatched limb-count/width choice, the reduction
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* constant is the clean 2^255 mod p = 19 with no extra scaling.
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*
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* Uses __int128 for multiply-accumulate (product of two ~51-bit limbs is
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* up to ~102 bits, summed across up to 5 terms per bucket -- needs a
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* wide type). Confirmed safe in this kernel's freestanding -nostdlib
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* build by direct toolchain testing (gcc/aarch64-linux-gnu-gcc/
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* riscv64-linux-gnu-gcc, matching Makefile.starkernel's exact flags):
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* __int128 multiply, add, and shift-by-constant all compile with zero
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* undefined symbols on all three target architectures. This is DIFFERENT
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* from __int128 DIVISION, which src/starkernel/arch/amd64/timer.c
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* documents as broken (needs libgcc's __udivti3, undefined in this
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* -nostdlib build) -- this file never divides __int128 values, so that
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* restriction doesn't apply here. An earlier draft of this file avoided
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* __int128 entirely (10 limbs, radix 2^26, int64_t only) out of
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* over-caution before this was checked directly; abandoned after running
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* into real bugs from that scheme's own complexity, not from __int128
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* unavailability -- __int128 was never actually the constraint once
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* verified.
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*/
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#ifndef FE25519_H
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#define FE25519_H
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#include <stdint.h>
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/* int64_t, not uint64_t: fe25519_sub produces negative intermediate
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* limbs (a[i] - b[i] can be < 0 for a specific limb even when the total
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* value a-b, mod p, is what's wanted), and fe25519_carry() relies on
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* arithmetic right shift to propagate negative "borrows" the same way
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* it propagates positive carries -- proven correct by the property-based
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* host test, not just assumed. */
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typedef struct { int64_t v[5]; } fe25519;
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void fe25519_0(fe25519 *r);
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void fe25519_1(fe25519 *r);
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void fe25519_copy(fe25519 *r, const fe25519 *a);
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void fe25519_add(fe25519 *r, const fe25519 *a, const fe25519 *b);
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void fe25519_sub(fe25519 *r, const fe25519 *a, const fe25519 *b);
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void fe25519_neg(fe25519 *r, const fe25519 *a);
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void fe25519_mul(fe25519 *r, const fe25519 *a, const fe25519 *b);
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void fe25519_sq(fe25519 *r, const fe25519 *a);
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void fe25519_invert(fe25519 *r, const fe25519 *a);
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void fe25519_mul_small(fe25519 *r, const fe25519 *a, uint32_t c);
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/* Pack to 32 little-endian bytes (fully reduced mod p) / unpack from same. */
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void fe25519_pack(uint8_t out[32], const fe25519 *a);
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void fe25519_unpack(fe25519 *r, const uint8_t in[32]);
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/* 1 if a == b (as field elements, after full reduction), else 0. */
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int fe25519_eq(const fe25519 *a, const fe25519 *b);
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/* Parity of the fully-reduced value's low bit (used for point decompression's sign bit). */
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int fe25519_parity(const fe25519 *a);
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#endif /* FE25519_H */
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