Module public_key 

Public-key building blocks.

This module starts with the arithmetic foundation needed by the public-key schemes here: a simple limb-based bigint representation, a reusable Montgomery toolkit, plus primality and modular-arithmetic helpers. The goal is fidelity to the published arithmetic in pure idiomatic Rust, not a replacement for industrial multiprecision libraries or a wrapper around external C code.

The public-key APIs are layered, but not every scheme exposes every layer with the same shape:

• arithmetic maps such as encrypt_raw, encrypt_with_nonce, encrypt_point_with_nonce, or sign_digest_with_nonce
• typed wrappers such as encrypt, decrypt, sign_message, and verify_message, which operate on the scheme’s natural plaintext, ciphertext, or signature representation
• byte wrappers such as encrypt_bytes, decrypt_bytes, verify_message_bytes, standard wire encodings, and crate-defined key blobs

The important design rule is that the math stays visible. The exact method set depends on what the underlying construction naturally supports: signature schemes do not grow encryption wrappers, key-agreement schemes do not pretend to be byte-to-byte encryption APIs, and schemes such as ECIES intentionally present a direct byte-oriented wrapper because the primitive is already hybrid encryption.

The arithmetic primitives remain directly accessible, and the wrapper layer adds:

• rsa_pkcs1 for OAEP encryption and PSS signatures
• rsa_io for standard RSA key serialization (PKCS #1, PKCS #8, SPKI) plus an optional flat XML export for symmetry with the other schemes
• internal io helpers for the crate-defined non-RSA key formats: a DER SEQUENCE of positive INTEGERs, custom PEM armor, and the shared flat XML form

Public-key naming is normalized crate-wide:

• prefer *_with_nonce for deterministic/external-randomness entry points
• prefer to_wire_bytes / from_wire_bytes for standard compact encodings that omit curve or algorithm parameters
• prefer to_key_blob / from_key_blob for crate-defined self-describing binary formats

This follows the crate-wide design rule: keep the implementation in Rust, avoid intrinsics and FFI, and add dependencies only where they materially improve interoperability or maintenance.

Modules

bigint

A small pure-Rust bigint foundation for public-key primitives.

cocks

Clifford Cocks’s original public-key scheme (CESG memo, 1973).

dh

Classical Diffie-Hellman (DH) key exchange over a prime-order subgroup.

dsa

Digital Signature Algorithm (DSA, FIPS 186-5).

ec

Elliptic-curve arithmetic over short-Weierstrass prime-field curves.

ec_edwards

Twisted Edwards curve arithmetic over prime fields.

ec_elgamal

Elliptic-curve ElGamal encryption.

ecdh

Elliptic-Curve Diffie-Hellman (ECDH) key exchange.

ecdsa

Elliptic-Curve Digital Signature Algorithm (ECDSA, FIPS 186-5).

ecies

Elliptic Curve Integrated Encryption Scheme (ECIES).

ed25519

RFC 8032 Ed25519.

eddsa

Edwards-curve Digital Signature Algorithm style signatures.

edwards_dh

Diffie-Hellman key agreement over twisted Edwards curves.

edwards_elgamal

ElGamal encryption over twisted Edwards curves.

elgamal

ElGamal public-key primitive (Taher ElGamal, 1985).

ml_dsa

ML-DSA (Dilithium) implemented in safe, idiomatic Rust from FIPS 204.

ml_kem

ML-KEM (Kyber) implemented in safe, idiomatic Rust from FIPS 203.

paillier

Paillier public-key primitive (Pascal Paillier, 1999).

primes

Primality and modular-arithmetic helpers for the public-key layer.

rabin

Rabin public-key primitive (Michael O. Rabin, 1979).

rsa

RSA public-key primitive (Rivest, Shamir, Adleman, 1978).

rsa_io

Modern RSA key externalization helpers.

rsa_pkcs1

PKCS #1 v2.2 wrappers for the raw RSA primitive.

schmidt_samoa

Schmidt-Samoa public-key primitive (Katja Schmidt-Samoa, 2005).

x448

X448 ECDH per RFC 7748 §5 over Curve448.

x25519

X25519 ECDH per RFC 7748 §5 over Curve25519.