RS256: RSA Asymmetric Signing

RS256 = RSA-Signature with SHA-256 (PKCS#1 v1.5).

Asymmetric:

• Private key signs.
• Public key verifies.

The verifier doesn't need to know the secret. This is critical for:

• OIDC / OAuth providers: Google's public key is public; anyone can verify Google-signed JWTs without being able to forge them.
• Microservices: a central auth service signs; many downstream services verify with public keys.

Algorithm:

hash = SHA-256(signing_input)
padded = PKCS#1_v1_5_pad(hash)             # add ASN.1 prefix + 0xFF padding
signature = padded ^ private_key_d (mod n)  # RSA encrypt with private key

Verifier:

recovered = signature ^ public_key_e (mod n)
expected  = PKCS#1_v1_5_pad(SHA-256(signing_input))
return recovered == expected

Key sizes: 2048-bit minimum (256 bytes), 4096-bit recommended for new keys. Generated keys come as PEM files; runtime parses to (n, e, d) integers.

For this lesson we model the signing input + comparison; full RSA implementation (Miller-Rabin primes, modular exponentiation) would be a course on its own.