Research seriesL3algorithms
RSA, Diffie-Hellman and elliptic curves fail long before any quantum computer arrives: through assumptions that are weaker than they look, padding that answers too many questions, keys generated without enough randomness, peers that choose their own public values, signature secrets that leak a few bits at a time, and implementations that reveal their work through timing and faults. This series analyses each failure class from the primary literature, states the exact conditions an attack needs, and maps which defence covers which failure, with an AI-agent deployment angle throughout.
Saying RSA or Diffie-Hellman rests on a hard problem hides at least five distinct claims. Separating them shows where real assurance comes from and where it quietly stops.
A server that reveals whether a decrypted message was well formed is answering questions about a secret. How one bit per answer becomes a recovered plaintext, and what actually stops it.
Three distinct ways RSA key generation has failed across whole populations of devices, why each needs its own detection method, and what that means for fleets of AI agents minting keys at machine speed.
Key agreement assumes the other party sends a legitimate public key. When an attacker chooses it instead, a reused private key can leak in pieces. Exactly when that works, and what each curve obliges you to check.
ECDSA keys fall not only to a repeated nonce but to a few leaked bits per signature, collected across many signatures. Why that works, where the bits leak from, and what deterministic signing does and does not fix.
Constant-time code, blinding and result checking are often treated as interchangeable side-channel defences for RSA. They are not. A coverage map of which defence stops which attack, and where gaps remain.