1Why RSA Works, and What the Chinese Remainder Theorem ChangesThe arithmetic that makes RSA decryption undo encryption, the rules the exponents must obey, and how splitting the work across two primes speeds it up and adds new duties.Advanced 2From Raw RSA to OAEP and PSSBare RSA arithmetic is correct but unsafe. Here is what goes wrong, how OAEP and PSS padding fix it, and the implementation details that still decide whether they hold.Advanced 3Diffie-Hellman Security Depends on the Group and the PeerDiffie-Hellman is only as strong as the group it runs in, the values the other side is allowed to send, the identity bound to the exchange and the secrets erased afterwards.Advanced 4ECDH in Practice: P-256 Versus X25519Two curves do the same job in very different ways. Their arithmetic, encodings and input rules decide which mistakes an implementation can make.Advanced 5ECDSA and EdDSA: The Per-Message Secret MattersEvery elliptic-curve signature hides a one-time secret. Reuse it once and the private key falls out, as two tiny signatures show. Here is how deterministic signing helps, and where it stops.Advanced 6Choosing Keys by Strength, Role and EncodingWhy a 256-bit curve key and a 3,072-bit RSA key are equally strong, how they differ in bytes, cost and custody, and why every key should have one job, one home and one lifetime.Advanced