Asymmetric Encryption and Key Exchange Questions

The construction and mathematics-adjacent mechanics of public-key (asymmetric) cryptography: how RSA, Diffie-Hellman, and elliptic-curve schemes actually work, including the group law and point-arithmetic formulas, scalar-multiplication algorithms (double-and-add, Montgomery ladder, windowed methods, GLV, multi-scalar batching), curve models and coordinate systems, and the hardness assumptions (integer factorization, discrete log, ECDLP) each scheme rests on. Covers key-establishment and authenticated key-exchange protocol design: forward-secrecy mechanics, key confirmation, downgrade protection, key-derivation and context binding, group and multi-party key agreement, and hybrid classical/post-quantum key-exchange composition. Also covers implementation-level attacks against these primitives and their mitigations: timing and side-channel leakage in modular exponentiation and scalar multiplication, invalid-curve and small-subgroup attacks, fault attacks, and padding-oracle attacks. Distinct from selecting, deploying, and operating these primitives in production: PKI certificate lifecycle, CA hierarchy, revocation, and key storage and rotation belong to applied cryptography and key management.