Number Theoretic Cryptography

Elliptic curves, isogenies and more


Since the beginnings of public key cryptography, number theory has been at the forefront of it. The Factorization (RSA) and Discrete logarithm (Diffie–Hellman, ECDH) problems are still the two pillars that support all our secure communication infrastructure today. The next generation of quantum-safe protocols also leans heavily on number theory: ideal lattices feature prominently in the future NIST standards (Kyber, Dilithium, Falcon), and isogenies of elliptic curves are a promising alternate solution for compact quantum-safe signatures (SQISign). At IBM we work on all aspects of number theoretic cryptography, from the development of new schemes, to cryptanalysis, and to the security of real-world implementations.