Number theory in cryptography

Summary

The main goal of the course is to introduce basic notions from public key cryptography (PKC) as well as basic number-theoretic methods and algorithms for cryptanalysis of protocols and schemes based on PKC.

Content

Basic notions and algorithms from public key cryptography such as RSA, ElGamal, key exchange protocols, zero knowledge proofs. Topics will include:

• modular and finite field arithmetic
• integer factorization algorithms
• index calculus and discrete logarithm-based schemes
• elliptic curve cryptography
• basic notions from lattice-based cryptography

Keywords

public key cryptography, key exchange, digital signatures, zero knowledge proofs, RSA, ElGamal, integer factorization, index calculus, elliptic curve cryptography

Teaching methods

lectures, homework exercises, additional references