Maths for Security

This course is about the low-level implementation aspects of cryptography in practice. It was shown by Gaudry and Golovnev in 2019 that the lack of a multi-precision integer library in a non-standardized context led to wrong practical choices and devastating flaws in the security, and a final attack in a few minutes on a laptop (https://arxiv.org/abs/1908.05127). The ElGamal encryption with keys of 256 bits instead of 2048 bits was implemented, despite all international key-size recommendations. The topic of this course is the development of a basic multi-precision library handling integers and modular integers, aiming at an implementation of the RSA public-key cryptosystem. If time allows it, we will also cover the finite field case with ElGamal and DSA. The lab sessions will make use of the C language. A minimal knowledge of C is expected, for example from the course LLP (Low-level Programming) in M1.