Projects
Efficient Implementation of Isogeny-based Diffie-Hellman Key Exchange on ARM processors
Previous phase: Fears of the emergence of quantum computers in the near future pose a serious threat against the security of widely-used public key cryptosystems such as RSA or Elliptic Curve Cryptography (ECC). Algorithms involving isogeny computations on elliptic curves have been shown to be difficult, even to quantum computers. Thus, isogeny-based protocols represent one new hope to provide quantum-resistant cryptography. In this project, we focus to employ new primes to speed up constant-time finite field arithmetic and perform isogenies quickly. Montgomery multiplication and reduction are employed to produce a remarkable speedup. For curve arithmetic, a uniform differential addition scheme for double point multiplication and constant-time arithmetic were used to protect the private keys from side-channel analysis attacks.
Current phase: We have already implemented two highly optimized versions of SIDH protocol on both ARMv7 and ARMv8 families of processors. Currently, we focus to develop new software which uses more generic parameters on various platforms with a reasonable performance compared to our optimized version.
Isogeny-based Post-Quantum Digital Signature
Previous phase: In this project, we presented the first general-purpose digital signature scheme based on supersingular elliptic curve isogenies secure against quantum adversaries in the quantum random oracle model with small key sizes. This scheme is an application of Unruh’s construction of non-interactive zero-knowledge proofs to an interactive zero-knowledge proof proposed by De Feo, Jao, and Plˆut. We implemented our proposed scheme on an x86- 64 PC platform as well as an ARM-powered device. We exploit the state of-the-art techniques to speed up the computations for general C and assembly.
Current phase: We are investigating to more efficient way of optimizing our library to attain better performance results. Moreover, we believe that there are plenty of rooms for developing compact formulae which can compute the isogenies of elliptic curves faster.