Fuzzy Matching Template Attacks on Multivariate Cryptography: A Case Study

Multivariate cryptography is one of the most promising candidates for post-quantum cryptography. Applying machine learning techniques in this paper, we experimentally investigate the side-channel security of the multivariate cryptosystems, which seriously threatens the hardware implementations of cryptographic systems. Generally, registers are required to store values of monomials and polynomials during the encryption of multivariate cryptosystems. Based on maximum-likelihood and fuzzy matching techniques, we propose a template-based least-square technique to efficiently exploit the side-channel leakage of registers. Using QUAD for a case study, which is a typical multivariate cryptosystem with provable security, we perform our attack against both serial and parallel QUAD implementations on field programmable gate array (FPGA). Experimental results show that our attacks on both serial and parallel implementations require only about 30 and 150 power traces, respectively, to successfully reveal the secret key with a success rate close to 100%. Finally, efficient and low-cost strategies are proposed to resist side-channel attacks.