Analysis of Dilithium post-quantum electronic signature resistance to fault attacks

Abstract

Analysis of a perspective variant of post-quantum electronic signature based on algebraic lattices of Dilithium is carried out. The central task of the analysis is to study the resistance of Dilithium to fault attacks, in particular differential ones. First, information is given about the ES scheme itself and its security, fault attacks, their development to differential fault attacks. Possibilities of carrying out these attacks and criteria of their successful execution are considered. The places of the ES algorithm that need protection against fault attacks were identified, such as hash function (the moment of access to it and operation of polynomials multiplying), the stage of loading the private key, the function of expanding seed. Also, nonce reuse and partial nonce reuse when generating keys poses a significant threat, and by carrying out such an attack, the attacker can fully recover the long-term Dilithium private key. Attacks countermeasures are formed based on the sources analysis, their advantages and negative effects are presented. Methods of protection against such attacks are: re-calculation of the signature; verification of signature after signing, which is three times faster than the previous method; introducing additional randomness to the deterministic noise sampling; checking the value of secret and false components (nonce); calculating the average value and variance of the sample, and checking them for belonging to a given range. The results of this work provide researchers with a guide for the development of secure post-quantum electronic signature schemes.