A New Method for Solving Polynomial Systems with Noise over $\mathbb{F}_2$ and Its Applications in Cold Boot Key Recovery

Abstract

The family of Max-PoSSo problems is about solving polynomial systems with noise, and is analogous to the well-known Max-SAT family of problems when the ground field is \(\mathbb{F}_2\). In this paper, we present a new method called ISBS for solving the family of Max-PoSSo problems over \(\mathbb{F}_2\). This method is based on the ideas of incrementally solving polynomial system and searching the values of polynomials with backtracking. The ISBS method can be combined with different algebraic methods for solving polynomial systems, such as the Grobner Basis method or the Characteristic Set(CS) method. By combining with the CS method, we implement ISBS and apply it in Cold Boot attacks. A Cold Boot attack is a type of side channel attack in which an attacker recover cryptographic key material from DRAM relies on the data remanence property of DRAM. Cold Boot key recovery problems of block ciphers can be modeled as Max-PoSSo problems over \(\mathbb{F}_2\). We apply the ISBS method to solve the Cold Boot key recovery problems of AES and Serpent, and obtain some experimental results which are better than the existing ones.