Analytic Tools for White-box and Lattice Cryptography

Abstract

In crypto world, the existence of analytic toolbox which can be used as the measure of security is very important in order to design cryptographic systems. In this thesis, we focus on white-box cryptography and lattice based cryptography, and present analytic tools for them.

White-box cryptography presented by Chow et al. is an obfuscation technique for protecting secret keys in software implementations even if an adversary has full access to the implementation of the encryption algorithm and full control over its execution platforms. Despite its practical importance, progress has not been substantial. In fact, it is repeated that as a proposal for a whitebox implementation is reported, an attack of lower complexity is soon announced. This is mainly because most cryptanalytic methods target specific implementations, and there is no general attack tool for white-box cryptography. In this thesis, we present an analytic toolbox on white-box implementations of the Chow et al.s style using lookup tables. Our toolbox could be used to measure the security of white-box implementations.

Lattice based cryptography is very interesting field of cryptography nowadays. Many hard problems on lattice can be reduced to some specific form of the shortest vector problem or closest vector problem, and hence related to problem of finding a short basis for given lattice. Therefore, good lattice reduction algorithm can play a role of analytic tools for lattice based cryptography. We proposed an algorithm for lattice basis reduction which uses block reduction. This provides some trade-off of reduction time and quality. This can gives a guideline for the parameter setting of lattice based cryptography.