Multidimensional Zero-Correlation Linear Cryptanalysis of the Block Cipher KASUMI

The block cipher KASUMI is widely used for security in many synchronous wireless standards. It was proposed by ETSI SAGE for usage in 3GPP (3rd Generation Partnership Project) ciphering algorthms in 2001. There are a great deal of cryptanalytic results on KASUMI, however, its security evaluation against the recent zero-correlation linear attacks is still lacking so far. In this paper, we select some special input masks to refine the general 5-round zero-correlation linear approximations combining with some observations on the $FL$ functions and then propose the 6-round zero-correlation linear attack on KASUMI. Moreover, zero-correlation linear attacks on the last 7-round KASUMI are also introduced under some weak keys conditions. These weak keys take $2^{-14}$ of the whole key space. The new zero-correlation linear attack on the 6-round needs about $2^{85}$ encryptions with $2^{62.8}$ known plaintexts. For the attack under weak keys conditions on the last 7 round, the data complexity is about $2^{62.1}$ known plaintexts and the time complexity $2^{110.5}$ encryptions

Multidimensional linear cryptanalysis

Linear cryptanalysis is an important tool for studying the security of symmetric ciphers. In 1993 Matsui proposed two algorithms, called Algorithm 1 and Algorithm 2, for recovering information about the secret key of a block cipher. The algorithms exploit a biased probabilistic relation between the input and output of the cipher. This relation is called the (one-dimensional) linear approximation of the cipher. Mathematically, the problem of key recovery is a binary hypothesis testing problem that can be solved with appropriate statistical tools. The same mathematical tools can be used for realising a distinguishing attack against a stream cipher. The distinguisher outputs whether the given sequence of keystream bits is derived from a cipher or a random source. Sometimes, it is even possible to recover a part of the initial state of the LFSR used in a key stream generator. Several authors considered using many one-dimensional linear approximations simultaneously in a key recovery attack and various solutions have been proposed. In this thesis a unified methodology for using multiple linear approximations in distinguishing and key recovery attacks is presented. This methodology, which we call multidimensional linear cryptanalysis, allows removing unnecessary and restrictive assumptions. We model the key recovery problems mathematically as hypothesis testing problems and show how to use standard statistical tools for solving them. We also show how the data complexity of linear cryptanalysis on stream ciphers and block ciphers can be reduced by using multiple approximations. We use well-known mathematical theory for comparing different statistical methods for solving the key recovery problems. We also test the theory in practice with reduced round Serpent. Based on our results, we give recommendations on how multidimensional linear cryptanalysis should be used

Multidimensional zero-correlation attacks on lightweight block cipher HIGHT: Improved cryptanalysis of an ISO standard

AbstractHIGHT is a block cipher designed in Korea with the involvement of Korea Information Security Agency. It was proposed at CHES 2006 for usage in lightweight applications such as sensor networks and RFID tags. Lately, it has been adopted as ISO standard. Though there is a great deal of cryptanalytic results on HIGHT, its security evaluation against the recent zero-correlation linear attacks is still lacking. At the same time, the Feistel-type structure of HIGHT suggests that it might be susceptible to this type of cryptanalysis. In this paper, we aim to bridge this gap.We identify zero-correlation linear approximations over 16 rounds of HIGHT. Based upon those, we attack 27-round HIGHT (round 4 to round 30) with improved time complexity and practical memory requirements. This attack of ours is the best result on HIGHT to date in the classical single-key setting. We also provide the first attack on 26-round HIGHT (round 4 to round 29) with the full whitening key

Roadmap on optical security

Postprint (author's final draft

Multivariate Profiling of Hulls for Linear Cryptanalysis

Extensions of linear cryptanalysis making use of multiple approximations, such as multiple and multidimensional linear cryptanalysis, are an important tool in symmetric-key cryptanalysis, among others being responsible for the best known attacks on ciphers such as Serpent and present. At CRYPTO 2015, Huang et al. provided a refined analysis of the key-dependent capacity leading to a refined key equivalence hypothesis, however at the cost of additional assumptions. Their analysis was extended by Blondeau and Nyberg to also cover an updated wrong key randomization hypothesis, using similar assumptions. However, a recent result by Nyberg shows the equivalence of linear dependence and statistical dependence of linear approximations, which essentially invalidates a crucial assumption on which all these multidimensional models are based. In this paper, we develop a model for linear cryptanalysis using multiple linearly independent approximations which takes key-dependence into account and complies with Nyberg’s result. Our model considers an arbitrary multivariate joint distribution of the correlations, and in particular avoids any assumptions regarding normality. The analysis of this distribution is then tailored to concrete ciphers in a practically feasible way by combining a signal/noise decomposition approach for the linear hulls with a profiling of the actual multivariate distribution of the signal correlations for a large number of keys, thereby entirely avoiding assumptions regarding the shape of this distribution. As an application of our model, we provide an attack on 26 rounds of present which is faster and requires less data than previous attacks, while using more realistic assumptions and far fewer approximations. We successfully extend the attack to present the first 27-round attack which takes key-dependence into account

Statistical Tests for Key Recovery Using Multidimensional Extension of Matsui\u27s Algorithm 1

In one dimension, there is essentially just one binomially distributed statistic, bias or correlation, for testing correctness of a key bit in Matsui\u27s Algorithm 1. In multiple dimensions, different statistical approaches for finding the correct key candidate are available. The purpose of this work is to investigate the efficiency of such test in theory and practice, and propose a new key class ranking statistic using distributions based on multidimensional linear approximation and generalisation of the ranking statistic presented by Selc cuk

Multiple Differential Cryptanalysis using \LLR and χ2\chi^2 Statistics

Recent block ciphers have been designed to be resistant against differential cryptanalysis. Nevertheless it has been shown that such resistance claims may not be as tight as wished due to recent advances in this field. One of the main improvements to differential cryptanalysis is the use of many differentials to reduce the data complexity. In this paper we propose a general model for understanding multiple differential cryptanalysis and propose new attacks based on tools used in multidimensional linear cryptanalysis (namely \LLR and \CHI statistical tests). Practical cases are considered on a reduced version of the cipher PRESENT to evaluate different approaches for selecting and combining the differentials considered. We also consider the tightness of the theoretical estimates corresponding to these attacks