Cryptanalysis of LowMC instances using single plaintext/ciphertext pair

Arguably one of the main applications of the LowMC family ciphers is in the post-quantum signature scheme PICNIC. Although LowMC family ciphers have been studied from a cryptanalytic point of view before, none of these studies were directly concerned with the actual use case of this cipher in PICNIC signature scheme. Due to the design paradigm of PICNIC, an adversary trying to perform a forgery attack on the signature scheme instantiated with LowMC would have access to only a single given plaintext/ciphertext pair, i.e. an adversary would only be able to perform attacks with data complexity 1 in a known-plaintext attack scenario. This restriction makes it impossible to employ classical cryptanalysis methodologies such as differential and linear cryptanalysis. In this paper we introduce two key-recovery attacks, both in known-plaintext model and of data complexity 1 for two variants of LowMC, both instances of the LowMC cryptanalysis challenge.

Analysis of lightweight stream ciphers

Simon Fischer

Stream ciphers are fast cryptographic primitives to provide confidentiality of electronically transmitted data. They can be very suitable in environments with restricted resources, such as mobile devices or embedded systems. Practical examples are cell phones, RFID transponders, smart cards or devices in sensor networks. Besides efficiency, security is the most important property of a stream cipher. In this thesis, we address cryptanalysis of modern lightweight stream ciphers. We derive and improve cryptanalytic methods for different building blocks and present dedicated attacks on specific proposals, including some eSTREAM candidates. As a result, we elaborate on the design criteria for the development of secure and efficient stream ciphers. The best-known building block is the linear feedback shift register (LFSR), which can be combined with a nonlinear Boolean output function. A powerful type of attacks against LFSR-based stream ciphers are the recent algebraic attacks, these exploit the specific structure by deriving low degree equations for recovering the secret key. We efficiently determine the immunity of existing and newly constructed Boolean functions against fast algebraic attacks. The concept of algebraic immunity is then generalized by investigating the augmented function of the stream cipher. As an application of this framework, we improve the cryptanalysis of a well-known stream cipher with irregularly clocked LFSR's. Algebraic attacks can be avoided by substituting the LFSR with a suitable nonlinear driving device, such as a feedback shift register with carry (FCSR) or the recently proposed class of T-functions. We investigate both replacement schemes in view of their security, and devise different practical attacks (including linear attacks) on a number of specific proposals based on T-functions. Another efficient method to amplify the nonlinear behavior is to use a round-based filter function, where each round consists of simple nonlinear operations. We use differential methods to break a reduced-round version of eSTREAM candidate Salsa20. Similar methods can be used to break a related compression function with a reduced number of rounds. Finally, we investigate the algebraic structure of the initialization function of stream ciphers and provide a framework for key recovery attacks. As an application, a key recovery attack on simplified versions of eSTREAM candidates Trivium and Grain-128 is given.

EPFL2008

Quantitative security of block ciphers

Thomas Baignères

Block ciphers probably figure in the list of the most important cryptographic primitives. Although they are used for many different purposes, their essential goal is to ensure confidentiality. This thesis is concerned by their quantitative security, that is, by measurable attributes that reflect their ability to guarantee this confidentiality. The first part of this thesis deals with well know results. Starting with Shannon's Theory of Secrecy, we move to practical implications for block ciphers, recall the main schemes on which nowadays block ciphers are based, and introduce the Luby-Rackoff security model. We describe distinguishing attacks and key-recovery attacks against block ciphers and show how to turn the firsts into the seconds. As an illustration, we recall linear cryptanalysis which is a classical example of statistical cryptanalysis. In the second part, we consider the (in)security of block ciphers against statistical cryptanalytic attacks and develop some tools to perform optimal attacks and quantify their efficiency. We start with a simple setting in which the adversary has to distinguish between two sources of randomness and show how an optimal strategy can be derived in certain cases. We proceed with the practical situation where the cardinality of the sample space is too large for the optimal strategy to be implemented and show how this naturally leads to the concept of projection-based distinguishers, which reduce the sample space by compressing the samples. Within this setting, we re-consider the particular case of linear distinguishers and generalize them to sets of arbitrary cardinality. We show how these distinguishers between random sources can be turned into distinguishers between random oracles (or block ciphers) and how, in this setting, one can generalize linear cryptanalysis to Abelian groups. As a proof of concept, we show how to break the block cipher TOY100, introduce the block cipher DEAN which encrypts blocks of decimal digits, and apply the theory to the SAFER block cipher family. In the last part of this thesis, we introduce two new constructions. We start by recalling some essential notions about provable security for block ciphers and about Serge Vaudenay's Decorrelation Theory, and introduce new simple modules for which we prove essential properties that we will later use in our designs. We then present the block cipher C and prove that it is immune against a wide range of cryptanalytic attacks. In particular, we compute the exact advantage of the best distinguisher limited to two plaintext/ciphertext samples between C and the perfect cipher and use it to compute the exact value of the maximum expected linear probability (resp. differential probability) of C which is known to be inversely proportional to the number of samples required by the best possible linear (resp. differential) attack. We then introduce KFC a block cipher which builds upon the same foundations as C but for which we can prove results for higher order adversaries. We conclude both discussions about C and KFC by implementation considerations.

EPFL2008

Cryptanalysis of the full MMB block cipher

Jorge Nakahara, Yue Sun

The block cipher MMB was designed by Daemen, Govaerts and Vandewalle, in 1993, as an alternative to the IDEA block cipher. We exploit and describe unusual properties of the modular multiplication in

Z_{2^{32} - 1}

, which lead to a differential attack on the full 6-round MMB cipher (both versions 1.0 and 2.0). Further contributions of this paper include detailed square and linear cryptanalysis of MMB. Concerning differential cryptanalysis (DC), we can break the full MMB with 2^118 chosen plaintexts, 2^95.91 6-round MMB encryptions and 2^64 counters, effectively bypassing the cipher's countermeasures against DC. For the square attack, we can recover the 128-bit user key for 4-round MMB with 2^34 chosen plaintexts, 2^126.32 4-round encryptions and 2^64 memory blocks. Concerning linear cryptanalysis, we present a key-recovery attack on 3-round MMB requiring 2^114.56 known-plaintexts and 2^126 encryptions. Moreover, we detail a ciphertext-only attack on 2-round MMB using 2^93.6 ciphertexts and 2^93.6 parity computations. These attacks do not depend on weak-key or weak-subkey assumptions, and are thus independent of the key schedule algorithm.

2009

Quantitative security of block ciphers

Thomas Baignères

EPFL2008

Cryptanalysis of the full MMB block cipher

Jorge Nakahara, Yue Sun

The block cipher MMB was designed by Daemen, Govaerts and Vandewalle, in 1993, as an alternative to the IDEA block cipher. We exploit and describe unusual properties of the modular multiplication in

Z_{2^{32} - 1}

2009

Analysis of lightweight stream ciphers

Simon Fischer

EPFL2008