Phase-shift Fault Analysis of Grain v1

This paper deals with the phase-shift fault analysisof stream cipher Grain v1. We assume that the attacker is ableto desynchronize the linear and nonlinear registers of the cipherduring the keystream generation phase by either forcing one ofthe registers to clock one more time, while the other register is notclocked, or by preventing one of the registers from clocking, whilethe other register is clocked. Using this technique, we are able toobtain the full inner state of the cipher in reasonable time (under12 hours on a single PC) by using 150 bits of unfaulted keystream,600 bits of faulted keystreams and by correctly guessing 28 bitsof the linear register

Differential Fault Attack on Grain v1, ACORN v3 and Lizard

Differential Fault Attack (DFA) is presently a very well known technique to evaluate security of a stream cipher. This considers that the stream cipher can be weakened by injection of the fault. In this paper we study DFA on three ciphers, namely Grain v1, Lizard and ACORN v3. We show that Grain v1 (an eStream cipher) can be attacked with injection of only 5 faults instead of 10 that has been reported in 2012. For the first time, we have mounted the fault attack on Lizard, a very recent design and show that one requires only 5 faults to obtain the state. ACORN v3 is a third round candidate of CAESAR and there is only one hard fault attack on an earlier version of this cipher. However, the `hard fault\u27 model requires a lot more assumption than the generic DFA. In this paper, we mount a DFA on ACORN v3 that requires 9 faults to obtain the state. In case of Grain v1 and ACORN v3, we can obtain the secret key once the state is known. However, that is not immediate in case of Lizard. While we have used the basic framework of DFA that appears in literature quite frequently, specific tweaks have to be explored to mount the actual attacks that were not used earlier. To the best of our knowledge, these are the best known DFA on these three ciphers

Probabilistic Signature Based Framework for Differential Fault Analysis of Stream Ciphers

Differential Fault Attack (DFA) has received serious attention in cryptographic literature and very recently such attacks have been mounted against several popular stream ciphers for example Grain v1, MICKEY 2.0 and Trivium, that are parts of the eStream hardware profile. The basic idea of the fault attacks consider injection of faults and the most general set-up should consider faults at random location and random time. Then one should identify the exact location and the exact timing of the fault (as well as multi bit faults) with the help of fault signatures. In this paper we consider this most general set-up and solve the problem of fault attack under a general framework, where probabilistic signatures are exploited. Our ideas subsume all the existing DFAs against the Grain family, MICKEY 2.0 and Trivium. In the process we provide improved fault attacks for all the versions of Grain family and also for MICKEY 2.0 (the attacks against Trivium are already quite optimal and thus there is not much scope to improve). Our generalized method can also take care of the cases where certain parts of the keystream bits are missing for authentication purpose. In particular, we show that the unsolved problem of identifying the faults in random time for Grain 128a can be solved in this manner. Our techniques can easily be applied to mount fault attack on any stream cipher of similar kind

Bitstream Modification of Trivium

In this paper we present a bitstream modification attack on the Trivium cipher, an international standard under ISO/IEC 29192-3. By changing the content of three LUTs in the bitstream, we reduce the non-linear state updating function of Trivium to a linear one. This makes it possible to recover the key from 288 keystream bits using at most $2^{19.41}$ operations. We also propose a countermeasure against bitstream modification attacks which obfuscates the bitstream using dummy and camouflaged LUTs which look legitimate to the attacker. We present an algorithm for injecting dummy LUTs directly into the bitstream without causing any performance or power penalty

Algebraic Fault Analysis of Katan

This paper presents a new and more realistic model for fault attacks and statistical and algebraic techniques to improve fault analysis in general. Our algebraic techniques is an adapted solver for systems of equations based on ElimLin and XSL. We use these techniques to introduce two new fault attacks on the hardware oriented block cipher Katan32 from the Katan family of block ciphers. We are able to break full Katan using $4$ faults and $2^{29.04}$ Katan evaluations with a theoretical statistical fault attack and $7.19$ faults in $2^{27.2}$ Katan evaluations with a tested algebraic one. This is a great improvement over the existing fault attacks which need $115$ and $140$ faults respectively. Furthermore, our algebraic attack can be executed on a normal computer

Fault Attack on the Authenticated Cipher ACORN v2

Fault attack is an efficient cryptanalysis method against cipher implementations and has attracted a lot of attention in recent public cryptographic literatures. In this work we introduce a fault attack on the CAESAR candidate ACORN v2. Our attack is done under the assumption of random fault injection into an initial state of ACORN v2 and contains two main steps: fault locating and equation solving. At the first step, we first present a fundamental fault locating method, which uses 99-bit output keystream to determine the fault injected location with probability 97.08%. And then several improvements are provided, which can further increase the probability of fault locating to almost 1. As for the system of equations retrieved at the first step, we give two solving methods at the second step, that is, linearization and guess-and-determine. The time complexity of our attack is not larger than c·2179.19-1.76N at worst, where N is the number of fault injections such that 31≤N≤88 and c is the time complexity of solving linear equations. Our attack provides some insights into the diffusion ability of such compact stream ciphers

On Selection of Samples in Algebraic Attacks and a New Technique to Find Hidden Low Degree Equations

The best way of selecting samples in algebraic attacks against block ciphers is not well explored and understood. We introduce a simple strategy for selecting the plaintexts and demonstrate its strength by breaking reduced-round KATAN, LBLOCK and SIMON. For each case, we present a practical attack on reduced round version which outperforms previous attempts of algebraic cryptanalysis whose complexities were close to exhaustive search. The attack is based on the selection of samples using cube attack and ELIMLIN which was presented at FSE'12, and a new technique called proning. In the case of LBLOCK, we break 10 out of 32 rounds. In KATAN, we break 78 out of 254 rounds. Unlike previous attempts which break smaller number of rounds, we do not guess any bit of the key and we only use structural properties of the cipher to be able to break a higher number of rounds with much lower complexity. We show that cube attacks owe their success to the same properties and therefore, can be used as a heuristic for selecting the samples in an algebraic attack. The performance of ELIMLIN is further enhanced by the new proning technique, which allows to discover linear equations that are not found by ELIMLIN

Cryptanalysis of Plantlet

Plantlet is a lightweight stream cipher designed by Mikhalev, Armknecht and Müller in \texttt{IACR ToSC} 2017. It has a Grain-like structure with two state registers of size $40$ and $61$ bits. In spite of this, the cipher does not seem to lose in security against generic Time-Memory-Data Tradeoff attacks due to the novelty of its design. The cipher uses a 80-bit secret key and a 90-bit IV. In this paper, we first present a key recovery attack on Plantlet that requires around $2^{76.26}$ Plantlet encryptions. The attack leverages the fact that two internal states of Plantlet that differ in the 43rd LFSR location are guaranteed to produce keystream that are either equal or unequal in 45 locations with probability 1. Thus an attacker can with some probability guess that when 2 segments of keystream blocks possess the 45 bit difference just mentioned, they have been produced by two internal states that differ only in the 43rd LFSR location. Thereafter by solving a system of polynomial equations representing the keystream bits, the attacker can find the secret key if his guess was indeed correct, or reach some kind of contradiction if his guess was incorrect. In the latter event, he would repeat the procedure for other keystream blocks with the given difference. We show that the process when repeated a finite number of times, does indeed yield the value of the secret key. In the second part of the paper, we observe that the previous attack was limited to internal state differences that occurred at time instances that were congruent to $0\bmod 80$. We further observe that by generalizing the attack to include internal state differences that are congruent to all equivalence classed modulo 80, we lower the total number of keystream bits required to perform the attack and in the process reduce the attack complexity to $2^{69.98}$ Plantlet encryptions

CDCL(Crypto) and Machine Learning based SAT Solvers for Cryptanalysis

Over the last two decades, we have seen a dramatic improvement in the efficiency of conflict-driven clause-learning Boolean satisfiability (CDCL SAT) solvers over industrial problems from a variety of applications such as verification, testing, security, and AI. The availability of such powerful general-purpose search tools as the SAT solver has led many researchers to propose SAT-based methods for cryptanalysis, including techniques for finding collisions in hash functions and breaking symmetric encryption schemes. A feature of all of the previously proposed SAT-based cryptanalysis work is that they are \textit{blackbox}, in the sense that the cryptanalysis problem is encoded as a SAT instance and then a CDCL SAT solver is invoked to solve said instance. A weakness of this approach is that the encoding thus generated may be too large for any modern solver to solve it efficiently. Perhaps a more important weakness of this approach is that the solver is in no way specialized or tuned to solve the given instance. Finally, very little work has been done to leverage parallelism in the context of SAT-based cryptanalysis. To address these issues, we developed a set of methods that improve on the state-of-the-art SAT-based cryptanalysis along three fronts. First, we describe an approach called \cdcl (inspired by the CDCL($T$) paradigm) to tailor the internal subroutines of the CDCL SAT solver with domain-specific knowledge about cryptographic primitives. Specifically, we extend the propagation and conflict analysis subroutines of CDCL solvers with specialized codes that have knowledge about the cryptographic primitive being analyzed by the solver. We demonstrate the power of this framework in two cryptanalysis tasks of algebraic fault attack and differential cryptanalysis of SHA-1 and SHA-256 cryptographic hash functions. Second, we propose a machine-learning based parallel SAT solver that performs well on cryptographic problems relative to many state-of-the-art parallel SAT solvers. Finally, we use a formulation of SAT into Bayesian moment matching to address heuristic initialization problem in SAT solvers