Key-Recovery Attacks on Full Kravatte

This paper presents a cryptanalysis of full Kravatte, an instantiation of the Farfalle construction of a pseudorandom function (PRF) with variable input and output length. This new construction, proposed by Bertoni et al., introduces an efficiently parallelizable and extremely versatile building block for the design of symmetric mechanisms, e.g. message authentication codes or stream ciphers. It relies on a set of permutations and on so-called rolling functions: it can be split into a compression layer followed by a two-step expansion layer. The key is expanded and used to mask the inputs and outputs of the construction. Kravatte instantiates Farfalle using linear rolling functions and permutations obtained by iterating the Keccak round function. We develop in this paper several attacks against this PRF, based on three different attack strategies that bypass part of the construction and target a reduced number of permutation rounds. A higher order differential distinguisher exploits the possibility to build an affine space of values in the cipher state after the compression layer. An algebraic meet-in-the-middle attack can be mounted on the second step of the expansion layer. Finally, due to the linearity of the rolling function and the low algebraic degree of the Keccak round function, a linear recurrence distinguisher can be found on intermediate states of the second step of the expansion layer. All the attacks rely on the ability to invert a small number of the final rounds of the construction. In particular, the last two rounds of the construction together with the final masking by the key can be algebraically inverted, which allows to recover the key. The complexities of the devised attacks, applied to the Kravatte specifications published on the IACR ePrint in July 2017, or the strengthened version of Kravatte recently presented at ECC 2017, are far below the security claimed

Interpolation Attacks on Round-Reduced Elephant, Kravatte and Xoofff

We introduce an interpolation attack using the \textsc{Moebius Transform}. This can reduce the time complexity to get a linear system of equations for specified intermediate state bits, which is general to cryptanalysis of some ciphers with update function of low algebraic degree. Along this line, we perform an interpolation attack against \textsc{Elephant-Delirium}, a round 2 submission of the ongoing NIST lightweight cryptography project. This is the first third-party cryptanalysis on this cipher. Moreover, we promote the interpolation attack by applying it to the \textbf{Farfalle} pseudo-random constructions \textsc{Kravatte} and \textsc{Xoofff}. Our attacks turn out to be the most efficient method for these ciphers thus far

Too Much Crypto

We show that many symmetric cryptography primitives would not be less safe with significantly fewer rounds. To support this claim, we review the cryptanalysis progress in the last 20 years, examine the reasons behind the current number of rounds, and analyze the risk of doing fewer rounds. Advocating a rational and scientific approach to round numbers selection, we propose revised number of rounds for AES, BLAKE2, ChaCha, and SHA-3, which offer more consistent security margins across primitives and make them much faster, without increasing the security risk

New MILP Modeling: Improved Conditional Cube Attacks on Keccak-based Constructions

In this paper, we propose a new MILP modeling to find better or even optimal choices of conditional cubes, under the general framework of conditional cube attacks. These choices generally find new or improved attacks against the keyed constructions based on Keccak permutation and its variants, including Keccak-MAC, KMAC, Keyak, and Ketje, in terms of attack complexities or the number of attacked rounds. Interestingly, conditional cube attacks were applied to round-reduced Keccak-MAC, but not to KMAC despite the great similarity between Keccak-MAC and KMAC, and the fact that KMAC is the NIST standard way of constructing MAC from SHA-3. As examples to demonstrate the effectiveness of our new modeling, we report key recovery attacks against KMAC128 and KMAC256 reduced to 7 and 9 rounds, respectively; the best attack against Lake Keyak with 128-bit key is improved from 6 to 8 rounds in the nonce-respected setting and 9 rounds of Lake Keyak can be attacked if the key size is of 256 bits; attack complexity improvements are found generally on other constructions. Our new model is also applied to Keccak-based full-state keyed sponge and gives a positive answer to the open question proposed by Bertoni et al. whether cube attacks can be extended to more rounds by exploiting full-state absorbing. To verify the correctness of our attacks, reduced-variants of the attacks are implemented and verified on a PC practically. It is remarked that this work does not threaten the security of any full version of the instances analyzed in this paper

Preface

International audienceIACR Transactions on Symmetric Cryptology (ToSC) is a forum for original results in all areas of symmetric cryptography, including the design and analysis of block ciphers, stream ciphers, encryption schemes, hash functions, message authentication codes, (cryptographic) permutations, authenticated encryption schemes, cryptanalysis and evaluation tools, and security issues and solutions regarding their implementation. ToSC implements an open-access journal/conference hybrid model following some other communities in computer science. All articles undergo a journal-style reviewing process and accepted papers are published in gold open access (in our case the Creative Commons License CC-BY 4.0). The review procedures that we have followed strictly adhere to the traditions of the journal world. Full papers are assigned to the members of the Editorial Board. These members write detailed and careful reviews (usually without relying on subreviewers). Moreover, we have had a rebuttal phase, allowing authors to respond to the review comments before the final decisions. If necessary, the review process enables further interactions between the authors and the reviewers, mediated by the Co-Editors-in-Chief. Detailed discussions among the reviewers lead to one of the following four decisions for each paper: accept, in which case the authors submit their final camera-ready manuscript after editorial corrections; accept with minor revision, which means that the authors revise their manuscript and go through one or more iterations and reviews of the manuscript until the comments have been addressed in a satisfactory way; major revision, which means that the authors are requested to make major changes to their manuscript before submitting again in one of the next rounds; and reject, which means that the manuscript is deemed to be not suitable for publication in ToSC. The last four issues we have tried to refine the method (new for a community used to only accept or reject decisions) and decide in a more fair way when to assign major revisions. The review process shares with the high quality conferences that it is double-blind and adheres to a strict timing; but unlike a traditional conference, there are multiple submission deadlines per year. Each paper received at least three reviews; for submissions by Editorial Board members this was increased to at least four. Overall, we are very pleased with the quality and quantity of submissions, the detailed review reports written by the reviewers and the substantial efforts by the authors to further improve the quality of their work. We think that the review process leads to an increased quality of the papers that are published. The papers selected by the Editorial Board for publication in the last four issues were presented at the conference Fast Software Encryption (FSE). This gave the authors the opportunity to advertise their results and engage in discussions on further work. we received 33 submissions, out of which 10 were accepted, 4 of these after minor revisions; the number of papers that received a major revision decision was 4. For Volume 2017, Issue 3, we received 32 submissions, out of which 13 were accepted, 9 of these after minor revisions; the number of papers that received a major revisio

From Farfalle to Megafono via Ciminion: The PRF Hydra for MPC Applications

The area of multi-party computation (MPC) has recently increased in popularity and number of use cases. At the current state of the art, Ciminion, a Farfalle-like cryptographic function, achieves the best performance in MPC applications involving symmetric primitives. However, it has a critical weakness. Its security highly relies on the independence of its subkeys, which is achieved by using an expensive key schedule. Many MPC use cases involving symmetric pseudo-random functions (PRFs) rely on secretly shared symmetric keys, and hence the expensive key schedule must also be computed in MPC. As a result, Ciminion\u27s performance is significantly reduced in these use cases. In this paper we solve this problem. Following the approach introduced by Ciminion\u27s designers, we present a novel primitive in symmetric cryptography called Megafono. Megafono is a keyed extendable PRF, expanding a fixed-length input to an arbitrary-length output. Similar to Farfalle, an initial keyed permutation is applied to the input, followed by an expansion layer, involving the parallel application of keyed ciphers. The main novelty regards the expansion of the intermediate/internal state for free , by appending the sum of the internal states of the first permutation to its output. The combination of this and other modifications, together with the impossibility for the attacker to have access to the input state of the expansion layer, make Megafono very efficient in the target application. As a concrete example, we present the PRF Hydra, an instance of Megafono based on the Hades strategy and on generalized versions of the Lai--Massey scheme. Based on an extensive security analysis, we implement Hydra in an MPC framework. The results show that it outperforms all MPC-friendly schemes currently published in the literature

ANALYSIS OF CRYPTOGRAPHIC ALGORITHMS AGAINST THEORETICAL AND IMPLEMENTATION ATTACKS

This thesis deals with theoretical and implementation analysis of cryptographic functions. Theoretical attacks exploit weaknesses in the mathematical structure of the cryptographic primitive, while implementation attacks leverage on information obtained by its physical implementation, such as leakage through physically observable parameters (side-channel analysis) or susceptibility to errors (fault analysis). In the area of theoretical cryptanalysis, we analyze the resistance of the Keccak-f permutations to differential cryptanalysis (DC). Keccak-f is used in different cryptographic primitives: Keccak (which defines the NIST standard SHA-3), Ketje and Keyak (which are currently at the third round of the CAESAR competition) and the authenticated encryption function Kravatte. In its basic version, DC makes use of differential trails, i.e. sequences of differences through the rounds of the primitive. The power of trails in attacks can be characterized by their weight. The existence of low-weight trails over all but a few rounds would imply a low resistance with respect to DC. We thus present new techniques to effciently generate all 6-round differential trails in Keccak-f up to a given weight, in order to improve known lower bounds. The limit weight we can reach with these new techniques is very high compared to previous attempts in literature for weakly aligned primitives. This allows us to improve the lower bound on 6 rounds from 74 to 92 for the four largest variants of Keccak-f. This result has been used by the authors of Kravatte to choose the number of rounds in their function. Thanks to their abstraction level, some of our techniques are actually more widely applicable than to Keccak-f. So, we formalize them in a generic way. The presented techniques have been integrated in the KeccakTools and are publicly available. In the area of fault analysis, we present several results on differential fault analysis (DFA) on the block cipher AES. Most DFA attacks exploit faults that modify the intermediate state or round key. Very few examples have been presented, that leverage changes in the sequence of operations by reducing the number of rounds. In this direction, we present four DFA attacks that exploit faults that alter the sequence of operations during the final round. In particular, we show how DFA can be conducted when the main operations that compose the AES round function are corrupted, skipped or repeated during the final round. Another aspect of DFA we analyze is the role of the fault model in attacks. We study it from an information theoretical point of view, showing that the knowledge that the attacker has on the injected fault is fundamental to mount a successful attack. In order to soften the a-priori knowledge on the injection technique needed by the attacker, we present a new approach for DFA based on clustering, called J-DFA. The experimental results show that J-DFA allows to successfully recover the key both in classical DFA scenario and when the model does not perfectly match the faults effect. A peculiar result of this method is that, besides the preferred candidate for the key, it also provides the preferred models for the fault. This is a quite remarkable ability because it furnishes precious information which can be used to analyze, compare and characterize different specific injection techniques on different devices. In the area of side-channel attacks, we improve and extend existing attacks against the RSA algorithm, known as partial key exposure attacks. These attacks on RSA show how it is possible to find the factorization of the modulus from the knowledge of some bits of the private key. We present new partial key exposure attacks when the countermeasure known as exponent blinding is used. We first improve known results for common RSA setting by reducing the number of bits or by simplifying the mathematical analysis. Then we present novel attacks for RSA implemented using the Chinese Remainder Theorem, a scenario that has never been analyzed before in this context

Inapplicability of Differential Fault Attacks against Cellular Automata based Lightweight Authenticated Cipher

Authenticated encryption (AE) schemes are a necessity to secure the physical devices connected to the Internet. Two AE schemes, TinyJambu and Elephant, are finalists of NIST lightweight cryptography competition. Another AE scheme, ACORN v3, a CAESAR competition finalist, has been shown to be particularly vulnerable against Differential Fault Attack (DFA), even more than its previous version ACORN v2. TinyJambu is also susceptible to DFA. An optimized interpolation attack has been proposed against one instance of Elephant, Delirium, recently. We propose methods to strengthen these schemes using the Cellular Automata (CA) and increase their resistance to these attacks. The Programmable Cellular Automata (PCA) 90-150 is effectively deployed to make these ciphers robust against DFA. We also provide mathematical analysis of the invigorated schemes and show that significant improvement is achieved in all the three enhanced schemes

Preimage Attacks on Round-reduced Keccak-224/256 via an Allocating Approach

We present new preimage attacks on standard Keccak-224 and Keccak-256 that are reduced to 3 and 4 rounds. An allocating approach is used in the attacks, and the whole complexity is allocated to two stages, such that fewer constraints are considered and the complexity is lowered in each stage. Specifically, we are trying to find a 2-block preimage, instead of a 1-block one, for a given hash value, and the first and second message blocks are found in two stages, respectively. Both the message blocks are constrained by a set of newly proposed conditions on the middle state, which are weaker than those brought by the initial values and the hash values. Thus, the complexities in the two stages are both lower than that of finding a 1-block preimage directly. Together with the basic allocating approach, an improved method is given to balance the complexities of two stages, and hence, obtains the optimal attacks. As a result, we present the best theoretical preimage attacks on Keccak-224 and Keccak-256 that are reduced to 3 and 4 rounds. Moreover, we practically found a (second) preimage for 3-round Keccak-224 with a complexity of 2^{39.39}

Key-Recovery Attacks on Full Kravatte

This paper presents a cryptanalysis of full Kravatte, an instantiation of the Farfalle construction of a pseudorandom function (PRF) with variable input and output length. This new construction, proposed by Bertoni et al., introduces an efficiently parallelizable and extremely versatile building block for the design of symmetric mechanisms, e.g. message authentication codes or stream ciphers. It relies on a set of permutations and on so-called rolling functions: it can be split into a compression layer followed by a two-step expansion layer. The key is expanded and used to mask the inputs and outputs of the construction. Kravatte instantiates Farfalle using linear rolling functions and permutations obtained by iterating the Keccak round function.We develop in this paper several attacks against this PRF, based on three different attack strategies that bypass part of the construction and target a reduced number of permutation rounds. A higher order differential distinguisher exploits the possibility to build an affine space of values in the cipher state after the compression layer. An algebraic meet-in-the-middle attack can be mounted on the second step of the expansion layer. Finally, due to the linearity of the rolling function and the low algebraic degree of the Keccak round function, a linear recurrence distinguisher can be found on intermediate states of the second step of the expansion layer. All the attacks rely on the ability to invert a small number of the final rounds of the construction. In particular, the last two rounds of the construction together with the final masking by the key can be algebraically inverted, which allows to recover the key.The complexities of the devised attacks, applied to the Kravatte specifications published on the IACR ePrint in July 2017, or the strengthened version of Kravatte recently presented at ECC 2017, are far below the security claimed