Elisabeth-4 is a stream cipher tailored for usage in hybrid homomorphic encryption applications that has been introduced by Cosseron et al. at ASIACRYPT 2022. In this paper, we present several variants of a key-recovery attack on the full Elisabeth-4 that break the 128-bit security claim of that cipher. Our most optimized attack is a chosen-IV attack with a time complexity of 2(88) elementary operations, a memory complexity of 254 bits and a data complexity of 2(41) bits. Our attack applies the linearization technique to a nonlinear system of equations relating some keystream bits to the key bits and exploits specificities of the cipher to solve the resulting linear system efficiently. First, due to the structure of the cipher, the system to solve happens to be very sparse, which enables to rely on sparse linear algebra and most notably on the Block Wiedemann algorithm. Secondly, the algebraic properties of the two nonlinear ingredients of the filtering function cause rank defects which can be leveraged to solve the linearized system more efficiently with a decreased data and time complexity. We have implemented our attack on a toy version of Elisabeth-4 to verify its correctness. It uses the efficient implementation of the Block Wiedemann algorithm of CADO-NFS for the sparse linear algebra.

NORX is an authenticated encryption scheme with associated data being publicly scrutinized as part of the ongoing CAESAR competition, where 14 other primitives are also competing. It is based on the sponge construction and relies on a simple permutation that allows efficient and versatile implementations. Thanks to research on the security of the sponge construction, the design of NORX, whose permutation is inspired from the permutations used in BLAKE and ChaCha, has evolved throughout three main versions (v1.0, v2.0 and v3.0). In this paper, we investigate the security of the full NORX v2.0 primitive that has been accepted as third-round candidate in the CAESAR competition. We show that some non-conservative design decisions probably motivated by implementation efficiency considerations result in at least one strong structural distinguisher of the underlying sponge permutation that can be turned into an attack on the full primitive. This attack yields a ciphertext-only forgery with time and data complexity 266 (resp. 2130) for the variant of NORX v2.0 using 128-bit (resp. 256-bit) keys and breaks the designers’ claim of a 128-bit, resp. 256-bit security. Furthermore, we show that this forgery attack can be extended to a key-recovery attack on the full NORX v2.0 with the same time and data complexities. We have implemented and experimentally verified the correctness of the attacks on a toy version of NORX. We emphasize that the scheme has recently been tweaked to NORX v3.0 at the beginning of the third round of the CAESAR competition: the main change introduces some key-dependent internal operations, which make NORX v3.0 immune to our attacks. However, the structural distinguisher of the permutation persists.

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.

The principle of padding oracle attacks has been known in the cryptography research community since 1998. It has been generalized to exploit any property of decrypted ciphertexts, either stemming from the encryption scheme, or the application data format. However, this attack principle is being leveraged time and again against proposed standards and real-world applications. This may be attributed to several factors, e.g., the backward compatibility with standards selecting oracle-prone mechanisms, the difficulty of safely implementing decryption operations, and the misuse of libraries by non cryptography-savvy developers. In this article, we present several format oracles discovered in applications and libraries implementing the OpenPGP message format, among which the popular GnuPG application. We show that, if the oracles they implement are made available to an adversary, e.g., by a front-end application, he can, by querying repeatedly these oracles, decrypt all OpenPGP symmetrically encrypted packets. The corresponding asymptotic query complexities range from 2 to \(2^8\) oracle requests per plaintext byte to recover.

PRINCE is a lightweight block cipher proposed by Borghoff et al. at Asiacrypt 2012. Due to its originality, novel design and low number of rounds, it has already attracted the attention of a large number of cryptanalysts. Several results on reduced versions have been published to date; the best one is an attack on 8 rounds out of the total number of 12 . In this paper we improve this result by two rounds: we provide an attack on 10 rounds of the cipher with a data complexity of 2^57.94 and a time complexity of 2^60.62 , corresponding to 118.56 security bits, instead of 126 for the generic attacks. Our attack uses multiple differentials and exploits some properties of PRINCE for recovering the whole key. PRINCE is defined as a member of a family of ciphers, differing by the choice of an Sbox among a distinguished set. We also show that the security offered by all the members of the family is not equivalent, by identifying an Sbox for which our attack can be extended up to 11 rounds with a data complexity of 2^59.81 and a time complexity of 2^62.43 .

Generating and standardizing elliptic curves to use them in a cryptographic context is a hard task. There have been several attempts to define public elliptic curves for a general cryptographic use, such as NIST FIPS 186–2 curves [53], Brainpool curves [47], SECG curves [58], ANSSI FRP256v1 [41], Curve25519 [7], and OSCCA SM2 [54]. Recent years have seen some distrust cast on previously standardized curves and the emergence of the need to standardize new curves. Different parties have spoken their point of view on the (dis)trust they have on previously standardized curves whether it is because of the properties they satisfy or don’t satisfy or the process used to generate them. Such analyses often come with a list of security and performance/implementation-related criteria a curve should satisfy, and a proposal on how to cor­ rectly generate such a curve in a way that can be trusted [10, 17, 18, 48, 2], together with a proposal of such a correctly generated curve [7, 17, 2].

PRINCE is a lightweight block cipher proposed by Borghoff et al. at Asiacrypt 2012. Due to its originality, novel design and low number of rounds, it has already attracted the attention of a large number of cryptanalysts. Several results on reduced versions have been published to date; the best one is an attack on 8 rounds out of the total number of 12. In this paper we improve this result by two rounds: we provide an attack on 10 rounds of the cipher with a data complexity of 2 and a time complexity of 2, corresponding to 118.56 security bits, instead of 126 for the generic attacks. Our attack uses multiple differentials and exploits some properties of PRINCE for recovering the whole key. PRINCE is defined as a member of a family of ciphers, differing by the choice of an Sbox among a distinguished set. We also show that the security offered by all the members of the family is not equivalent, by identifying an Sbox for which our attack can be extended up to 11 rounds with a data complexity of 2 and a time complexity of 2.

In the recent years, several hash constructions have been introduced that aim at achieving enhanced security margins by strengthening the Merkle-Damgård mode. However, their security analysis have been conducted independently and using a variety of proof methodologies. This paper unifies these results by proposing a unique indifferentiability proof that considers a broadened form of the general compression function introduced by Stam at FSE09. This general definition enables us to capture in a realistic model most of the features of the mode of operation (e.g., message encoding, blank rounds, message insertion,...) within the pre-processing and post-processing functions. Furthermore, it relies on an inner primitive which can be instantiated either by an ideal block cipher, or by an ideal permutation. Then, most existing hash functions can be seen as the Chop-MD construction applied to some compression function which fits the broadened Stam model. Our result then gives the tightest known indifferentiability bounds for several general modes of operations, including Chop-MD, Haifa or sponges. Moreover, we show that it applies in a quite automatic way, by providing the security bounds for 7 out of the 14 second round SHA-3 candidates, which are in some cases improved over previously known ones.

In this paper we investigate the security of the two most recent versions of the message authentication code 128-EIA3, which is considered for adoption as a third integrity algorithm in the emerging 3GPP standard LTE. We first present an efficient existential forgery attack against the June 2010 version of the algorithm. This attack allows, given any message and the associated MAC value under an unknown integrity key and an initial vector, to predict the MAC value of a related message under the same key and the same initial vector with a success probability 1/2. We then briefly analyse the tweaked version of the algorithm that was introduced in January 2011 to circumvent this attack. We give some evidence that while this new version offers a provable resistance against similar forgery attacks under the assumption that (key, IV) pairs are never reused by any legitimate sender or receiver, some of its design features limit its resilience against IV reuse.

The National Institute of Standards and Technology (NIST) opened a public competition on November 2, 2007 to develop a new cryptographic hash algorithm – SHA-3, which will augment the hash algorithms currently specified in the Federal Information Processing Standard (FIPS) 180-3, Secure Hash Standard. The competition was NIST’s response to advances in the cryptanalysis of hash algorithms. NIST received sixty-four submissions in October 2008, and selected fifty-one candidate algorithms as the first-round candidates on December 10, 2008, and fourteen as the second-round candidates on July 24, 2009. One year was allocated for the public review of the second-round candidates. On December 9, 2010, NIST announced five SHA-3 finalists to advance to the third (and final) round of the competition. This report summarizes the evaluation and selection of the five finalists – BLAKE, Grøstl, JH, Keccak and Skein.

In this note we show that the message authentication code 128-EIA3 considered for adoption as a third integrity algorithm in the emerging mobile standard LTE is vulnerable to a simple existential forgery attack. This attack allows, given any message and the associated MAC value under an unknown integrity key and an initial vector, to predict the MAC value of a related message under the same key and the same initial vector with a success probability 1/2.

Shabal is based on a new provably secure mode of operation. Some related-key distinguishers for the underlying keyed permutation have been exhibited recently by Aumasson et al. and Knudsen et al., but with no visible impact on the security of Shabal. This paper then aims at extensively studying such distinguishers for the keyed permutation used in Shabal, and at clarifying the impact that they exert on the security of the full hash function. Most interestingly, a new security proof for Shabal's mode of operation is provided where the keyed permutation is not assumed to be an ideal cipher anymore, but observes a distinguishing property i.e., an explicit relation verified by all its inputs and outputs. As a consequence of this extended proof, all known distinguishers for the keyed permutation are proven not to weaken the security of Shabal. In our study, we provide the foundation of a generalization of the indifferentiability framework to biased random primitives, this part being of independent interest.

VEST is a set of four stream cipher families submitted by S. O'Neil, B. Gittins and H. Landman to the eSTREAM call for stream cipher proposals of the European project ECRYPT. The state of any family member is made of three components: a counter, a counter diffusor and a core accumulator. We show that collisions can be found in the counter during the IV Setup. Moreover they can be combined with a collision in the linear counter diffusor to form collisions on the whole cipher. As a consequence, it is possible to retrieve 53 bits of the keyed state of the stream cipher by performing a chosen IV attack. For the default member of a VEST family, we present a "long" IV attack which requires 222.24 IV setups, and a "short" IV attack which requires 228.73 IV setups on average. The 53 bits retrieved can be used to reduce the complexity of the exhaustive key search. The chosen IV attack can be turned into a chosen message attack on a MAC based on VEST.