We propose efficient, post-quantum threshold ring signatures constructed from one-wayness of AES encryption and the VOLE-in-the-Head zero-knowledge proof system. Our scheme scales efficiently to large rings and extends the linkable ring signatures paradigm. We define and construct key-binding deterministic tags for signature linkability, that also enable succinct aggregation with approximate lower bound arguments of knowledge; this allows us to achieve succinct aggregation of our signatures...

At FSE'15, Mennink introduced two tweakable block ciphers, $\widetilde{F}[1]$ and $\widetilde{F}[2]$, both utilizing an $n$-bit tweak. It was demonstrated that $\widetilde{F}[1]$ is secure for up to $2^{2n/3}$ queries, while $\widetilde{F}[2]$ is secure for up to $2^n$ queries, assuming the underlying block cipher is an ideal cipher with $n$-bit key and $n$-bit data. Later, at ASIACRYPT'16, Wang et al. showed a birthday bound attack on Mennink's design (which was later corrected in the...

The interest in realizing generic PQC KEM-based PAKEs has increased significantly in the last few years. One such PAKE is the CAKE protocol, proposed by Beguinet et al. (ACNS ’23). However, despite its simple design based on the well-studied PAKE protocol EKE by Bellovin and Merritt (IEEE S&P ’92), both CAKE and its variant OCAKE do not fully protect against quantum adversaries, as they rely on the Ideal Cipher (IC) model. Related and follow-up works, including Pan and Zeng (ASIACRYPT ’23),...

In ASIACRYPT 2019, Andreeva et al. introduced a new symmetric key primitive called the $\textit{forkcipher}$, designed for lightweight applications handling short messages. A forkcipher is a keyed function with a public tweak, featuring fixed-length input and fixed-length (expanding) output. They also proposed a specific forkcipher, ForkSkinny, based on the tweakable block cipher SKINNY, and its security was evaluated through cryptanalysis. Since then, several efficient AEAD and MAC schemes...

We develop and implement AlgoROM, a tool to systematically analyze the security of a wide class of symmetric primitives in idealized models of computation. The schemes that we consider are those that can be expressed over an alphabet consisting of XOR and function symbols for hash functions, permutations, or block ciphers. We implement our framework in OCaml and apply it to a number of prominent constructions, which include the Luby–Rackoff (LR), key-alternating Feistel (KAF), and...

MPC-in-the-Head (MPCitH) has recently gained traction as a foundation for post-quantum signature schemes, offering robust security without trapdoors. Despite its strong security profile, MPCitH-based schemes suffer from high computational overhead and large signature sizes, limiting their practical application. This work addresses these inefficiencies by relaxing vector commitments within MPCitH-based schemes. We introduce the concept of vector semi-commitment, which relaxes the binding...

In FSE'16, Luykx et al. have proposed $\textsf{LightMAC}$ that provably achieves a query length independent PRF security bound. To be precise, the construction achieves security roughly in the order of $O(q^2/2^n)$, when instantiated with two independently keyed $n$-bit block ciphers and $q$ is the total number of queries made by the adversary. Subsequently, in ASIACRYPT'17, Naito proposed a beyond-birthday-bound variant of the $\textsf{LightMAC}$ construction, dubbed as...

We extend the Linicrypt framework for characterizing hash function security as proposed by McQuoid, Swope, and Rosulek (TCC 2018) to support constructions in the ideal cipher model. In this setting, we give a characterization of collision- and second-preimage-resistance in terms of a linear-algebraic condition on Linicrypt programs, and present an efficient algorithm for determining whether a program satisfies the condition. As an application, we consider the case of the block cipherbased...

MRAE security is an important goal for many AEAD applications where the nonce uniqueness cannot be maintained and security risks are significant. However, MRAE schemes can be quite expensive. Two of the SoTA MRAE-secure schemes; Deoxys-II and AES-GCM-SIV rely on internal parallelism and special instructions to achieve competitive performance. However, they both suffer from the same bottleneck, they have at least one call to the underlying primitive that cannot be parallelized to any other...

Ciphertext-independent updatable encryption (UE) allows to rotate encryption keys and update ciphertexts via a token without the need to first download the ciphertexts. Although, syntactically, UE is a symmetric-key primitive, ciphertext-independent UE with forward secrecy and post-compromise security is known to imply public-key encryption (Alamati, Montgomery and Patranabis, CRYPTO 2019). Constructing post-quantum secure UE turns out to be a difficult task. While lattices offer the...

Driven by the NIST's post-quantum standardization efforts and the selection of Kyber as a lattice-based Key-Encapsulation Mechanism (KEM), several Password Authenticated Key Exchange (PAKE) protocols have been recently proposed that leverage a KEM to create an efficient, easy-to-implement and secure PAKE. In two recent works, Beguinet et al. (ACNS 2023) and Pan and Zeng (ASIACRYPT 2023) proposed generic compilers that transform KEM into PAKE, relying on an Ideal Cipher (IC) defined over a...

We revisit the construction of signature schemes using the MPC-in-the-head paradigm. We obtain two main contributions: – We observe that previous signatures in the MPC-in-the-head paradigm must rely on a salted version of the GGM puncturable pseudorandom function (PPRF) to avoid collision attacks. We design a new efficient PPRF construction that is provably secure in the multi-instance setting. The security analysis of our PPRF, in the ideal cipher model, is quite involved and forms a...

We continue the study of $t$-wise independence of substitution-permutation networks (SPNs) initiated by the recent work of Liu, Tessaro, and Vaikuntanathan (CRYPTO 2021). Our key technical result shows that when the S-boxes are randomly and independently chosen and kept secret, an $r$-round SPN with input length $n = b \cdot k$ is $2^{-\Theta(n)}$-close to $t$-wise independent within $r = O(\min\{k, \log t\})$ rounds for any $t$ almost as large as $2^{b/2}$. Here, $b$ is the input length of...

ZK-SNARKs, a fundamental component of privacy-oriented payment systems, identity protocols, or anonymous voting systems, are advanced cryptographic protocols for verifiable computation: modern SNARKs allow to encode the invariants of a program, expressed as an arithmetic circuit, in an appropriate constraint language from which short, zero-knowledge proofs for correct computations can be constructed. One of the most important computations that is run through SNARK systems is the...

The KHAPE-HMQV protocol is a state-of-the-art highly efficient asymmetric password-authenticated key exchange protocol that provides several desirable security properties, but has the drawback of being vulnerable to quantum adversaries due to its reliance on discrete logarithm-based building blocks: solving a single discrete logarithm allows the attacker to perform an offline dictionary attack and recover the password. We show how to modify KHAPE-HMQV to make the protocol quantum-annoying: a...

We revisit OCAKE (ACNS 23), a generic recipe that constructs password-based authenticated key exchange (PAKE) from key encapsulation mechanisms (KEMs), to allow instantiations with post-quantums KEM like KYBER. The ACNS23 paper left as an open problem to argue security against quantum attackers, with its security proof being in the universal composability (UC) framework. This is common for PAKE, however, at the time of this submission’s writing, it was not known how to prove (computational)...

We propose a generic construction of password-based authenticated key exchange (PAKE) from key encapsulation mechanisms (KEM). Assuming that the KEM is oneway secure against plaintext-checkable attacks (OW-PCA), we prove that our PAKE protocol is \textit{tightly secure} in the Bellare-Pointcheval-Rogaway model (EUROCRYPT 2000). Our tight security proofs require ideal ciphers and random oracles. The OW-PCA security is relatively weak and can be implemented tightly with the Diffie-Hellman...

The random oracle model is an instrument used for proving that protocol has no structural flaws when settling with standard hash properties is impossible or fairly difficult. In practice, however, random oracles have to be instantiated with some specific hash functions, which are not random oracles. Hence, in the real world, an adversary has broader capabilities than considered in the random oracle proof — it can exploit the peculiarities of a specific hash function to achieve its goal. In a...

The hash function Romulus-H is a finalist in the NIST Lightweight Cryptography competition. It is based on the Hirose double block-length (DBL) construction which is provably secure when used with an ideal block cipher. However, in practice, ideal block ciphers can only be approximated. Therefore, the security of concrete instantiations must be cryptanalyzed carefully; the security margin may be higher or lower than in the secret-key setting. So far, the Hirose DBL construction has been...

Constructions based on two public permutation calls are very common in today’s cryptographic community. However, each time a new construction is introduced, a dedicated proof must be carried out to study the security of the construction. In this work, we propose a new tool to analyze the security of these constructions in a modular way. This tool is built on the idea of the classical mirror theory for block cipher based constructions, such that it can be used for security proofs in the ideal...

Automated cryptanalysis has taken center stage in the arena of cryptanalysis since the pioneering work by Mouha et al. which showcased the power of Mixed Integer Linear Programming (MILP) in solving cryptanalysis problems that otherwise, required significant effort. Since its inception, research in this area has moved in primarily two directions. One is to model more and more classical cryptanalysis tools as optimization problems to leverage the ease provided by state-of-the-art solvers. The...

We construct non-malleable codes in the split-state model with codeword length $m + 3\lambda$ or $m+5\lambda$, where $m$ is the message size and $\lambda$ is the security parameter, depending on how conservative one is. Our scheme is very simple and involves a single call to a block cipher meeting a new security notion which we dub entropic fixed-related-key security, which essentially means that the block cipher behaves like a pseudorandom permutation when queried upon inputs sampled from a...

Impossible differential (ID) cryptanalysis is one of the most important attacks on block ciphers. The Mixed Integer Linear Programming (MILP) model is a popular method to determine whether a specific difference pair is an ID. Unfortunately, due to the huge search space (approximately $2^{2n}$ for a cipher with a block size $n$ bits), we cannot leverage this technique to exhaust all difference pairs, which is a well-known long-standing problem. In this paper, we propose a systematic...

This paper provides the first analysis of reflection ciphers such as PRINCE from a provable security viewpoint. As a first contribution, we initiate the study of key-alternating reflection ciphers in the ideal permutation model. Specifically, we prove the security of the two-round case and give matching attacks. The resulting security bound takes form \(O(qp^2/2^{2n}+q^2/2^n)\), where \(q\) is the number of construction evaluations and \(p\) is the number of direct adversarial queries to...

In CRYPTO'21, Shen et al. have proved in the ideal cipher model that $\textsf{Two-Keyed-DbHtS}$ construction is secure up to $2^{2n/3}$ queries in the multi-user setting independent of the number of users, where the underlying double-block hash function $\textsf{H}$ of the \textsf{Two-Keyed-DbHtS} construction is realized as the concatenation of two independent $n$-bit keyed hash functions $(\textsf{H}_{K_h,1}, \textsf{H}_{K_h, 2})$ such that each of the $n$-bit keyed hash function is...

Selective opening (SO) security is one of the most important security notions of public key encryption (PKE) in a multi-user setting. Even though messages and random coins used in some ciphertexts are leaked, SO security guarantees the confidentiality of the other ciphertexts. Actually, it is shown that there exist PKE schemes which meet the standard security such as indistinguishability against chosen ciphertext attacks (IND-CCA security) but do not meet SO security against chosen...

Currently, a vast majority of symmetric-key cryptographic schemes are built as block cipher modes. The block cipher is designed to be hard to distinguish from a random permutation and this is supported by cryptanalysis, while (good) modes can be proven secure if a random permutation takes the place of the block cipher. As such, block ciphers form an abstraction level that marks the border between cryptanalysis and security proofs. In this paper, we investigate a re-factored version of...

Indifferentiability is a powerful notion in cryptography. If a construction is proven to be indifferentiable from an ideal object, it can under certain assumptions instantiate that ideal object in higher-level constructions. Indifferentiability is a particularly useful model for cryptographic hash functions, and myriad results are known proving that a hash function behaves like a random oracle under the assumption that the underlying primitive (typically a compression function, a block...

The goal of this paper is to investigate linear approximations of random functions and permutations. Our motivation is twofold. First, before the distinguishability of a practical cipher from an ideal one can be analysed, the cryptanalyst must have an accurate understanding of the statistical behaviour of the ideal cipher. Secondly, this issue has been neglected both in old and in more recent studies, particularly when multiple linear approximations are being used simultaneously. Traditional...

COMETv1, by Gueron, Jha and Nandi, is a mode of operation for nonce-based authenticated encryption with associated data functionality. It was one of the second round candidates in the ongoing NIST Lightweight Cryptography Standardization Process. In this paper, we study a generalized version of COMETv1, that we call gCOMET, from provable security perspective. First, we present a comprehensive and complete security proof for gCOMET in the ideal cipher model. Second, we view COMET, the...

Energy efficiency is critical in battery-driven devices, and designing energy- optimal symmetric-key ciphers is one of the goals for the use of ciphers in such environments. In the paper by Banik et al. (IACR ToSC 2018), stream ciphers were identified as ideal candidates for low-energy solutions. One of the main conclusions of this paper was that Trivium, when implemented in an unrolled fashion, was by far the most energy-efficient way of encrypting larger quantity of data. In fact, it was...

In this paper, we report the first quantum key-recovery attack on a symmetric block cipher design, using classical queries only, with a more than quadratic time speedup compared to the best classical attack. We study the 2XOR-Cascade construction of Ga{\v{z}}i and Tessaro (EUROCRYPT~2012). It is a key length extension technique which provides an n-bit block cipher with 5n/2 bits of security out of an n-bit block cipher with 2n bits of key, with a security proof in the ideal model. We show...

In this paper, we show that standard model black-box reductions naturally lift to various setup assumptions, such as the random oracle (ROM) or ideal cipher model. Concretely, we prove that a black-box reduction from a security notion P to security notion Q in the standard model can be turned into a non-programmable black-box reduction from P_O to Q_O in a model with a setup assumption O, where P_O and Q_O are the natural extensions of P and Q to a model with a setup assumption O. Our...

OPAQUE [Jarecki et al., Eurocrypt 2018] is an asymmetric password authenticated key exchange (aPAKE) protocol that is being developed as an Internet standard and for use within TLS 1.3. OPAQUE combines an Oblivious PRF (OPRF) with an authenticated key exchange to provide strong security properties, including security against pre-computation attacks (called saPAKE security). However, the security of OPAQUE relies crucially on the security of the OPRF. If the latter breaks (by cryptanalysis,...

Should quantum computers become available, they will reduce the effective key length of basic secret-key primitives, such as blockciphers. To address this we will either need to use blockciphers with inherently longer keys or develop key-length extension techniques to amplify the security of a blockcipher to use longer keys. We consider the latter approach and revisit the FX and double encryption constructions. Classically, FX was proven to be a secure key-length extension technique, while...

Symmetric password-authenticated key exchange (sPAKE) can be seen as an extension of traditional key exchange where two parties agree on a shared key if and only if they share a common secret (possibly low-entropy) password. We present the first sPAKE protocol to simultaneously achieve the following properties: - only two exponentiations per party, the same as plain unauthenticated Diffie-Hellman key agreement (and likely optimal); - optimal round complexity: a single flow (one message...

We provide a new definitional framework capturing the multi-user security of encryption schemes and pseudorandom functions in the face of adversaries that can adaptively compromise users' keys. We provide a sequence of results establishing the security of practical symmetric encryption schemes under adaptive compromise in the random oracle or ideal cipher model. The bulk of analysis complexity for adaptive compromise security is relegated to the analysis of lower-level primitives such as...

In an early version of CRYPTO’17, Mennink and Neves pro- posed EWCDMD, a dual of EWCDM, and showed n-bit security, where n is the block size of the underlying block cipher. In CRYPTO’19, Chen et al. proposed permutation based design SoKAC21 and showed 2n/3- bit security, where n is the input size of the underlying permutation. In this paper we show birthday bound attacks on EWCDMD and SoKAC21, invalidating their security claims. Both attacks exploit an inherent com- position nature present...

Authenticity can be compromised by information leaked via side-channels (e.g., power consumption). Examples of attacks include direct key recoveries and attacks against the tag verification which may lead to forgeries. At FSE 2018, Berti et al. described two authenticated encryption schemes which provide authenticity assuming a “leak-free implementation” of a Tweakable Block Cipher (TBC). Precisely, security is guaranteed even if all the intermediate computations of the target implementation...

We present distinguishing attacks (based on the Birthday Paradox) which show that the use of $2^{\ell}$ permutations for a block cipher is insufficient to obtain a security of $\ell$ bits in the Ideal Cipher Model. The context is that of an Oracle that can provide an Adversary the ciphertexts of a very small number of known plaintexts under a large number of (session) keys and IVs/nonces. Our attacks distinguish an ideal cipher from a ``perfectly ideal'' block cipher, realised as an Oracle...

We study the concrete security of high-performance implementations of half-gates garbling, which all rely on (hardware-accelerated)~AES. We find that current instantiations using $k$-bit wire labels can be completely broken---in the sense that the circuit evaluator learns all the inputs of the circuit garbler---in time $O(2^k/C)$, where $C$ is the total number of (non-free) gates that are garbled, possibly across multiple independent executions. The attack can be applied to existing...

We study the security of symmetric primitives against key-correlated attacks (KCA), whereby an adversary can arbitrarily correlate keys, messages, and ciphertexts. Security against KCA is required whenever a primitive should securely encrypt key-dependent data, even when it is used under related keys. KCA is a strengthening of the previously considered notions of related-key attack (RKA) and key-dependent message (KDM) security. This strengthening is strict, as we show that 2-round...

In this article, we propose two new families of very lightweight and efficient authenticated encryption with associated data (AEAD) modes, Romulus and Remus, that provide security beyond the birthday bound with respect to the block-length $n$. The former uses a tweakable block cipher (TBC) as internal primitive and can be proven secure in the standard model. The later uses a block cipher (BC) as internal primitive and can be proven secure in the ideal cipher model. Both our modes allow to...

The goal of this paper is to investigate the linear cryptanalysis of random functions and permutations. The motivation of this work is twofold. First, before a practical cipher can be distinguished from an ideal one, the cryptanalyst must have an accurate understanding of the statistical behavior of the ideal cipher. Secondly, this issue has been neglected both in old and in more recent studies, particularly when multiple linear approximations are being used simultaneously. Traditionally,...

Oblivious Transfer has played a crucial role in the design of secure multi party computation. Nevertheless, there are not many practical solutions that achieve simulation based security and at the same time instantiable based on different assumptions. In this work, we consider a simulation based security notion that we call endemic security. We show how to construct highly efficient oblivious transfer in the random oracle model that achieves endemic security under a wide range of...

We initiate the study of indifferentiability for public key encryption and other public key primitives. Our main results are definitions and constructions of public key cryptosystems that are indifferentiable from ideal cryptosystems, in the random oracle model. Cryptosystems include Public key encryption, Digital signatures, Non-interactive key agreement. Our schemes are based on standard public key assumptions. By being indifferentiable from an ideal object, our schemes satisfy any...

We introduce password-authenticated public-key encryption (PAPKE), a new cryptographic primitive. PAPKE enables secure end-to-end encryption between two entities without relying on a trusted third party or other out-of-band mechanisms for authentication. Instead, resistance to man-in-the-middle attacks is ensured in a human-friendly way by authenticating the public key with a shared password, while preventing offline dictionary attacks given the authenticated public key and/or the...

The need for high-quality randomness in cryptography makes random-number generation one of its most fundamental tasks. A recent important line of work (initiated by Dodis et al., CCS ’13) focuses on the notion of *robustness* for *pseudorandom number generators (PRNGs) with inputs*—these are primitives that use various sources to accumulate sufficient entropy into a state, from which pseudorandom bits are extracted. Robustness ensures that PRNGs remain secure even under state compromise and...

In the last decade, several works have focused on finding the best way to model the leakage in order to obtain provably secure implementations. One of the most realistic models is the noisy leakage model, introduced in [PR13,DDF14] together with secure constructions. These works suffer from various limitations, in particular the use of ideal leak-free gates in [PR13] and an important loss (in the size of the field) in the reduction in [DDF14]. In this work, we provide new strategies to...

We present hash functions that are almost optimally one-way in the quantum setting. Our hash functions are based on the Merkle-Damgård construction iterating a Davies-Meyer compression function, which is built from a block cipher. The quantum setting that we use is a natural extention of the classical ideal cipher model. Recent work has revealed that symmetric-key schemes using a block cipher or a public permutation, such as CBC-MAC or the Even-Mansour cipher, can get completely broken with...

We propose a new construction of tweakable block ciphers from standard block ciphers. Our construction, dubbed XHX2, is the cascade of two independent XHX block ciphers, so it makes two call to the underlying block cipher using tweak-dependent keys. We prove the security of XHX2 up to min{2^{2(n+m)/3},2^{n+m/2}} queries (ignoring logarithmic factors) in the ideal cipher model, when the block cipher operates on n-bit blocks using m-bit keys. The XHX2 tweakable block cipher is the first...

The random-permutation model (RPM) and the ideal-cipher model (ICM) are idealized models that offer a simple and intuitive way to assess the conjectured standard-model security of many important symmetric-key and hash-function constructions. Similarly, the generic-group model (GGM) captures generic algorithms against assumptions in cyclic groups by modeling encodings of group elements as random injections and allows to derive simple bounds on the advantage of such...

We give a framework for trapdoor-permutation-based sequential aggregate signatures (SAS) that unifies and simplifies prior work and leads to new results. The framework is based on ideal ciphers over large domains, which have recently been shown to be realizable in the random oracle model. The basic idea is to replace the random oracle in the full-domain-hash signature scheme with an ideal cipher. Each signer in sequence applies the ideal cipher, keyed by the message, to the output of the...

Algebraic Manipulation Detection (AMD) codes [CDF+08] are keyless message authentication codes that protect messages against additive tampering by the adversary assuming that the adversary cannot "see" the codeword. For certain applications, it is unreasonable to assume that the adversary computes the added offset without any knowledge of the codeword c. Recently, Ahmadi and Safavi-Naini [AS13], and then Lin, Safavi-Naini, and Wang [LSW16] gave a construction of leakage-resilient AMD codes...

Tweakable block ciphers are important primitives for designing cryptographic schemes with high security. In the absence of a standardized tweakable block cipher, constructions built from classical block ciphers remain an interesting research topic in both theory and practice. Motivated by Mennink's F[2] publication from 2015, Wang et al. proposed 32 optimally secure constructions at ASIACRYPT'16, all of which employ two calls to a classical block cipher each. Yet, those constructions were...

We introduce identity-based format-preserving encryption (IB-FPE) as a way to localize and limit the damage to format-preserving encryption (FPE) from key exposure. We give definitions, relations between them, generic attacks and two transforms of FPE schemes to IB-FPE schemes. As a special case, we introduce and cover identity-based tweakable blockciphers. We apply all this to analyze DFF, an FPE scheme proposed to NIST for standardization.

Hidden vector encryption (HVE), introduced by Boneh and Waters in TCC'07, is an expressive sub-class of predicate encryption, that allows conjunctive, subset, range and comparison queries over encrypted data. All existing HVE constructions in the cryptographic literature use bilinear pairings over either composite order or prime order groups. In this paper, we address the open problem of constructing a lightweight symmetric-key HVE scheme that does not use bilinear pairings, but only...

A number of cryptographic schemes are built from (keyless) permutations, which are either designed in an ad-hoc fashion or are obtained by fixing the key in a block cipher. Security proofs for these schemes, however, idealize this permutation, i.e., making it random and accessible, as an oracle, to all parties. Finding plausible concrete assumptions on such permutations that guarantee security of the resulting schemes has remained an elusive open question. This paper initiates the study of...

The iterated Even--Mansour (EM) ciphers form the basis of many block cipher designs. Several results have established their security in the CPA/CCA models, under related-key attacks, and in the indifferentiability framework. In this work, we study the Even--Mansour ciphers under key-dependent message (KDM) attacks. KDM security is particularly relevant for block ciphers since non-expanding mechanisms are convenient in setting such as full disk encryption (where various forms of...

Two types of tweakable blockciphers based on classical blockciphers have been presented over the last years: non-tweak-rekeyable and tweak-rekeyable, depending on whether the tweak may influence the key input to the underlying blockcipher. In the former direction, the best possible security is conjectured to be $2^{\sigma n/(\sigma+1)}$, where $n$ is the size of the blockcipher and $\sigma$ is the number of blockcipher calls. In the latter direction, Mennink and Wang et al. presented...

Linear cryptanalysis makes use of statistical models that consider linear approximations over practical and ideal block ciphers as binary random variables. Recently, more complex models have been proposed that take also into account the statistical behavior of correlations of linear approximations over the key space of the cipher and over the randomness of the ideal cipher. The goal of this ongoing work is to investigate independence properties of linear approximations and their...

It is widely known that double encryption does not substantially increase the security of a block cipher. Indeed, the classical meet-in-the middle attack recovers the $2k$-bit secret key at the cost of roughly $2^k$ off-line enciphering operations, in addition to very few known plaintext-ciphertext pairs. Thus, essentially as efficiently as for the underlying cipher with a $k$-bit key. This paper revisits double encryption under the lens of multi-user security. We prove that its security...

Group Password-Based Authenticated Key Exchange (GPAKE) allows a group of users to establish a secret key, as long as all of them share the same password. However, in existing GPAKE protocols as soon as one user runs the protocol with a non-matching password, all the others abort and no key is established. In this paper we seek for a more flexible, yet secure, GPAKE and put forward the notion of partitioned GPAKE. Partitioned GPAKE tolerates users that run the protocol on different...

Ever since Keccak won the SHA3 competition, sponge-based constructions are being suggested for many different applications, including pseudo-random number generators (PRNGs). Sponges are very desirable, being well studied, increasingly efficient to implement and simplistic in their design. The initial construction of a sponge-based PRNG (Bertoni et al. CHES 2010) based its security on the well known sponge indifferentiability proof in the random permutation model and provided no forward...

The concrete security bounds for some blockcipher-based constructions sometimes become worrisome or even vacuous; for example, when a light-weight blockcipher is used, when large amounts of data are processed, or when a large number of connections need to be kept secure. Rotating keys helps, but introduces a ``hybrid factor'' $m$ equal to the number of keys used. In such instances, analysis in the ideal-cipher model (ICM) can give a sharper picture of security, but this heuristic is called...

The confidentiality notion of security against selective opening attacks considers adver- saries that obtain challenge ciphertexts and are allowed to adaptively open them, thereby revealing the encrypted message and the randomness used to encrypt. The SO notion is stronger than that of CCA security and is often required when formally arguing towards the security of multi-user applications. While different ways of achieving correspondingly secure schemes are known, as they generally employ...

BLAKE2 is a hash function introduced at ACNS 2013, which has been adopted in many constructions and applications. It is a successor to the SHA-3 finalist BLAKE, which received a significant amount of security analysis. Nevertheless, BLAKE2 introduces sufficient changes so that not all results from BLAKE carry over, meaning new analysis is necessary. To date, all known cryptanalysis done on BLAKE2 has focused on its underlying building blocks, with little focus placed on understanding...

Shannon defined an ideal $(\kappa,n)$-blockcipher as a secrecy system consisting of $2^{\kappa}$ independent $n$-bit random permutations. In this paper, we revisit the following question: in the ideal cipher model, can a cascade of several ideal $(\kappa,n)$-blockciphers realize an ideal $(2\kappa,n)$-blockcipher? The motivation goes back to Shannon's theory on product secrecy systems, and similar question was considered by Even and Goldreich (CRYPTO '83) in different settings. We give the...

We initiate the study of multi-user (mu) security of authenticated encryption (AE) schemes as a way to rigorously formulate, and answer, questions about the "randomized nonce" mechanism proposed for the use of the AE scheme GCM in TLS 1.3. We (1) Give definitions of mu ind (indistinguishability) and mu kr (key recovery) security for AE (2) Characterize the intent of nonce randomization as being improved mu security as a defense against mass surveillance (3) Cast the method as a (new) AE...

Hash functions are often constructed based on permutations or blockciphers, and security proofs are typically done in the ideal permutation or cipher model. However, once these random primitives are instantiated, vulnerabilities of these instantiations may nullify the security. At ASIACRYPT 2007, Knudsen and Rijmen introduced known-key security of blockciphers, which gave rise to many distinguishing attacks on existing blockcipher constructions. In this work, we analyze the impact of such...

Recent advances in block-cipher theory deliver security analyses in models where one or more underlying components (e.g., a function or a permutation) are {\em ideal} (i.e., randomly chosen). This paper addresses the question of finding {\em new} constructions achieving the highest possible security level under minimal assumptions in such ideal models. We present a new block-cipher construction, derived from the Swap-or-Not construction by Hoang et al. (CRYPTO '12). With $n$-bit block...

We propose and analyze the LIZARD-construction, a way to construct keystream generator (KSG) based stream ciphers with provable $\frac{2}{3} n$-security with respect to generic time-memory-data tradeoff attacks. Note that for the vast majority of known practical KSG-based stream ciphers such attacks reduce the effective key length to the birthday bound $n/2$, where $n$ denotes the inner state length of the underlying KSG. This implies that practical stream ciphers have to have a...

We revisit the security (as a pseudorandom permutation) of cascading-based constructions for block-cipher key-length extension. Previous works typically considered the extreme case where the adversary is given the entire codebook of the construction, the only complexity measure being the number $q_e$ of queries to the underlying ideal block cipher, representing adversary's secret-key-independent computation. Here, we initiate a systematic study of the more natural case of an adversary...

In authenticated encryption schemes, there are two techniques for handling long ciphertexts while working within the constraints of a low buffer size: Releasing unverified plaintext (RUP) or Producing intermediate tags (PIT). In this paper, in addition to the two techniques, we propose another way to handle a long ciphertext with a low buffer size by storing and releasing only one (generally, or only few) intermediate state without releasing or storing any part of an unverified plaintext and...

This paper discusses provable security of two types of cascade encryptions. The first construction $\CE^l$, called $l$-cascade encryption, is obtained by sequentially composing $l$ blockcipher calls with independent keys. The security of $\CE^l$ has been a longstanding open problem until Gaži and Maurer~\cite{GM09} proved its security up to $2^{\ka+\min\{\frac{n}{2},\ka\}}$ query complexity for large cascading length, where $\ka$ and $n$ denote the key size and the block size of the...

We present security proofs for the BLT signature scheme in the model, where hash functions are built from ideal components (random oracles, ideal ciphers, etc.). We show that certain strengthening of the Pre-image Awareness (PrA) conditions like boundedness of the extractor, and certain natural properties (balancedness and the so-called output one-wayness) of the hash function are sufficient for existential unforgeability of the BLT signature scheme.

Computer log files constitute a precious resource for system administrators for discovering and comprehending security breaches. A prerequisite of any meaningful log analysis is that attempts of intruders to cover their traces by modifying log entries are thwarted by storing them in a tamper-resistant manner. Some solutions employ cryptographic authentication when storing log entries locally, and let the authentication scheme's property of forward security ensure that the cryptographic keys...

In this paper, we introduce a new class of double-block-length hash functions. Using the ideal cipher model, we prove that these hash functions, dubbed \MJH, are asymptotically collision resistant up to $O(2^{n(1-\epsilon)})$ query complexity for any $\epsilon>0$ in the iteration, where $n$ is the block size of the underlying blockcipher. When based on $n$-bit key blockciphers, our construction, being of rate 1/2, provides better provable security than MDC-2, the only known construction of...

In this paper, we revisit the old problem asking the exact provable security of triple encryption in the ideal cipher model. For a blockcipher with key length k and block size n, triple encryption is known to be secure up to 2^{k+min{k/2,n/2}} queries, while the best attack requires 2^{k+min{k,n/2}} query complexity. So there is a gap between the upper and lower bounds for the security of triple encryption. We close this gap by proving the security up to 2^{k+min{k,n/2}} query complexity....

The equivalence of the random-oracle model and the ideal-cipher model has been studied in a long series of results. Holenstein, Künzler, and Tessaro (STOC, 2011) have recently completed the picture positively, assuming that, roughly speaking, equivalence is indifferentiability from each other. However, under the stronger notion of reset indifferentiability this picture changes significantly, as Demay et al. (EUROCRYPT, 2013) and Luykx et al. (ePrint, 2012) demonstrate. We complement these...

Preneel et al.~(Crypto 1993) assessed 64 possible ways to construct a compression function out of a blockcipher. They conjectured that 12 out of these 64 so-called PGV constructions achieve optimal security bounds for collision resistance and preimage resistance. This was proven by Black et al.~(Journal of Cryptology, 2010), if one assumes that the blockcipher is ideal. This result, however, does not apply to ``non-ideal'' blockciphers such as AES. To alleviate this problem, we revisit the...

The indifferentiability framework by Maurer, Renner and Holenstein (MRH; TCC 2004) formalizes a sufficient condition to safely replace a random oracle by a construction based on a (hopefully) weaker assumption such as an ideal cipher. Indeed, many indifferentiable hash functions have been constructed and could since be used in place of random oracles. Unfortunately, Ristenpart, Shacham, and Shrimpton (RSS; Eurocrypt 2011) discovered that for a large class of security notions, the MRH...

The Advanced Encryption Standard (AES) is the most widely used block cipher. The high level structure of AES can be viewed as a (10-round) key-alternating cipher, where a t-round key-alternating cipher KA_t consists of a small number $t$ of fixed permutations P_i on n bits, separated by key addition: KA_t(K,m)= k_t + P_t(... k_2 + P_2(k_1 + P_1(k_0 + m))...), where (k_0,...,k_t) are obtained from the master key K using some key derivation function. For t=1, KA_1 collapses to the...

Cascading-based constructions represent the predominant approach to the problem of key-length extension for block ciphers. Besides the plain cascade, existing works also consider its modification containing key-whitening steps between the invocations of the block cipher, called randomized cascade or XOR-cascade. We contribute to the understanding of the security of these two designs by giving the following attacks and security proofs, assuming an underlying ideal block cipher with key...

A double-block-length (DBL) hash mode of block ciphers, MJH has been proved to be collision-resistant in the ideal cipher model upto $2^{2n/3- \log n}$ queries. In this paper we provide first cryptanalytic results for MJH. We show that a collision attack on MJH has the time complexity below the birthday bound. When block ciphers with 128-bit blocks are used, it has time complexity around $2^{124}$, which is to be compared to the birthday attack having complexity $2^{128}$. We also give a...

We revisit the problem of building dual-model secure (DMS) hash functions that are simultaneously provably collision resistant (CR) in the standard model and provably pseudorandom oracle (PRO) in an idealized model. Designing a DMS hash function was first investigated by Ristenpart and Shrimpton (ASIACRYPT 2007); they put forth a generic approach, called Mix-Compress-Mix (MCM), and showed the feasibility of the MCM approach with a secure (but inefficient) construction. An improved...

We present the notion of PROG-KDM security for public-key encryption schemes. This security notion captures both KDM security and revealing of secret keys (key corruptions) in a single definition. This is achieved by requiring the existence of a simulator that can program ciphertexts when a secret key is revealed, i.e., the simulator can delay the decision what plaintext is contained in what ciphertext to the moment where the ciphertext is opened. The definition is formulated in the random...

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...

We present the first collision and preimage security analysis of MDC-4, a 24 years old construction for transforming an n-bit block cipher into a 2n-bit hash function. We start with the MDC-4 compression function based on two independent block ciphers, and prove that any adversary with query access to the underlying block ciphers requires at least 2^{5n/8} queries (asymptotically) to find a collision, and at least 2^{5n/4} queries to find a preimage. These results then directly carry over to...

There are four somewhat classical double length block cipher based compression functions known: MDC-2, MDC-4, Abreast-DM, and Tandem-DM. They all have been developed over 20 years ago. In recent years, cryptographic research has put a focus on block cipher based hashing and found collision security results for three of them (MDC-2, Abreast-DM, Tandem-DM). In this paper, we add MDC-4, which is part of the IBM CLiC cryptographic module (FIPS 140-2 Security Policy for IBM CrytoLite in C,...

This paper considers---for the first time---the concept of key-alternating ciphers in a provable security setting. Key-alternating ciphers can be seen as a generalization of a construction proposed by Even and Mansour in 1991. This construction builds a block cipher $PX$ from an $n$-bit permutation $P$ and two $n$-bit keys $k_0$ and $k_1$, setting $PX_{k_0,k_1}(x)=k_1\oplus P(x\oplus k_0)$. Here we consider a (natural) extension of the Even-Mansour construction with $t$ permutations...

We analyze the security of the SHA-3 finalist BLAKE. The BLAKE hash function follows the HAIFA design methodology, and as such it achieves optimal preimage, second preimage and collision resistance, and is indifferentiable from a random oracle up to approximately 2^{n/2} assuming the underlying compression function is ideal. In our work we show, however, that the compression function employed by BLAKE exhibits a non-random behavior and is in fact differentiable in only 2^{n/4} queries. Our ...

Since Rijndael was chosen as the Advanced Encryption Standard, improving upon 7-round attacks on the 128-bit key variant or upon 8-round attacks on the 256-bit key variant has been one of the most difficult challenges in the cryptanalysis of block ciphers for more than a decade. In this paper we present a novel technique of block cipher cryptanalysis with bicliques, which leads to the following results: - The first key recovery attack on 9 out of 14 rounds of AES-256 with computational...

Bellare and Kohno introduced a formal framework for the study of related-key attacks against blockciphers. They established sufficient conditions (output-unpredictability and collision-resistance) on the set of related-key-deriving (RKD) functions under which an ideal cipher is secure against related-key attacks, and suggested this could be used to derive security goals for real blockciphers. However, to do so requires the reinterpretation of results proven in the ideal-cipher model for the...

We give improved bounds on the preimage security of the three ``classical'' double-block-length, double-call, blockcipher-based compression functions, these being Abreast-DM, Tandem-DM and Hirose's scheme. For Hirose's scheme, we show that an adversary must make at least $2^{2n-5}$ blockcipher queries to achieve chance $0.5$ of inverting a randomly chosen point in the range. For Abreast-DM and Tandem-DM we show that at least $2^{2n-10}$ queries are necessary. These bounds improve upon the...

The random oracle model and the ideal cipher model were proven equivalent after Coron et al. (CRYPTO 08) showed that six Feistel rounds are indifferentiable from an ideal cipher. This result, however, does not imply the inexistence of superpolynomial-time attacks outperforming generic (exponential-time) attacks. The finding of such attacks was left open by Coron et al., and is of utmost importance to evaluate the security of concrete fixed-parameters systems, as deployed in practice, for...

We prove that Tandem-DM, one of the two ``classical'' schemes for turning a blockcipher of $2n$-bit key into a double block length hash function, has birthday-type collision resistance in the ideal cipher model. A collision resistance analysis for Tandem-DM achieving a similar birthday-type bound was already proposed by Fleischmann, Gorski and Lucks at FSE 2009. As we detail, however, the latter analysis is wrong, thus leaving the collision resistance of Tandem-DM as an open problem until now.

This paper fills an important foundational gap with the first proofs, under standard assumptions and in the standard model, of the existence of pseudorandom functions (PRFs) and pseudorandom permutations (PRPs) resisting rich and relevant forms of related-key attacks (RKA). An RKA allows the adversary to query the function not only under the target key but under other keys derived from it in adversary-specified ways. Based on the Naor-Reingold PRF we obtain an RKA-PRF whose keyspace is a...

We describe the first domain extender for ideal ciphers, {\sl i.e.} we show a construction that is indifferentiable from a $2n$-bit ideal cipher, given a $n$-bit ideal cipher. Our construction is based on a $3$-round Feistel, and is more efficient than first building a $n$-bit random oracle from a $n$-bit ideal cipher and then a $2n$-bit ideal cipher from a $n$-bit random oracle (using a $6$-round Feistel). We also show that $2$ rounds are not enough for indifferentiability by exhibiting a...

We provide the first proof of security for Abreast-DM, one of the oldest and most well-known constructions for turning a block cipher with $n$-bit block length and $2n$-bit key length into a 2n-bit cryptographic hash function. In particular, we prove that when Abreast-DM is instantiated with AES-256, i.e. a block cipher with 128-bit block length and 256-bit key length, any adversary that asks less than 2^124.42 queries cannot find a collision with success probability greater than 1/2....