## CryptoDB

### Bart Mennink

#### Publications

**Year**

**Venue**

**Title**

2024

TOSC

Permutation-Based Hashing Beyond the Birthday Bound
Abstract

It is known that the sponge construction is tightly indifferentiable from a random oracle up to around 2c/2 queries, where c is the capacity. In particular, it cannot provide generic security better than half of the underlying permutation size. In this paper, we aim to achieve hash function security beating this barrier. We present a hashing mode based on two b-bit permutations named the double sponge. The double sponge can be seen as the sponge embedded within the double block length hashing paradigm, making two permutation calls in parallel interleaved with an efficient mixing function. Similarly to the sponge, the permutation size is split as b = r+c, and the underlying compression function absorbs r bits at a time. We prove that the double sponge is indifferentiable from a random oracle up to around 22c/3 queries. This means that the double sponge achieves security beyond the birthday bound in the capacity. In addition, if c > 3b/4, the double sponge beats the birthday bound in the primitive size, to our knowledge being the first hashing mode based on a permutation that accomplices this feature.

2024

TOSC

Tightening Leakage Resilience of the Suffix Keyed Sponge
Abstract

Lightweight cryptographic constructions are often optimized on multiple aspects that put the security bounds to the limit. In this respect, it is important to obtain security bounds that are tight and give an accurate and exact indication of the generic security. However, whereas for black-box security bounds it has become common practice to argue tightness of security bounds, for leakage resilience security bounds this is not the case. This is unfortunate, as for leakage resilience results, tightness is even more important as there is already a lossiness incurred in capturing the actual leakage by a theoretical model in the first place.In this work, we consider the SuKS (Suffix Keyed Sponge) PRF construction and investigate tightness of the leakage resilience bound of Dobraunig and Mennink (ToSC 2019). We observe that, although their black-box security result is tight, their leakage resilience bound is not tight in their bounded leakage term λ. We observe that this is caused by the fact that parts of the security bound contain a term covering multicollisions and a term covering leakage, but an adversary is unable to combine both. We next consider improved security of the SuKS for two types of leakage: fixed position leakage, where the adversary directly learns the value of λ bits of a secret state, and Hamming weight leakage, where the Hamming weight of a fixed part of the state is leaked. For fixed position leakage, a very generous form of bounded leakage, we improve the original bound by making wise use of the multicollision limit function of Daemen et al. (ASIACRYPT 2017). For the more realistic setting of Hamming weight leakage, we structurally revisit the multicollision limit function analysis by including Hamming weight in the computation, a problem that is difficult on its own due to the non-uniform character of this type of leakage. In both cases, we improve and tighten the leakage resilience bound of Dobraunig and Mennink. The improved bound for the SuKS has immediate consequences for the leakage resilience of the NIST lightweight cryptography competition finalist ISAP v2, an authenticated encryption scheme that uses the SuKS internally.

2023

CRYPTO

Revisiting the Indifferentiability of the Sum of Permutations
Abstract

The sum of two $n$-bit pseudorandom permutations is known to behave like a pseudorandom function with $n$ bits of security. A recent line of research has investigated the security of two public $n$-bit permutations and its degree of indifferentiability. Mandal et al. (INDOCRYPT 2010) proved $2n/3$-bit security, Mennink and Preneel (ACNS 2015) pointed out a non-trivial flaw in their analysis and re-proved $2n/3$-bit security. Bhattacharya and Nandi (EUROCRYPT 2018) eventually improved the result to $n$-bit security. Recently, Gunsing at CRYPTO 2022 already observed that a proof technique used in this line of research only holds for sequential indifferentiability. We revisit the line of research in detail, and observe that the strongest bound of $n$-bit security has two other serious issues in the reasoning, the first one is actually the same non-trivial flaw that was present in the work of Mandal et al., while the second one discards biases in the randomness influenced by the distinguisher. More concretely, we introduce two attacks that show limited potential of different approaches. We (i) show that the latter issue that discards biases only holds up to $2^{3n/4}$ queries, and (ii) perform a differentiability attack against their simulator in $2^{5n/6}$ queries. On the upside, we revive the result of Mennink and Preneel and show $2n/3$-bit regular indifferentiability security of the sum of public permutations.

2023

TOSC

Understanding the Duplex and Its Security
Abstract

At SAC 2011, Bertoni et al. introduced the keyed duplex construction as a tool to build permutation based authenticated encryption schemes. The construction was generalized to full-state absorption by Mennink et al. (ASIACRYPT 2015). Daemen et al. (ASIACRYPT 2017) generalized it further to cover much more use cases, and proved security of this general construction, and Dobraunig and Mennink (ASIACRYPT 2019) derived a leakage resilience security bound for this construction. Due to its generality, the full-state keyed duplex construction that we know today has plethora applications, but the flip side of the coin is that the general construction is hard to grasp and the corresponding security bounds are very complex. Consequently, the state-of-the-art results on the full-state keyed duplex construction are not used to the fullest. In this work, we revisit the history of the duplex construction, give a comprehensive discussion of its possibilities and limitations, and demonstrate how the two security bounds (of Daemen et al. and Dobraunig and Mennink) can be interpreted in particular applications of the duplex.

2023

TOSC

EliMAC: Speeding Up LightMAC by around 20%
Abstract

Universal hash functions play a prominent role in the design of message authentication codes and the like. Whereas it is known how to build highly efficient sequential universal hash functions, parallel non-algebraic universal hash function designs are always built on top of a PRP. In such case, one employs a relatively strong primitive to obtain a function with a relatively weak security model. In this work, we present EliHash, a construction of a parallel universal hash function from non-compressing universal hash functions, and we back it up with supporting security analysis. We use this construction to design EliMAC, a message authentication code similar to LightMAC. We consider a heuristic instantiation of EliMAC with roundreduced AES, and argue that this instantiation of EliMAC is much more efficient than LightMAC, it is around 21% faster, and additionally allows for precomputation of the keys, albeit with a stronger assumption on the AES primitive than in LightMAC. These observations are backed up with an implementation of our scheme.

2023

ASIACRYPT

Generic Security of the SAFE API and Its Applications
Abstract

We provide security foundations for SAFE, a recently introduced API framework for sponge-based hash functions tailored to prime-field-based protocols. SAFE aims to provide a robust and foolproof interface, has been implemented in the Neptune hash framework and some zero-knowledge proof projects, but despite its usability and applicability it currently lacks any security proof. Such a proof would not be straightforward as SAFE abuses the inner part of the sponge and fills it with protocol-specific data.
In this work we identify the SAFECore as versatile variant sponge construction underlying SAFE, we prove indifferentiability of SAFECore for all (binary and prime) fields up to around $|\mathbb{F}_p|^{c/2}$ queries, where $\mathbb{F}_p$ is the underlying field and $c$ the capacity, and we apply this security result to various use cases. We show that the SAFE-based protocols of plain hashing, authenticated encryption, verifiable computation, non-interactive proofs, and commitment schemes are secure against a wide class of adversaries, including those dealing with multiple invocations of a sponge in a single application. Our results pave the way of using SAFE with the full taxonomy of hash functions, including SNARK-, lattice-, and x86-friendly hashes.

2022

CRYPTO

Tight Preimage Resistance of the Sponge Construction
📺
Abstract

The cryptographic sponge is a popular method for hash function design. The construction is in the ideal permutation model proven to be indifferentiable from a random oracle up to the birthday bound in the capacity of the sponge. This result in particular implies that, as long as the attack complexity does not exceed this bound, the sponge construction achieves a comparable level of collision, preimage, and second preimage resistance as a random oracle. We investigate these state-of-the-art bounds in detail, and observe that while the collision and second preimage security bounds are tight, the preimage bounds not tight. We derive an improved and tight preimage security bound for the cryptographic sponge construction.
The result has direct implications for various lightweight cryptographic hash functions. For example, the NIST Lightweight Cryptography finalist Ascon-Hash does not generically achieve $2^{128}$ preimage security as claimed, but even $2^{192}$ preimage security. Comparable improvements are obtained for the modes of Spongent, PHOTON, ACE, Subterranean 2.0, and QUARK, among others.

2022

ASIACRYPT

Security of Truncated Permutation Without Initial Value
📺
Abstract

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 cipher, or a permutation) is random. Recently, advances have been made in proving indifferentiability of one-way functions with fixed input length. One such example is truncation of a permutation. If one evaluates a random permutation on an input value concatenated with a fixed initial value, and truncates the output, one obtains a construction that is indifferentiable from a random function up to a certain bound (Dodis et al., FSE 2009; Choi et al., ASIACRYPT 2019). Security of this construction, however, is in part determined by the length of the initial value; omission of this fixed value yields an insecure construction.
In this paper, we reconsider truncation of a permutation, and prove that the construction is indifferentiable from a random oracle, even if this fixed initial value is replaced by a randomized value. This randomized value may be the same for different evaluations of the construction, or freshly generated, up to the discretion of the adversary. The security level is the same as that of truncation with fixed initial value, up to collisions in the randomized value.
We show that our construction has immediate implications in the context of parallel variable-length digest generation. In detail, we describe Cascade-MGF, that operates on top of any cryptographic hash function and uses the hash function output as randomized initial value in truncation. We demonstrate that Cascade-MGF compares favorably over earlier parallel variable-length digest generation constructions, namely Counter-MGF and Chained-MGF, in almost all settings.

2021

EUROCRYPT

Leakage Resilient Value Comparison With Application to Message Authentication
📺
Abstract

Side-channel attacks are a threat to secrets stored on a device, especially if an adversary has physical access to the device. As an effect of this, countermeasures against such attacks for cryptographic algorithms are a well-researched topic. In this work, we deviate from the study of cryptographic algorithms and instead focus on the side-channel protection of a much more basic operation, the comparison of a known attacker-controlled value with a secret one. Comparisons sensitive to side-channel leakage occur in tag comparisons during the verification of message authentication codes (MACs) or authenticated encryption, but are typically omitted in security analyses. Besides, also comparisons performed as part of fault countermeasures might be sensitive to side-channel attacks. In this work, we present a formal analysis on comparing values in a leakage resilient manner by utilizing cryptographic building blocks that are typically part of an implementation anyway. Our results indicate that there is no need to invest additional resources into implementing a protected comparison operation itself if a sufficiently protected implementation of a public cryptographic permutation, or a (tweakable) block cipher, is already available. We complement our contribution by applying our findings to the SuKS message authentication code used by lightweight authenticated encryption scheme ISAP, and to the classical Hash-then-PRF construction.

2021

ASIACRYPT

Categorization of Faulty Nonce Misuse Resistant Message Authentication
📺
Abstract

A growing number of lightweight block ciphers are proposed for environments such as the Internet of Things. An important contribution to the reduced implementation cost is a block length n of 64 or 96 bits rather than 128 bits. As a consequence, encryption modes and message authentication code (MAC) algorithms require security beyond the 2^{n/2} birthday bound. This paper provides an extensive treatment of MAC algorithms that offer beyond birthday bound PRF security for both nonce-respecting and nonce-misusing adversaries. We study constructions that use two block cipher calls, one universal hash function call and an arbitrary number of XOR operations.
We start with the separate problem of generically identifying all possible secure n-to-n-bit pseudorandom functions (PRFs) based on two block cipher calls. The analysis shows that the existing constructions EDM, SoP, and EDMD are the only constructions of this kind that achieve beyond birthday bound security.
Subsequently we deliver an exhaustive treatment of MAC algorithms, where the outcome of a universal hash function evaluation on the message may be entered at any point in the computation of the PRF. We conclude that there are a total amount of nine schemes that achieve beyond birthday bound security, and a tenth construction that cannot be proven using currently known proof techniques. For these former nine MAC algorithms, three constructions achieve optimal n-bit security in the nonce-respecting setting, but are completely insecure if the nonce is reused. The remaining six constructions have 3n/4-bit security in the nonce-respecting setting, and only four out of these six constructions still achieve beyond the birthday bound security in the case of nonce misuse.

2020

TOSC

Errata to Sound Hashing Modes of Arbitrary Functions, Permutations, and Block Ciphers
Abstract

In ToSC 2018(4), Daemen et al. performed an in-depth investigation of sound hashing modes based on arbitrary functions, permutations, or block ciphers. However, for the case of invertible primitives, there is a glitch. In this errata, we formally fix this glitch by adding an extra term to the security bound, q/2b−n, where q is query complexity, b the width of the permutation or the block size of the block cipher, and n the size of the hash digest. For permutations that are wider than two times the chaining value this term is negligible. For block cipher based hashing modes where the block size is close to the digest size, the term degrades the security significantly.

2020

TOSC

Deck-Based Wide Block Cipher Modes and an Exposition of the Blinded Keyed Hashing Model
📺
Abstract

We present two tweakable wide block cipher modes from doubly-extendable cryptographic keyed (deck) functions and a keyed hash function: double-decker and docked-double-decker. Double-decker is a direct generalization of Farfalle-WBC of Bertoni et al. (ToSC 2017(4)), and is a four-round Feistel network on two arbitrarily large branches, where the middle two rounds call deck functions and the first and last rounds call the keyed hash function. Docked-double-decker is a variant of double-decker where the bulk of the input to the deck functions is moved to the keyed hash functions. We prove that the distinguishing advantage of the resulting wide block ciphers is simply two times the sum of the pseudorandom function distinguishing advantage of the deck function and the blinded keyed hashing distinguishing advantage of the keyed hash functions. We demonstrate that blinded keyed hashing is more general than the conventional notion of XOR-universality, and that it allows us to instantiate our constructions with keyed hash functions that have a very strong claim on bkh security but not necessarily on XOR-universality, such as Xoofffie (ePrint 2018/767). The bounds of double-decker and docked-double-decker are moreover reduced tweak-dependent, informally meaning that collisions on the keyed hash function for different tweaks only have a limited impact. We describe two use cases that can exploit this property opportunistically to get stronger security than what would be achieved with prior solutions: SSD encryption, where each sector can only be written to a limited number of times, and incremental tweaks, where one includes the state of the system in the variable-length tweak and appends new data incrementally.

2020

TOSC

Release of Unverified Plaintext: Tight Unified Model and Application to ANYDAE
📺
Abstract

Authenticated encryption schemes are usually expected to offer confidentiality and authenticity. In case of release of unverified plaintext (RUP), an adversary gets separated access to the decryption and verification functionality, and has more power in breaking the scheme. Andreeva et al. (ASIACRYPT 2014) formalized RUP security using plaintext awareness, informally meaning that the decryption functionality gives no extra power in breaking confidentiality, and INT-RUP security, covering authenticity in case of RUP. We describe a single, unified model, called AERUP security, that ties together these notions: we prove that an authenticated encryption scheme is AERUP secure if and only if it is conventionally secure, plaintext aware, and INT-RUP secure. We next present ANYDAE, a generalization of SUNDAE of Banik et al. (ToSC 2018/3). ANYDAE is a lightweight deterministic scheme that is based on a block cipher with block size n and arbitrary mixing functions that all operate on an n-bit state. It is particularly efficient for short messages, it does not rely on a nonce, and it provides maximal robustness to a lack of secure state. Whereas SUNDAE is not secure under release of unverified plaintext (a fairly simple attack can be mounted in constant time), ANYDAE is. We make handy use of the AERUP security model to prove that ANYDAE achieves both conventional security as RUP security, provided that certain modest conditions on the mixing functions are met. We describe two simple instances, called MONDAE and TUESDAE, that conform to these conditions and that are competitive with SUNDAE, in terms of efficiency and optimality.

2020

TOSC

Security of the Suffix Keyed Sponge
📺
Abstract

We formalize and analyze the general suffix keyed sponge construction, a pseudorandom function built on top of a cryptographic permutation. The construction hashes its data using the (keyless) sponge construction, transforms part of the state using the secret key, and generates the tag from the output of a final permutation call. In its simplest form, if the key and tag size are at most the rate of the sponge, one can see the suffix keyed sponge as a simple sponge function evaluation whose input is the plaintext appended with the key. The suffix keyed sponge is, however, much more general: the key and tag size may exceed the rate without any need to make extra permutation calls. We prove that the suffix keyed sponge construction achieves birthday-bound PRF security in the capacity, even if key and tag size exceed the rate. Furthermore, we prove that if the absorption of the key into the state happens in a leakage resilient manner, the suffix keyed sponge itself is leakage resilient as well. Our findings show that the suffix keyed sponge compares favorably with the hash-then-MAC construction. For instance, to reach a security level of k bits, the side-channel protected component in the suffix keyed sponge just needs to process k bits of input besides the key, whereas schemes following the hash-then-MAC construction need a side-channel protected MAC function that processes 2k bits of input besides the key. Moreover, even if we just consider black-box attacks, the MAC function in a hash-then-MAC scheme needs to be cryptographically strong whereas in the suffix keyed sponge the key may be absorbed by a simple XOR. The security proofs are performed using the H-coefficient technique, and make effective use of the multicollision limit function results of Daemen et al. (ASIACRYPT 2017), both for arguing that state manipulation larger than the rate is tolerated after key processing and for upper bounding the amount of leakage an attacker may gain about the secret key.

2020

CRYPTO

The Summation-Truncation Hybrid: Reusing Discarded Bits for Free
📺
Abstract

A well-established PRP-to-PRF conversion design is truncation: one evaluates an $n$-bit pseudorandom permutation on a certain input, and truncates the result to $a$ bits. The construction is known to achieve tight $2^{n-a/2}$ security. Truncation has gained popularity due to its appearance in the GCM-SIV key derivation function (ACM CCS 2015). This key derivation function makes four evaluations of AES, truncates the outputs to $n/2$ bits, and concatenates these to get a $2n$-bit subkey.
In this work, we demonstrate that truncation is wasteful. In more detail, we present the Summation-Truncation Hybrid (STH). At a high level, the construction consists of two parallel evaluations of truncation, where the truncated $(n-a)$-bit chunks are not discarded but rather summed together and appended to the output. We prove that STH achieves a similar security level as truncation, and thus that the $n-a$ bits of extra output is rendered for free. In the application of GCM-SIV, the current key derivation can be used to output $3n$ bits of random material, or it can be reduced to three primitive evaluations. Both changes come with no security loss.

2020

TOSC

Dumbo, Jumbo, and Delirium: Parallel Authenticated Encryption for the Lightweight Circus
📺
Abstract

With the trend to connect more and more devices to the Internet, authenticated encryption has become a major backbone in securing the communication, not only between these devices and servers, but also the direct communication among these devices. Most authenticated encryption algorithms used in practice are developed to perform well on modern high-end devices, but are not necessarily suited for usage on resource-constrained devices. We present a lightweight authenticated encryption scheme, called Elephant. Elephant retains the advantages of GCM such as parallelism, but is tailored to the needs of resource-constrained devices. The two smallest instances of Elephant, Dumbo and Jumbo, are based on the 160-bit and 176-bit Spongent permutation, respectively, and are particularly suited for hardware; the largest instance of Elephant, Delirium, is based on 200-bit Keccak and is developed towards software use. All three instances are parallelizable, have a small state size while achieving a high level of security, and are constant time by design.

2020

TOSC

Isap v2.0
📺
Abstract

We specify Isap v2.0, a lightweight permutation-based authenticated encryption algorithm that is designed to ease protection against side-channel and fault attacks. This design is an improved version of the previously published Isap v1.0, and offers increased protection against implementation attacks as well as more efficient implementations. Isap v2.0 is a candidate in NIST’s LightWeight Cryptography (LWC) project, which aims to identify and standardize authenticated ciphers that are well-suited for applications in constrained environments. We provide a self-contained specification of the new Isap v2.0 mode and discuss its design rationale. We formally prove the security of the Isap v2.0 mode in the leakage-resilient setting. Finally, in an extensive implementation overview, we show that Isap v2.0 can be implemented securely with very low area requirements.
https://isap.iaik.tugraz.at

2020

ASIACRYPT

Beyond Birthday Bound Secure Fresh Rekeying: Application to Authenticated Encryption
📺
Abstract

Fresh rekeying is a well-established method to protect a primitive or mode against side-channel attacks: an easy to protect but cryptographically not so involved function generates a subkey from the master key, and this subkey is then used for the block encryption of a single or a few messages. It is an efficient way to achieve side-channel protection, but current solutions only achieve birthday bound security in the block size of the cipher and thus halve its security (except if more involved primitives are employed). We present generalized solutions to parallel block cipher rekeying that, for the first time, achieve security beyond the birthday bound in the block size $n$. The first solution involves, next to the subkey generation, one multiplication and the core block cipher call and achieves $2^{2n/3}$ security. The second solution makes two block cipher calls, and achieves optimal $2^n$ security. Our third solution uses a slightly larger subkey generation function but requires no adaptations to the core encryption and also achieves optimal security. The construction seamlessly generalizes to permutation based fresh rekeying. Central to our schemes is the observation that fresh rekeying and generic tweakable block cipher design are two very related topics, and we can take lessons from the advanced results in the latter to improve our understanding and development of the former. We subsequently use these rekeying schemes in a constructive manner to deliver three authenticated encryption modes that achieve beyond birthday bound security and are easy to protect against side-channel attacks.

2020

TOSC

Tightness of the Suffix Keyed Sponge Bound
📺
Abstract

Generic attacks are a vital ingredient in the evaluation of the tightness of security proofs. In this paper, we evaluate the tightness of the suffix keyed sponge (SuKS) bound. As its name suggests, SuKS is a sponge-based construction that absorbs the key after absorbing the data, but before producing an output. This absorption of the key can be done via an easy to invert operation, like an XOR, or a hard to invert operation, like a PRF. Using SuKS with a hard to invert absorption provides benefits with respect to its resistance against side-channel attacks, and such a construction is used as part of the authenticated encryption scheme Isap. We derive two key recovery attacks against SuKS with easy to invert key absorption, and a forgery in case of hard to invert key absorption. The attacks closely match the terms in the PRF security bound of SuKS by Dobraunig and Mennink, ToSC 2019(4), and therewith show that these terms are justified, even if the function used to absorb the key is a PRF, and regardless of whether SuKS is used as a PRF or a MAC.

2019

CRYPTO

How to Build Pseudorandom Functions from Public Random Permutations
📺
Abstract

Pseudorandom functions are traditionally built upon block ciphers, but with the trend of permutation based cryptography, it is a natural question to investigate the design of pseudorandom functions from random permutations. We present a generic study of how to build beyond birthday bound secure pseudorandom functions from public random permutations. We first show that a pseudorandom function based on a single permutation call cannot be secure beyond the $$2^{n/2}$$ birthday bound, where n is the state size of the function. We next consider the Sum of Even-Mansour (SoEM) construction, that instantiates the sum of permutations with the Even-Mansour construction. We prove that SoEM achieves tight $$2n{/}3$$-bit security if it is constructed from two independent permutations and two randomly drawn keys. We also demonstrate a birthday bound attack if either the permutations or the keys are identical. Finally, we present the Sum of Key Alternating Ciphers (SoKAC) construction, a translation of Encrypted Davies-Meyer Dual to a public permutation based setting, and show that SoKAC achieves tight $$2n{/}3$$-bit security even when a single key is used.

2019

ASIACRYPT

Leakage Resilience of the Duplex Construction
Abstract

Side-channel attacks, especially differential power analysis (DPA), pose a serious threat to cryptographic implementations deployed in a malicious environment. One way to counter side-channel attacks is to design cryptographic schemes to withstand them, an area that is covered amongst others by leakage resilient cryptography. So far, however, leakage resilient cryptography has predominantly focused on block cipher based designs, and insights in permutation based leakage resilient cryptography are scarce. In this work, we consider leakage resilience of the keyed duplex construction: we present a model for leakage resilient duplexing, derive a fine-grained bound on the security of the keyed duplex in said model, and map it to ideas of Taha and Schaumont (HOST 2014) and Dobraunig et al. (ToSC 2017) in order to use the duplex in a leakage resilient manner.

2019

JOFC

Beyond Conventional Security in Sponge-Based Authenticated Encryption Modes
Abstract

The Sponge function is known to achieve $$2^{c/2}$$ 2 c / 2 security, where c is its capacity. This bound was carried over to its keyed variants, such as SpongeWrap, to achieve a $$\min \{2^{c/2},2^\kappa \}$$ min { 2 c / 2 , 2 κ } security bound, with $$\kappa $$ κ the key length. Similarly, many CAESAR competition submissions were designed to comply with the classical $$2^{c/2}$$ 2 c / 2 security bound. We show that Sponge-based constructions for authenticated encryption can achieve the significantly higher bound of $$\min \{2^{b/2},2^c,2^\kappa \}$$ min { 2 b / 2 , 2 c , 2 κ } , with $$b>c$$ b > c the permutation size, by proving that the CAESAR submission NORX achieves this bound. The proof relies on rigorous computation of multi-collision probabilities, which may be of independent interest. We additionally derive a generic attack based on multi-collisions that matches the bound. We show how to apply the proof to five other Sponge-based CAESAR submissions: Ascon, CBEAM/STRIBOB, ICEPOLE, Keyak, and two out of the three PRIMATEs. A direct application of the result shows that the parameter choices of some of these submissions are overly conservative. Simple tweaks render the schemes considerably more efficient without sacrificing security. We finally consider the remaining one of the three PRIMATEs, APE, and derive a blockwise adaptive attack in the nonce-respecting setting with complexity $$2^{c/2}$$ 2 c / 2 , therewith demonstrating that the techniques cannot be applied to APE.

2018

TOSC

Short Non-Malleable Codes from Related-Key Secure Block Ciphers
Abstract

A non-malleable code is an unkeyed randomized encoding scheme that offers the strong guarantee that decoding a tampered codeword either results in the original message, or in an unrelated message. We consider the simplest possible construction in the computational split-state model, which simply encodes a message m as k||Ek(m) for a uniformly random key k, where E is a block cipher. This construction is comparable to, but greatly simplifies over, the one of Kiayias et al. (ACM CCS 2016), who eschewed this simple scheme in fear of related-key attacks on E. In this work, we prove this construction to be a strong non-malleable code as long as E is (i) a pseudorandom permutation under leakage and (ii) related-key secure with respect to an arbitrary but fixed key relation. Both properties are believed to hold for “good” block ciphers, such as AES-128, making this non-malleable code very efficient with short codewords of length |m|+2τ (where τ is the security parameter, e.g., 128 bits), without significant security penalty.

2018

TCC

Towards Tight Security of Cascaded LRW2
Abstract

The Cascaded LRW2 tweakable block cipher was introduced by Landecker et al. at CRYPTO 2012, and proven secure up to $$2^{2n/3}$$ queries. There has not been any attack on the construction faster than the generic attack in $$2^n$$ queries. In this work we initiate the quest towards a tight bound. We first present a distinguishing attack in $$2n^{1/2}2^{3n/4}$$ queries against a generalized version of the scheme. The attack is supported with an experimental verification and a formal success probability analysis. We subsequently discuss non-trivial bottlenecks in proving tight security, most importantly the distinguisher’s freedom in choosing the tweak values. Finally, we prove that if every tweak value occurs at most $$2^{n/4}$$ times, Cascaded LRW2 is secure up to $$2^{3n/4}$$ queries.

2018

ASIACRYPT

Short Variable Length Domain Extenders with Beyond Birthday Bound Security
Abstract

Length doublers are cryptographic functions that transform an n-bit cryptographic primitive into an efficient and secure cipher that length-preservingly encrypts strings of length in $$[n,2n-1]$$. All currently known constructions are only proven secure up to the birthday bound, and for all but one construction this bound is known to be tight. We consider the remaining candidate, $$\mathrm {LDT}$$ by Chen et al. (ToSC 2017(3)), and prove that it achieves beyond the birthday bound security for the domain [n, 3n / 2). We generalize the construction to multiple rounds and demonstrate that by adding one more encryption layer to $$\mathrm {LDT} $$, beyond the birthday bound security can be achieved for all strings of length in $$[n,2n-1]$$: security up to around $$2^{2n/3}$$ for the encryption of strings close to n and security up to around $$2^{n}$$ for strings of length close to 2n. The security analysis of both schemes is performed in a modular manner through the introduction and analysis of a new concept called “harmonic permutation primitives.”

2018

TOSC

Key Prediction Security of Keyed Sponges
📺
Abstract

The keyed sponge is a well-accepted method for message authentication. It processes data at a certain rate by sequential evaluation of an underlying permutation. If the key size k is smaller than the rate, currently known bounds are tight, but if it exceeds the rate, state of the art only dictates security up to 2k/2. We take closer inspection at the key prediction security of the sponge and close the remaining gap in the existing security analysis: we confirm key security up to close to 2k, regardless of the rate. The result impacts all applications of the keyed sponge and duplex that process at a rate smaller than the key size, including the STROBE protocol framework, as well as the related constructions such as HMAC-SHA-3 and the sandwich sponge.

2018

TOSC

Sound Hashing Modes of Arbitrary Functions, Permutations, and Block Ciphers
📺
Abstract

Cryptographic hashing modes come in many flavors, including Merkle-Damgård with various types of strengthening, Merkle trees, and sponge functions. As underlying primitives, these functions use arbitrary functions, permutations, or block ciphers. In this work we provide three simple proofs, one per primitive type, that cover all modes where the input to the primitive consists of message bits, chaining value bits, and bits that only depend on the mode and message length. Our approach generalizes and simplifies over earlier attempts of Dodis et al. (FSE 2009) and Bertoni et al. (Int. J. Inf. Sec. 2014). We prove tight indifferentiability bounds for modes using each of these three primitive types provided that the mode satisfies some easy to verify conditions.

2017

CRYPTO

2017

TOSC

Understanding RUP Integrity of COLM
Abstract

The authenticated encryption scheme COLM is a third-round candidate in the CAESAR competition. Much like its antecedents COPA, ELmE, and ELmD, COLM consists of two parallelizable encryption layers connected by a linear mixing function. While COPA uses plain XOR mixing, ELmE, ELmD, and COLM use a more involved invertible mixing function. In this work, we investigate the integrity of the COLM structure when unverified plaintext is released, and demonstrate that its security highly depends on the choice of mixing function. Our results are threefold. First, we discuss the practical nonce-respecting forgery by Andreeva et al. (ASIACRYPT 2014) against COPA’s XOR mixing. Then we present a noncemisusing forgery against arbitrary mixing functions with practical time complexity. Finally, by using significantly larger queries, we can extend the previous forgery to be nonce-respecting.

2017

TOSC

Efficient Length Doubling From Tweakable Block Ciphers
Abstract

We present a length doubler, LDT, that turns an n-bit tweakable block cipher into an efficient and secure cipher that can encrypt any bit string of length [n..2n − 1]. The LDT mode is simple, uses only two cryptographic primitive calls (while prior work needs at least four), and is a strong length-preserving pseudorandom permutation if the underlying tweakable block ciphers are strong tweakable pseudorandom permutations. We demonstrate that LDT can be used to neatly turn an authenticated encryption scheme for integral data into a mode for arbitrary-length data.

2017

TOSC

Optimal PRFs from Blockcipher Designs
Abstract

Cryptographic modes built on top of a blockcipher usually rely on the assumption that this primitive behaves like a pseudorandom permutation (PRP). For many of these modes, including counter mode and GCM, stronger security guarantees could be derived if they were based on a PRF design. We propose a heuristic method of transforming a dedicated blockcipher design into a dedicated PRF design. Intuitively, the method consists of evaluating the blockcipher once, with one or more intermediate state values fed-forward. It shows strong resemblance with the optimally secure EDMD construction by Mennink and Neves (CRYPTO 2017), but the use of internal state values make their security analysis formally inapplicable. In support of its security, we give the rationale of relying on the EDMD function (as opposed to alternatives), and present analysis of simplified versions of our conversion method applied to the AES. We conjecture that our main proposal AES-PRF, AES with a feed-forward of the middle state, achieves close to optimal security. We apply the design to GCM and GCM-SIV, and demonstrate how it entails significant security improvements. We furthermore demonstrate how the technique extends to tweakable blockciphers and allows for security improvements in, for instance, PMAC1.

2016

EUROCRYPT

2016

TOSC

Security Analysis of BLAKE2's Modes of Operation
Abstract

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 BLAKE2’s generic security. We prove that BLAKE2’s compression function is indifferentiable from a random function in a weakly ideal cipher model, which was not the case for BLAKE. This implies that there are no generic attacks against any of the modes that BLAKE2 uses.

2015

ASIACRYPT

#### Program Committees

- Crypto 2024
- Crypto 2023
- Crypto 2022
- Asiacrypt 2022
- Eurocrypt 2021
- Eurocrypt 2020
- FSE 2020
- Eurocrypt 2019
- FSE 2019
- Eurocrypt 2018
- Asiacrypt 2018
- FSE 2018
- FSE 2017
- Asiacrypt 2017
- Eurocrypt 2017
- FSE 2016
- Asiacrypt 2015

#### Coauthors

- Elena Andreeva (7)
- Gilles Van Assche (3)
- Mario Marhuenda Beltrán (1)
- Henk Berendsen (1)
- Tim Beyne (1)
- Ritam Bhaumik (1)
- Begül Bilgin (1)
- Andrey Bogdanov (5)
- Christina Boura (1)
- Donghoon Chang (1)
- Yu Long Chen (5)
- Joan Daemen (5)
- Yuanxi Dai (1)
- Nilanjan Datta (2)
- Itai Dinur (1)
- Christoph Dobraunig (7)
- Yevgeniy Dodis (1)
- Avijit Dutta (1)
- Maria Eichlseder (1)
- Serge Fehr (1)
- Robert Granger (1)
- Lorenzo Grassi (1)
- Aldo Gunsing (4)
- Ashwin Jha (1)
- Philipp Jovanovic (3)
- Pierre Karpman (1)
- Dmitry Khovratovich (1)
- Eran Lambooij (1)
- Jooyoung Lee (1)
- Charlotte Lefevre (2)
- Atul Luykx (10)
- Stefan Mangard (1)
- Florian Mendel (1)
- Nicky Mouha (2)
- Mridul Nandi (3)
- Samuel Neves (5)
- Kenneth G. Paterson (1)
- Bart Preneel (4)
- Robert Primas (1)
- Reza Reyhanitabar (1)
- Somitra Sanadhya (1)
- Yu Sasaki (1)
- Yaobin Shen (1)
- Ferdinand Sibleyras (1)
- John P. Steinberger (2)
- Elmar Tischhauser (1)
- Thomas Unterluggauer (1)
- Damian Vizár (1)
- Kan Yasuda (5)