International Association
for Cryptologic Research

The Center for Security and Privacy at the School of Computer Science of the University of Birmingham has an open PhD position in post-quantum cryptography. The supervision will be shared by Rishiraj Bhattacharyya and Christophe Petit. We invite applications from candidates with interests in Cryptography and Computer Algebra. The ideal candidate will have a strong background in Mathematics, Computer Science, Physics or a related area.

The primary research theme for the call is in the foundations and cryptanalysis of post-quantum cryptosystems. The exact projects could be tailored to match the candidate's background and interests.

The review of applications will start immediately and the call remains open until September 2024. For more information, please reach out to Rishiraj (r.bhattacharyya@bham.ac.uk) and Christophe (c.petit.1@bham.ac.uk).

Closing date for applications:

Contact: Rishiraj Bhattacharyya (r.bhattacharyya@bham.ac.uk) and Christophe Petit (c.petit.1@bham.ac.uk)

The Learning with Errors (LWE) problem with its variants over structured lattices has been widely exploited in efficient post-quantum cryptosystems. Recently, May suggests the Meet-LWE attack, which poses a significant advancement in the line of work on the Meet-in-the-Middle approach to analyze LWE with ternary secrets.

In this work, we generalize and extend the idea of Meet-LWE by introducing ternary trees, which result in diverse representations of the secrets. More precisely, we split the secrets into three pieces with the same dimension and expand them into a ternary tree to leverage the increased representations to improve the overall attack complexity. We carefully analyze and optimize the time and memory costs of our attack algorithm exploiting ternary trees, and compare them to those of the Meet-LWE attack. With asymptotic and non-asymptotic comparisons, we observe that our attack provides improved estimations for all parameter settings, including those of the practical post-quantum schemes, compared to the Meet-LWE attack. We also evaluate the security of the Round 2 candidates of the KpqC competition which aims to standardize post-quantum public key cryptosystems in the Republic of Korea, and report that the estimated complexities for our attack applied to SMAUG-T are lower than the claimed for some of the recommended parameters.

A function secret sharing (FSS) scheme ($\mathsf{gen},\mathsf{eval}$) for a class of programs $\mathcal{F}$ allows a dealer to secret share any function $f \in \mathcal{F}$, such that each function share hides the function, and the shares can be used to non-interactively compute additive shares of $f(x)$ for any input $x$. All FSS related applications often requires the dealer to generate and share secret sharings for a batch of functions. We initiate the study of batched function secret sharing - where the objective is to secret share a set of functions from the class $\mathcal{F}$ while minimizing the size of the collection of FSS keys.

We use standard homomorphic secret sharing (HSS) schemes, variant of the Learning with Parity Noise assumption and the Quadratic Residuosity assumption to construct batched FSS schemes for point functions with single-bit and multi-bit output. Our scheme is asymptotically superior than naively batching state of the art FSS schemes for point functions. Concretely our batch key sizes are smaller by a factor of $3-80\times$ as batch size is increased from $2^{13}$ to $2^{19}$. Although our protocol relies on public key operations, it exhibits inefficiency in a LAN setting. However, it demonstrates up to a 120-fold improvement in a WAN setting with slow network bandwidth.

As a building block in our protocols, we introduce a new HSS ciphertext compression algorithm, that can decompress a short compressed ciphertext to give low noise ciphertexts of array of input message bits. This primitive might be of independent interest for other HSS related applications.

In this paper, we present two early stopping Byzantine agreement protocols in the authenticated setting against a corrupt minority $t < n/2$, where $t$ represents the maximum number of malicious parties. Early stopping protocols ensure termination within a number of rounds determined solely by the actual number of malicious nodes $f$ present during execution, irrespective of $t$.

Our first protocol is deterministic and ensures early stopping termination in $ (d+5) \cdot (\lfloor f/d \rfloor +3)$ rounds, where $d$ is a fixed constant. For example, for all $d\ge 6$, our protocol runs in at most $(1+\epsilon )\cdot f$ rounds (where $0<\epsilon<1$), improving (for large $f$) upon the best previous early stopping deterministic broadcast protocol by Perry and Toueg~\cite{Perry}, which terminates in $min(2f+4,2t+2)$ rounds. Additionally, our second protocol is randomized, ensuring termination in an expected constant number of rounds and achieving early stopping in $(d+9) \cdot (\lfloor f/d \rfloor +2)$ rounds in the worst case. This marks a significant improvement over a similar result by Goldreich and Petrank[GOLDREICH1990], which always requires an expected constant number of rounds and $O(t)$ rounds in the worst case, i.e., does not have the early stopping property.

We present a general framework for constructing attribute-based encryption (ABE) schemes for arbitrary function class based on lattices from two ingredients, i) a noisy linear secret sharing scheme for the class and ii) a new type of inner-product functional encryption (IPFE) scheme, termed *evasive* IPFE, which we introduce in this work. We propose lattice-based evasive IPFE schemes and establish their security under simple conditions based on variants of evasive learning with errors (LWE) assumption recently proposed by Wee [EUROCRYPT ’22] and Tsabary [CRYPTO ’22].

Our general framework is modular and conceptually simple, reducing the task of constructing ABE to that of constructing noisy linear secret sharing schemes, a more lightweight primitive. The versatility of our framework is demonstrated by three new ABE schemes based on variants of the evasive LWE assumption.

- We obtain two ciphertext-policy ABE schemes for all polynomial-size circuits with a predetermined depth bound. One of these schemes has *succinct* ciphertexts and secret keys, of size polynomial in the depth bound, rather than the circuit size. This eliminates the need for tensor LWE, another new assumption, from the previous state-of-the-art construction by Wee [EUROCRYPT ’22].

- We develop ciphertext-policy and key-policy ABE schemes for deterministic finite automata (DFA) and logspace Turing machines ($\mathsf{L}$). They are the first lattice-based public-key ABE schemes supporting uniform models of computation. Previous lattice-based schemes for uniform computation were limited to the secret-key setting or offered only weaker security against bounded collusion.

Lastly, the new primitive of evasive IPFE serves as the lattice-based counterpart of pairing-based IPFE, enabling the application of techniques developed in pairing-based ABE constructions to lattice-based constructions. We believe it is of independent interest and may find other applications.

We present a new approach to garbling arithmetic circuits using techniques from homomorphic secret sharing, obtaining constructions with high rate that support free addition gates. In particular, we build upon non-interactive protocols for computing distributed discrete logarithms in groups with an easy discrete-log subgroup, further demonstrating the versatility of tools from homomorphic secret sharing. Relying on distributed discrete log for the Damgård-Jurik cryptosystem (Roy and Singh, Crypto `21), whose security follows from the decisional composite residuosity assumption (DCR), we get the following main results:

[**Two ciphertexts per multiplication, from IND-CPA security of Damgård-Jurik.**] Assuming the Damgård-Jurik cryptosystem is semantically secure (which follows from DCR), there is a garbling scheme for circuits with $B$-bounded integer arithmetic using only two ciphertexts per multiplication. The total bit-size of the resulting garbled circuit is: $$(n + 2s_\times+2D_\times)\cdot (\zeta + 1) \cdot \log N$$ where $n$ is the number of inputs, $s_\times$ is the number of multiplications, $D_\times$ is the multiplicative depth of the circuit, $N$ is an RSA modulus and $N^{\zeta-1}$ is a rough bound on the magnitude of wire values in the computation.

[**One ciphertext per multiplication, from KDM security of Damgård-Jurik.**] Assuming the Damgård-Jurik encryption scheme remains secure given encryption of the key and its inverse, the construction achieves rate-$1$. The total bit-size of the resulting garbled circuit is: $$(n + s_\times + 1) \cdot (\zeta + 1) \cdot \log N$$ where the parameters are as above, except $N^{\zeta-2}$ is the magnitude bound.

As a side result, we show that our scheme based on IND-CPA security achieves rate $3/5$ for levelled circuits.

In this paper, we present a new efficient stand-alone MAC construct based on processing using the FSM part of the stream cipher family SNOW, which in turn uses the AES round function. It offers a combination of very high speed in software and hardware with a truncatable tag. Two concrete versions of SMAC are proposed with different security levels, although other use cases are also possible. For example, SMAC can be combined with an external ciphering engine in AEAD mode. Every design choice is justified and supported by the results of our analysis and simulations. A novelty of the proposal is that it meets future performance requirements but is still not directly vulnerable to attacks using repeated nonce when the tag size is short, as is the case for other very fast MACs (MACs based on polynomial hashing). This can be an important aspect in practical applications.

The universal composability (UC) model provides strong security guarantees for protocols used in arbitrary contexts. While these guarantees are highly desirable, in practice, schemes with a standalone proof of security, such as the Groth16 proof system, are preferred. This is because UC security typically comes with undesirable overhead, sometimes making UC-secure schemes significantly less efficient than their standalone counterparts. We establish the UC security of Groth16 without any significant overhead. In the spirit of global random oracles, we design a global (restricted) observable generic group functionality that models a natural notion of observability: computations that trace back to group elements derived from generators of other sessions are observable. This notion turns out to be surprisingly subtle to formalize. We provide a general framework for proving protocols secure in the presence of global generic groups, which we then apply to Groth16.

In this paper, we present three types of variations of the ALTEQ cryptosystem, a recent submission to the NIST's additional call for signatures. We name these Dangerous Variations of ALTEQ (DVA), as there is always a certain danger in stepping out of usual constructions, although we attempt to maintain heuristic security. First, we present DVA-GG (Graph Generalization), that can be seen as a more abstract point-of-view on the operations done in ALTEQ and encourages more research on the algebraic variants. In particular, we show this approach can lead to a patch counter to Beullens' recent seed collision attack on ALTEQ that only depends on the primitive, and showcase some fancy usages of the primitive for experimental protocols. Second, we present DVA-PC (Precomputations) which is ``likely'' as secure as ALTEQ in the random oracle model, and allow to drastically reduce the intermediate memory requirements within both the signature and verification process through an easily parallelizable extra operation. In particular, this facilitates precomputation variants with online phases that only depends on the complexity of basic matrix operations. We can then choose between either a tiny offline memory per signature, or get one of the fastest online signing speed for post-quantum cryptography. Third, we present DVA-DM (Distinct Matrices), some cryptanalytic targets that deviates from ALTEQ's original algebraic structure. Those structures can serve as plain computational acceleration or just compress data sizes, and provide good options to motivate the study of specialized cryptanalysis for ALTEQ: if those are safe, then ALTEQ gain safe variants, and otherwise, we gain further understanding of the problems. In particular, the ideas can be applied beyond ALTEQ and beyond, and hopefully extend to MEDS, LESS, and group-action-based cryptography.

Interactive Oracle Proofs (IOPs) allow a probabilistic verifier interacting with a prover to verify the validity of an NP statement while reading only few bits from the prover messages. IOPs generalize standard Probabilistically-Checkable Proofs (PCPs) to the interactive setting, and in the few years since their introduction have already exhibited major improvements in main parameters of interest (such as the proof length and prover and verifier running times), which in turn led to significant improvements in constructions of succinct arguments. Zero-Knowledge (ZK) IOPs additionally guarantee that the view of any query-bounded (possibly malicious) verifier can be efficiently simulated. ZK-IOPs are the main building block of succinct ZK arguments which use the underlying cryptographic object (e.g., a collision-resistant hash function) as a black box.

In this work, we construct the first ZK-IOPs approaching the witness length for a natural NP problem. More specifically, we design constant-query and constant-round IOPs for 3SAT in which the total communication is $(1+\gamma)m$, where $m$ is the number of variables and $\gamma>0$ is an arbitrarily small constant, and ZK holds against verifiers querying $m^\beta$ bits from the prover's messages, for a constant $\beta>0$. This gives a ZK variant of a recent result of Ron-Zewi and Rothblum (FOCS `20), who construct (non-ZK) IOPs approaching the witness length for a large class of NP languages. Previous constructions of ZK-IOPs incurred an (unspecified) large constant multiplicative overhead in the proof length, even when restricting to ZK against the honest verifier.

We obtain our ZK-IOPs by improving the two main building blocks underlying most ZK-IOP constructions, namely ZK codes and ZK-IOPs for sumcheck. More specifically, we give the first ZK-IOPs for sumcheck that achieve both sublinear communication for sumchecking a general tensor code, and a ZK guarantee. We also show a strong ZK preservation property for tensors of ZK codes, which extends a recent result of Bootle, Chiesa, and Liu (EC `22). Given the central role of these objects in designing ZK-IOPs, these results might be of independent interest.

In this paper, we introduce a new probability function parameter in the instantiations of the Goldreich-Micali-Wigderson with Fiat-Shamir and unbalanced challenges used in ALTEQ, a recent NIST PQC candidate in the call for additional signatures. This probability set at 100% does not bring any changes in the scheme, but modifies the public challenge generation process when below 100%, by injecting potential rejections in otherwise completely valid inputs. From a theoretical point of view, this does not improve the asymptotical hardness of the scheme and negatively affects the efficiency of the signatory, and might itself seem trivial. However, from a practical point of view, implementation-wise and performance-wise, this triviality allows an extra degree of freedom in optimizing parameters, as the heuristic security level is also increased against forgers: previously valid combinations now can be deemed invalid. This allows us to make trade-offs to reduce the computational load in verifiers, accelerating verifications, marginally reduce the signature size, at the cost of making signatures slower and unlikely to be constant-time. In particular, this extra degree of freedom allows to make implementation choices that enable smoother and faster executions of the aforementioned protocols, especially in the context of parallelization using vectorized instructions. We also demonstrate the usefulness of our proposal to ALTEQ for other options, when slowing down the signing process is not an issue: significantly smaller signatures but longer verifications, or lower public key sizes. The ideas presented apply to any primitive, and can be used beyond ALTEQ.

This work introduces homomorphic secret sharing (HSS) with succinct share size. In HSS, private inputs are shared between parties, who can then homomorphically evaluate a function on their shares, obtaining a share of the function output. In succinct HSS, a portion of the inputs can be distributed using shares whose size is sublinear in the number of such inputs. The parties can then locally evaluate a function $f$ on the shares, with the restriction that $f$ must be linear in the succinctly shared inputs.

We construct succinct, two-party HSS for branching programs, based on either the decisional composite residuosity assumption, a DDH-like assumption in class groups, or learning with errors with a superpolynomial modulus-to-noise ratio. We then give several applications of succinct HSS, which were only previously known using fully homomorphic encryption, or stronger tools:

- Succinct vector oblivious linear evaluation (VOLE): Two parties can obtain secret shares of a long, arbitrary vector $\vec x$, multiplied by a scalar $\Delta$, with communication sublinear in the size of the vector. - Batch, multi-party distributed point functions: A protocol for distributing a batch of secret, random point functions among $N$ parties, for any polynomial $N$, with communication sublinear in the number of DPFs. - Sublinear MPC for any number of parties: Two new constructions of MPC with sublinear communication complexity, with $N$ parties for any polynomial $N$: (1) For general layered Boolean circuits of size $s$, with communication $O(N s/\log\log s)$, and (2) For layered, sufficiently wide Boolean circuits, with communication $O(N s/\log s)$.

We explain how to extend the Bitcoin backbone model of Garay et al. (Eurocrypt, 2015) to accommodate for redactable blockchains. Our extension captures fluid blockchain-based databases (with mutability requirements) and compliance with existing legislation, such as the GDPR right to be forgotten, or the need to erase offending data from nodes’ databases that would otherwise provoke legal shutdowns. Our redactable backbone protocol retains the essential properties of blockchains. Leveraging zero-knowledge proofs, old data can be erased without requiring trusted third parties or heuristics about past chain validation. Our solution can be implemented on Bitcoin immediately without hard-forks, and it is scalable. It allows the redaction of data from UTXOs or unconfirmed transactions that have not yet flooded the network, while guaranteeing invariance of the Bitcoin state. Thus, offending data does not need to persist in the system, not even temporarily.

In a recent Eurocrypt'24 paper, Manulis and Nguyen have proposed a new CCA security notion, vCCA, and associated construction blueprints to leverage both CPA-secure and correct FHE beyond the CCA1 security barrier. However, because their approach is only valid under the correctness assumption, it leaves a large part of the FHE spectrum uncovered as many FHE schemes used in practice turn out to be approximate and, as such, do not satisfy the correctness assumption. In this paper, we improve their work by defining and investigating a variant of their security notion which is suitable for a more general case where approximate FHE are included. As the passive security of approximate FHE schemes is more appropriately captured by CPAD rather than CPA security, we start from the former notion to define our vCCAD new security notion. Although, we show that vCCA and vCCAD are equivalent when the correctness assumption holds, we establish that vCCAD security is strictly stronger than vCCA security in the general case. In doing so, we interestingly establish several new separation results between variants of CPAD security of increasing strength. This allows us to clarify the relationship between vCCA security and CPAD security, and to reveal that the security notions landscape is much simpler for exact FHE than when approximate ones are included --- in which case, for example, we establish that multiple challenges security notions are strictly stronger than single-challenge ones for both CPAD and vCCAD security. Lastly, we also give concrete construction blueprints, showing how to leverage some of the blueprints proposed by Manulis and Nguyen to achieve vCCAD security. As a result, vCCAD security is the strongest CCA security notion so far known to be achievable by both correct and approximate FHE schemes.

Traceable threshold secret sharing schemes, introduced by Goyal, Song and Srinivasan (CRYPTO'21), allow to provably trace leaked shares to the parties that leaked them. The authors give the first definition and construction of traceable secret sharing schemes. However, the size of the shares in their construction are quadratic in the size of the secret. Boneh, Partap and Rotem (CRYPTO'24) recently proposed a new definition of traceable secret sharing and the first practical constructions. In their definition, one considers a reconstruction box $R$ that contains $f$ leaked shares and, on input $t-f$ additional shares, outputs the secret $s$. A scheme is traceable if one can find out the leaked shares inside the box $R$ by only getting black-box access to $R$. Boneh, Partap and Rotem give constructions from Shamir's secret sharing and Blakely's secret sharing. The constructions are efficient as the size of the secret shares is only twice the size of the secret.

In this work we present the first traceable secret sharing scheme based on the Chinese remainder theorem. This was stated as an open problem by Boneh, Partap and Rotem, as it gives rise to traceable secret sharing with weighted threshold access structures. The scheme is based on Mignotte's secret sharing and increases the size of the shares of the standard Mignotte secret sharing scheme by a factor of $2$.

In this paper, we study the robustness of Kyber, the Learning With Errors (LWE)-based Key Encapsulation Mechanism (KEM) chosen for standardization by NIST, against key mismatch attacks. We demonstrate that Kyber's security levels can be compromised with a few mismatch queries by striking a balance between the parallelization level and the cost of lattice reduction for post-processing. This highlights the imperative need to strictly prohibit key reuse in CPA-secure Kyber.

We further propose an adaptive method to enhance parallel mismatch attacks, initially proposed by Shao et al. at AsiaCCS 2024, thereby significantly reducing query complexity. This method combines the adaptive attack with post-processing via lattice reduction to retrieve the final secret key entries. Our method proves its efficacy by reducing query complexity by 14.6 % for Kyber512 and 7.5 % for Kyber768/Kyber1024.

Furthermore, this approach has the potential to substantially improve multi-value Plaintext-Checking (PC) oracle-based side-channel attacks against the CCA-secure version of Kyber KEM.

This paper deals with reducing the secret key computation time of small scale variants of the AES cipher using algebraic cryptanalysis, which is accelerated by data mining methods. This work is based on the known plaintext attack and aims to speed up the calculation of the secret key by processing the polynomial equations extracted from plaintext-ciphertext pairs. Specifically, we propose to transform the overdefined system of polynomial equations over GF(2) into a new system so that the computation of the Gröbner basis using the F4 algorithm takes less time than in the case of the original system. The main idea is to group similar polynomials into clusters, and for each cluster, sum the two most similar polynomials, resulting in simpler polynomials. We compare different data mining techniques for finding similar polynomials, such as clustering or locality-sensitive hashing (LSH). Experimental results show that using the LSH technique, we get a system of equations for which we can calculate the Gröbner basis the fastest compared to the other methods that we consider in this work. Experimental results also show that the time to calculate the Gröbner basis for the transformed system of equations is significantly reduced compared to the case when the Gröbner basis was calculated from the original non-transformed system. This paper demonstrates that reducing an overdefined system of equations reduces the computation time for finding a secret key.

Arma is a Byzantine Fault Tolerant (BFT) consensus system designed to achieve horizontal scalability across all hardware resources: network bandwidth, CPU, and disk I/O. As opposed to preceding BFT protocols, Arma separates the dissemination and validation of client transactions from the consensus process, restricting the latter to totally ordering only metadata of batches of transactions. This separation enables each party to distribute compute and storage resources for transaction validation, dissemination and disk I/O among multiple machines, resulting in horizontal scalability. Additionally, Arma ensures censorship resistance by imposing a maximum time limit on the inclusion of client transactions. We built and evaluated two Arma prototypes. The first is an independent system handling over 200,000 transactions per second, the second integrated into Hyperledger Fabric, speeding its consensus by an order of magnitude.

Understanding the fault tolerance of Byzantine Agreement protocols is an important question in distributed computing. While the setting of Byzantine faults has been thoroughly explored in the literature, the (arguably more realistic) omission fault setting is far less studied. In this paper, we revisit the recent work of Loss and Stern who gave the first protocol in the mixed fault model tolerating $t$ Byzantine faults, $s$ send faults, and $r$ receive faults, when $2t+r+s2$, or a broadcast protocol for $s+r=n$ and $s>1$ even without overlapping faults.

Resettable statistical zero-knowledge [Garg--Ostrovsky--Visconti--Wadia, TCC 2012] is a strong privacy notion that guarantees statistical zero-knowledge even when the prover uses the same randomness in multiple proofs.

In this paper, we show an equivalence of resettable statistical zero-knowledge arguments for $NP$ and witness encryption schemes for $NP$. - Positive result: For any $NP$ language $L$, a resettable statistical zero-knowledge argument for $L$ can be constructed from a witness encryption scheme for $L$ under the assumption of the existence of one-way functions. - Negative result: The existence of even resettable statistical witness-indistinguishable arguments for $NP$ imply the existence of witness encryption schemes for $NP$ under the assumption of the existence of one-way functions. The positive result is obtained by naturally extending existing techniques (and is likely to be already well-known among experts). The negative result is our main technical contribution.

To explore workarounds for the negative result, we also consider resettable security in a model where the honest party's randomness is only reused with fixed inputs. We show that resettable statistically hiding commitment schemes are impossible even in this model.