International Association
for Cryptologic Research

The security guarantees of most isogeny-based protocols rely on the computational hardness of finding an isogeny between two supersingular isogenous curves defined over a prime field $\mathbb{F}_q$ with $q$ a power of a large prime $p$. In most scenarios, the isogeny is known to be of degree $\ell^e$ for some small prime $\ell$. We call this problem the Supersingular Fixed-Degree Isogeny Path (SIPFD) problem. It is believed that the most general version of SIPFD is not solvable faster than in exponential time by classical as well as quantum attackers.

In a classical setting, a meet-in-the-middle algorithm is the fastest known strategy for solving the SIPFD. However, due to its stringent memory requirements, it quickly becomes infeasible for moderately large SIPFD instances. In a practical setting, one has therefore to resort to time-memory trade-offs to instantiate attacks on the SIPFD. This is particularly true for GPU platforms, which are inherently more memory-constrained than CPU architectures. In such a setting, a van Oorschot-Wiener-based collision finding algorithm offers a better asymptotic scaling. Finding the best algorithmic choice for solving instances under a fixed prime size, memory budget and computational platform remains so far an open problem.

To answer this question, we present a precise estimation of the costs of both strategies considering most recent algorithmic improvements. As a second main contribution, we substantiate our estimations via optimized software implementations of both algorithms. In this context, we provide the first optimized GPU implementation of the van Oorschot-Wiener approach for solving the SIPFD. Based on practical measurements we extrapolate the running times for solving different-sized instances. Finally, we give estimates of the costs of computing a degree-$2^{88}$ isogeny using our CUDA software library running on an NVIDIA A100 GPU server.

We introduce the idea of input obfuscation for secure two-party computation ($\textsf{io2PC}$). Suppose Alice holds a private value $x$ and wants to allow clients to learn $f(x,y_i)$, for their choice of $y_i$, via a secure computation protocol. The goal of $\textsf{io2PC}$ is for Alice to encode $x$ so that an adversary who compromises her storage gets only oracle access to the function $f(x,\cdot)$. At the same time, there must be a 2PC protocol for computing $f(x,y)$ that takes only this encoding (and not the plaintext $x$) as input. We show how to achieve $\textsf{io2PC}$ for functions that have virtual black-box (VBB) obfuscation in either the random oracle model or generic group model. For functions that can be VBB-obfuscated in the random oracle model, we provide an $\textsf{io2PC}$ protocol by replacing the random oracle with an oblivious PRF. For functions that can be VBB-obfuscated in the generic group model, we show how Alice can instantiate a "personalized" generic group. A personalized generic group is one where only Alice can perform the algebraic operations of the group, but where she can let others perform operations in that group via an oblivious interactive protocol.

At the early stage of the design process, many security vulnerability assessment solutions require fast and precise extraction of the finite state machines (FSMs) present in the register-transfer level (RTL) description of the design. FSMs should be accurately extracted for watermark insertion, fault injection assessment of control paths in a system-on-chip (SoC), information leakage assessment, control-flow reverse engineering in RTL abstraction, logic obfuscation, etc. However, it is quite unfortunate that, as of today, existing state-of-the-art synthesis tools cannot provide accurate and reliable extraction of all FSMs from the provided high-level RTL code. Precise identification of all FSM state registers and the pure combinational state transition logic described in the RTL code with numerous registers and other combinational logic makes it quite challenging to develop such a solution. In this paper, we propose a framework named RTL-FSMx to extract FSMs from high-level RTL codes written in Verilog HDL. RTL-FSMx utilizes node-based analysis on the abstract syntax tree (AST) representation of the RTL code to isolate FSM state registers from other registers. RTL-FSMx automatically extracts state transition graphs (STGs) for each of the detected FSM state registers and additional information of the extracted FSMs. Experimental results on a large number of benchmark circuits demonstrate that RTL-FSMx accurately recovers all control FSMs from RTL codes with various complexity and size within just a few seconds.

One PhD position is available. Candidates with a background in cryptography in general, and multi-party computation specifically, are encouraged to apply. The University of Virginia is among the top 25 best universities and the top 3 public universities in the US (according to USNews). Full financial support (including full tuition coverage and a stipend of ~$2500 after-tax) will be guaranteed. The living cost is very reasonable (~$500-$1000 depending on the floor plan, e.g., if you live in a 3-bedroom apartment, ~$500 would suffice).

Closing date for applications:

Contact: Tianhao Wang

The IMDEA Software Institute offers a postdoc position in the area of cryptography. Topics of particular interest include secure multiparty computation, zero knowledge proofs, and verifiable computation. The postdoc will work under the supervision of Ignacio Cascudo.
Who should apply?
Applicants should have (or be about to complete) a PhD in cryptography or a related topic.
Working at IMDEA Software
The position is based in Madrid, Spain, where the IMDEA Software Institute is situated. The institute provides for travel expenses and an internationally competitive stipend. The working language at the institute is English.
Dates
The position has guaranteed funding for at least 2 years. The starting date is flexible and is available from February 2023.
How to apply?
Applicants interested in the position should submit their application at https://careers.software.imdea.org/ using reference code 2022-10-postdoc-securecomp. Deadline for applications is December 15th, 2022. We encourage early applications and review of applications will begin immediately.

Closing date for applications:

Contact: Ignacio Cascudo: ignacio.cascudo (at) imdea.org

More information: https://software.imdea.org/open_positions/2022-10-postdoc-securecomp.html

Secure aggregation enables a server to learn the sum of client-held vectors in a privacy-preserving way, and has been successfully applied to distributed statistical analysis and machine learning. In this paper, we both introduce a more efficient secure aggregation construction and extend secure aggregation by enabling input validation, in which the server can check that clients' inputs satisfy required constraints such as $L_0$, $L_2$, and $L_\infty$ bounds. This prevents malicious clients from gaining disproportionate influence on the computed aggregated statistics or machine learning model.

Our new secure aggregation protocol improves the computational efficiency of the state-of-the-art protocol of Bell et al. (CCS 2020) both asymptotically and concretely: we show via experimental evaluation that it results in $2$-$8$X speedups in client computation in practical scenarios. Likewise, our extended protocol with input validation improves on prior work by more than $30$X in terms of client communiation (with comparable computation costs). Compared to the base protocols without input validation, the extended protocols incur only $0.1$X additional communication, and can process binary indicator vectors of length $1$M, or 16-bit dense vectors of length $250$K, in under $80$s of computation per client.

Multi-key homomorphic encryption is a generalized notion of homomorphic encryption supporting arbitrary computation on ciphertexts, possibly encrypted under different keys. In this paper, we revisit the work of Chen, Chillotti and Song (ASIACRYPT 2019) and present yet another multi-key variant of the TFHE scheme.

The previous construction by Chen et al. involves a blind rotation procedure where the complexity of each iteration gradually increases as it operates on ciphertexts under different keys. Hence, the complexity of gate bootstrapping grows quadratically with respect to the number of associated keys. On the other hand, our scheme is based on a new blind rotation algorithm which consists of two separate phases. We first split a given multi-key ciphertext into several single-key ciphertexts, take each of them as input to the blind rotation procedure, and obtain accumulators corresponding to individual keys. Then, we merge these single-key accumulators into a single multi-key accumulator. In particular, we develop a novel homomorphic operation between single-key RLEV and multi-key RLWE ciphertexts to instantiate our pipeline.

Therefore, our construction achieves an almost linear time complexity since the gate bootstrapping is dominated by the first phase of blind rotation which requires only independent single-key operations. It also enjoys with great advantages of parallelizability and key-compatibility. Finally, we implement the proposed scheme and provide its performance benchmark. For example, our experiment of 16-key gate bootstrapping demonstrates about 5.3x speedup over prior work.

A fully homomorphic encryption (FHE) scheme allows a client to encrypt and delegate its data to a server that performs computation on the encrypted data that the client can then decrypt. While FHE gives confidentiality to clients' data, it does not protect the server's input and computation. Nevertheless, FHE schemes are still helpful in building delegation protocols that reduce communication complexity, as FHE ciphertext's size is independent of the size of the computation performed on them.

We can further extend FHE by a property called circuit privacy, which guarantees that the result of computing on ciphertexts reveals no information on the computed function and the inputs of the server. Thereby, circuit private FHE gives rise to round optimal and communication efficient secure two-party computation protocols. Unfortunately, despite significant efforts and much work put into the efficiency and practical implementations of FHE schemes, very little has been done to provide useful and practical FHE supporting circuit privacy. In this work, we address this gap and design the first randomized bootstrapping algorithm whose single invocation sanitizes a ciphertext and, consequently, servers as a tool to provide circuit privacy. We give an extensive analysis, propose parameters, and provide a C++ implementation of our scheme. Our bootstrapping can sanitize a ciphertext to achieve circuit privacy at an 80-bit statistical security level in 1.4 seconds. In addition, we can perform non-sanitized bootstrapping in around 0.14 seconds on a laptop without additional public keys. Crucially, we do not need to increase the parameters significantly to perform computation before or after the sanitization takes place. For comparison's sake, we revisit the Ducas-Stehl\'e washing machine method. In particular, we give a tight analysis, estimate efficiency, review old and provide new parameters.

During the last decades there has been an increasing interest in Elliptic curve cryptography (ECC) and, especially, the Elliptic Curve Digital Signature Algorithm (ECDSA) in practice. The rather recent developments of emergent technologies, such as blockchain and the Internet of Things (IoT), have motivated researchers and developers to construct new cryptographic hardware accelerators for ECDSA. Different types of optimizations (either platform dependent or algorithmic) were presented in the literature. In this context, we turn our attention to ECC and propose a new method for generating ECDSA moduli with a predetermined portion that allows one to double the speed of Barrett's algorithm. Moreover, we take advantage of the advancements in the Artificial Intelligence (AI) field and bring forward an AI-based approach that enhances Schoof's algorithm for finding the number of points on an elliptic curve in terms of implementation efficiency. Our results represent algorithmic speed-ups exceeding the current paradigm as we are also preoccupied by other particular security environments meeting the needs of governmental organizations.

Secure Non-Interactive Reductions (SNIR) is a recently introduced, but fundamental cryptographic primitive. The basic question about SNIRs is how to determine if there is an SNIR from one 2-party correlation to another. While prior work provided answers for several pairs of correlations, the possibility that this is an undecidable problem in general was left open. In this work we show that the existence of an SNIR between any pair of correlations can be determined by an algorithm.

At a high-level, our proof follows the blueprint of a similar (but restricted) result by Khorasgani et al. But combining the spectral analysis of SNIRs by Agrawal et al. (Eurocrypt 2022) with a new variant of a "junta theorem" by Kindler and Safra, we obtain a complete resolution of the decidability question for SNIRs. The new junta theorem that we identify and prove may be of independent interest.

Ascon family is one of the finalists of the National Institute of Standards and Technology (NIST) lightweight cryptography standardization process. The family includes three Authenticated Encryption with Associated Data (AEAD) schemes: Ascon-128 (primary), Ascon-128a, and Ascon-80pq. In this paper, we study the resistance of the Ascon~family against conditional cube attacks in nonce-misuse setting, and present new state- and key-recovery attacks. Our attack recovers the full state information and the secret key of Ascon-128a using 7-round Ascon-permutation for the encryption phase, with $2^{117}$ data and $2^{116.2}$ time. This is the best known attack result for Ascon-128a as far as we know. We also show that the partial state information of Ascon-128 can be recovered with $2^{44.8}$ data. Finally, by assuming that the full state information of Ascon-80pq was recovered by Baudrin et al.'s attack, we show that the 160-bit secret key of Ascon-80pq can be recovered with $2^{128}$ time. Although our attacks do not invalidate designers' claim, those allow us to understand the security of Ascon in nonce-misuse setting.

Cuckoo hashing is a powerful primitive that enables storing items using small space with efficient lookups. At a high level, cuckoo hashing maps $n$ items into $b$ entries storing at most $\ell$ items such that each item is placed into one of $k$ randomly chosen entries. Additionally, there is an overflow stash that can store at most $s$ items. Many cryptographic primitives rely upon cuckoo hashing to privately and efficiently embed data. It is integral to ensure small failure probability for constructing cuckoo hashing tables as it directly relates to the privacy.

As our main result, we present a more efficient cuckoo hashing construction using more hash functions. For construction failure probability $\epsilon$, the query complexity of our cuckoo hashing scheme is $O(\sqrt{\log(1/\epsilon)/\log n})$. This is a quadratic improvement over previously known cuckoo hashing constructions that used larger stashes or entries. We also prove lower bounds matching our construction.

We also initiate the study of robust cuckoo hashing where the input set may be chosen with knowledge of the hash functions. We present a cuckoo hashing scheme with query overhead $\tilde{O}(\log \lambda)$ that is robust against PPT adversaries except with ${\bf negl}(\lambda)$ probability. Furthermore, we present lower bounds showing that this construction is tight and that extending previous approaches of large stashes or entries cannot obtain robustness except with $\Omega(n)$ query overhead. In other words, robust cuckoo hashing may only be obtained efficiently with a large number of hash functions.

As applications of our results, we obtain improved constructions for batch codes and private information retrieval. In particular, we present the most efficient explicit batch code and blackbox reduction from single-query PIR to batch PIR.

Users of decentralized financial networks suffer from inventive security exploits. Identity-based fraud prevention methods are inapplicable in these networks, as they contradict their privacy-minded design philosophy. Novel mitigation strategies are therefore needed. Their rollout, however, may damage other desirable network properties.

In this work, we introduce an evaluation framework for mitigation strategies in decentralized financial networks. This framework allows researchers and developers to examine and compare proposed protocol modifications along multiple axes, such as privacy, security, and user experience.

As an example, we focus on the jamming attack in the Lightning Network. Lightning is a peer-to-peer payment channel network on top of Bitcoin. Jamming is a cheap denial-of-service attack that allows an adversary to temporarily disable Lightning channels by flooding them with failing payments.

We propose a practical solution to jamming that combines unconditional fees and peer reputation. Guided by the framework, we show that, while discouraging jamming, our solution keeps the protocol incentive compatible. It also preserves security, privacy, and user experience, and is straightforward to implement. We support our claims analytically and with simulations. Moreover, our anti-jamming solution may help alleviate other Lightning issues, such as malicious channel balance probing.

Since their introduction in the 1970s, multi-party computation protocols have become the prevalent method for two or more parties to jointly compute an agreed upon function on private inputs without revealing them to other parties. While some efficiency gains in the offline phase of MPC protocols have been achieved, most works in the past have focused on optimising the online phase. Improvements to the online phase typically shifted significant workload to the offline phase. In this work we explore a novel approach to streamline the offline phase of secret sharing based MPC protocols by introducing a helper party that executes the preprocessing for the parties engaged in the online phase. We prove, that the security guarantees provided by the MPC protocols stay unchanged and demonstrate the efficiency of our approach in two sets of benchmarks. We furthermore give three examples of real world instantiations of the helper party to demonstrate that our approach is not only of a theoretical nature.

CRYSTALS-Kyber has been recently selected by the NIST as a new public-key encryption and key-establishment algorithm to be standardized. This makes it important to assess how well CRYSTALS-Kyber implementations withstand side-channel attacks. Software implementations of CRYSTALS-Kyber have been already analyzed and the discovered vulnerabilities were patched in the subsequently released versions. In this paper, we present a profiling side-channel attack on a hardware implementation of CRYSTALS-Kyber with the security parameter $k = 3$, Kyber768. Since hardware implementations carry out computation in parallel, they are typically more difficult to break than their software counterparts. We demonstrate a successful message (session key) recovery by deep learning-based power analysis. Our results indicate that currently available hardware implementations of CRYSTALS-Kyber need better protection against side-channel attacks.

In attribute-based signatures (ABS) for inner products, the digital signature analogue of attribute-based encryption for inner products (Katz et al., EuroCrypt'08), a signing-key (resp. signature) is labeled with an $n$-dimensional vector $\mathbf{x}\in\mathbf{Z}_p^n$ (resp. $\mathbf{y}\in\mathbf{Z}_p^n$) for a prime $p$, and the signing succeeds iff their inner product is zero, i.e., $ \langle \mathbf{x}, \mathbf{y} \rangle=0 \pmod p$. We generalize it to ABS for range of inner product (ARIP), requiring the inner product to be within an arbitrarily-chosen range $[L,R]$. As security notions, we define adaptive unforgeablity and perfect signer-privacy. The latter means that any signature reveals no more information about $\mathbf{x}$ than $\langle \mathbf{x}, \mathbf{y} \rangle \in[L,R]$. We propose two efficient schemes, secure under some Diffie-Hellman type assumptions in the standard model, based on non-interactive proof and linearly homomorphic signatures. The 2nd (resp. 1st) scheme is independent of the parameter $n$ in secret-key size (resp. signature size and verification cost). We show that ARIP has many applications, e.g., ABS for range evaluation of polynomials/weighted averages, fuzzy identity-based signatures, time-specific signatures, ABS for range of Hamming/Euclidean distance and ABS for hyperellipsoid predicates.

Adaptor signatures are a new cryptographic primitive that binds the authentication of a message to the revelation of a secret value. In recent years, this primitive has gained increasing popularity both in academia and practice due to its versatile use-cases in different Blockchain applications such as atomic swaps and payment channels. The security of these applications, however, crucially relies on users storing and maintaining the secret values used by adaptor signatures in a secure way. For standard digital signature schemes, cryptographic wallets have been introduced to guarantee secure storage of keys and execution of the signing procedure. However, no prior work has considered cryptographic wallets for adaptor signatures.

In this work, we introduce the notion of adaptor wallets. Adaptor wallets allow parties to securely use and maintain adaptor signatures in the Blockchain setting. Our adaptor wallets are both deterministic and operate in the hot/cold paradigm, which was first formalized by Das et al. (CCS 2019) for standard signature schemes. We introduce a new cryptographic primitive called adaptor signatures with rerandomizable keys, and use it to generically construct adaptor wallets. We further show how to instantiate adaptor signatures with rerandomizable keys from the ECDSA signature scheme and discuss that they can likely be built for Schnorr and Katz-Wang schemes as well. Finally, we discuss the limitations of the existing ECDSA- and Schnorr-based adaptor signatures w.r.t. deterministic wallets in the hot/cold setting and prove that it is impossible to overcome these drawbacks given the current state-of-the-art design of adaptor signatures.

Threshold cryptographic algorithms achieve robustness against key and access compromise by distributing secret keys among multiple entities. Most prior work focuses on threshold public-key primitives, despite extensive use of authenticated encryption in practice. Though the latter can be deployed in a threshold manner using multi-party computation (MPC), doing so incurs a high communication cost. In contrast, dedicated constructions of threshold authenticated encryption algorithms can achieve high performance. However to date, few such algorithms are known, most notably DiSE (distributed symmetric encryption) by Agrawal et al. (ACM CCS 2018). To achieve threshold authenticated encryption} (TAE), prior work does not suffice, due to shortcomings in definitions, analysis, and design, allowing for potentially insecure schemes, an undesirable similarity between encryption and decryption, and insufficient understanding of the impact of parameters due to lack of concrete analysis. In response, we revisit the problem of designing secure and efficient TAE schemes. (1) We give new TAE security definitions in the fully malicious setting addressing the aforementioned concerns. (2) We construct efficient schemes satisfying our definitions and perform concrete and more modular security analyses. (3) We conduct an extensive performance evaluation of our constructions, against prior ones.

The longest-chain paradigm introduced by the Bitcoin protocol allows Byzantine consensus with fluctuating participation where nodes can spontaneously become active and inactive anytime. Since then, there have been several follow-up works that aim to achieve similar guarantees without Bitcoin's computationally expensive proof of work. However, existing solutions do not fully inherit Bitcoin's dynamic participation support. Specifically, they have to assume malicious nodes are always active, i.e., no late joining or leaving is allowed for malicious nodes, due to a problem known as costless simulation. Another problem of Bitcoin is its notoriously large latency. A series of works try to improve the latency while supporting dynamic participation. The work of Momose-Ren (CCS 2022) eventually achieved constant latency, but its concrete latency is still large. This work addresses both of these problems by presenting a protocol that has $3$ round latency, tolerates one-third malicious nodes, and allows fully dynamic participation of both honest and malicious nodes. We also present a protocol with $2$ round latency with slightly lower fault tolerance.

We present a protocol for checking the values of a committed polynomial $\phi(X)$ over a mutliplicative subgroup $V\subset \mathbb{F}$ of size $m$ are contained in a table $T\in \mathbb{F}^N$. After an $O(N \log^2 N)$ preprocessing step, the prover algorithm runs in *quasilinear* time $O(m\log ^2 m)$. We improve upon the recent breakthrough results Caulk[ZBK+22] and Caulk+[PK22], which were the first to achieve the complexity sublinear in the full table size $N$ with prover time being $O(m^2+m\log N)$ and $O(m^2)$, respectively. We pose further improving this complexity to $O(m\log m)$ as the next important milestone for efficient zk-SNARK lookups.