### Volume 1, Issue 1

##### Published 2024-04-09

##### Bit Security as Cost to Demonstrate Advantage

Keewoo Lee

We revisit the question of what the definition of bit security should be, previously answered by Micciancio-Walter (Eurocrypt 2018) and Watanabe-Yasunaga (Asiacrypt 2021). Our new definition is simple, but (i) captures both search and decision primitives in a single framework like Micciancio-Walter, and (ii) has a firm operational meaning like Watanabe-Yasunaga. It also matches intuitive expectations and can be well-formulated regarding Hellinger distance. To support and justify the new definition, we prove several classic security reductions with respect to our bit security. We also provide pathological examples that indicate the ill-definedness of bit security defined in Micciancio-Walter and Watanabe-Yasunaga.

##### Proximity Testing with Logarithmic Randomness

Benjamin E. Diamond, Jim Posen

A fundamental result dating to Ligero (Des. Codes Cryptogr. '23) establishes that each fixed linear block code exhibits proximity gaps with respect to the collection of affine subspaces, in the sense that each given subspace either resides entirely close to the code, or else contains only a small portion which resides close to the code. In particular, any given subspace's failure to reside entirely close to the code is necessarily witnessed, with high probability, by a uniformly randomly sampled element of that subspace. We investigate a variant of this phenomenon in which the witness is not sampled uniformly from the subspace, but rather from a much smaller subset of it. We show that a logarithmic number of random field elements (in the dimension of the subspace) suffice to effect an analogous proximity test, with moreover only a logarithmic (multiplicative) loss in the possible prevalence of false witnesses. We discuss applications to recent noninteractive proofs based on linear codes, including Brakedown (CRYPTO '23).

##### Verifiable Encryption from MPC-in-the-Head

Akira Takahashi, Greg Zaverucha

Verifiable encryption (VE) is a protocol where one can provide assurance that an encrypted plaintext satisfies certain properties, or relations. It is an important building block in cryptography with many useful applications, such as key escrow, group signatures, optimistic fair exchange, and others. However, the majority of previous VE schemes are restricted to instantiation with specific public-key encryption schemes or relations. In this work, we propose a novel framework that realizes VE protocols using zero-knowledge proof systems based on the MPC-in-the-head paradigm (Ishai et al. STOC 2007). Our generic compiler can turn a large class of zero-knowledge proofs into secure VE protocols for any secure public-key encryption scheme with the undeniability property, a notion that essentially guarantees binding of encryption when used as a commitment scheme. Our framework is versatile: because the circuit proven by the MPC-in-the-head prover is decoupled from a complex encryption function, the work of the prover is focused on proving the encrypted data satisfies the relation, not the proof of plaintext knowledge. Hence, our approach allows for instantiation with various combinations of properties about the encrypted data and encryption functions. We then consider concrete applications, to demonstrate the efficiency of our framework, by first giving a new approach and implementation to verifiably encrypt discrete logarithms in any prime order group more efficiently than was previously known. Then we give the first practical verifiable encryption scheme for AES keys with post-quantum security, along with an implementation and benchmarks.

##### Impossibility of Post-Quantum Shielding Black-Box Constructions of CCA from CPA

Loïs Huguenin-Dumittan, Serge Vaudenay

Proving whether it is possible to build IND-CCA public-key encryption (PKE) from IND-CPA PKE in a black-box manner is a major open problem in theoretical cryptography. In a significant breakthrough, Gertner, Malkin and Myers showed in 2007 that shielding black-box reductions from IND-CCA to IND-CPA do not exist in the standard model. Shielding means that the decryption algorithm of the IND-CCA scheme does not call the encryption algorithm of the underlying IND-CPA scheme. In other words, it implies that every tentative construction of IND-CCA from IND-CPA must have a re-encryption step when decrypting.

This result was only proven with respect to classical algorithms. In this work we show that it stands in a post-quantum setting. That is, we prove that there is no post-quantum shielding black-box construction of IND-CCA PKE from IND-CPA PKE. In the type of reductions we consider, i.e. post-quantum ones, the constructions are still classical in the sense that the schemes must be computable on classical computers, but the adversaries and the reduction algorithm can be quantum. This suggests that considering quantum notions, which are stronger than their classical counterparts, and allowing for quantum reductions does not make building IND-CCA public-key encryption easier.

##### Optimizations and Practicality of High-Security CSIDH

Fabio Campos, Jorge Chávez-Saab, Jesús-Javier Chi-Domínguez, Michael Meyer, Krijn Reijnders, Francisco Rodríguez-Henríquez, Peter Schwabe, Thom Wiggers

In this work, we assess the real-world practicality of CSIDH, an isogeny-based non-interactive key exchange. We provide the first thorough assessment of the practicality of CSIDH in higher parameter sizes for conservative estimates of quantum security, and with protection against physical attacks.

This requires a three-fold analysis of CSIDH. First, we describe two approaches to efficient high-security CSIDH implementations, based on SQALE and CTIDH. Second, we optimize such high-security implementations, on a high level by improving several subroutines, and on a low level by improving the finite field arithmetic. Third, we benchmark the performance of high-security CSIDH. As a stand-alone primitive, our implementations outperform previous results by a factor up to 2.53×.

As a real-world use case considering network protocols, we use CSIDH in TLS variants that allow early authentication through a NIKE. Although our instantiations of CSIDH have smaller communication requirements than post-quantum KEM and signature schemes, even our highly-optimized implementations result in too-large handshake latency (tens of seconds), showing that CSIDH is only practical in niche cases.

##### Using Predicate Extension for Predicate Encryption to Generically Obtain Chosen-Ciphertext Security and Signatures

Marloes Venema, Leon Botros

Predicate encryption (PE) is a type of public-key encryption that captures many useful primitives such as attribute-based encryption (ABE). Although much progress has been made to generically achieve security against chosen-plaintext attacks (CPA) efficiently, in practice, we also require security against chosen-ciphertext attacks (CCA). Because achieving CCA-security on a case-by-case basis is a complicated task, several generic conversion methods have been proposed, which typically target different subclasses of PE such as ciphertext-policy ABE. As is common, such conversion methods may sacrifice some efficiency. Notably, for ciphertext-policy ABE, all proposed generic transformations incur a significant decryption overhead. Furthermore, depending on the setting in which PE is used, we may also want to require that messages are signed. To do this, predicate signature schemes can be used. However, such schemes provide a strong notion of privacy for the signer, which may be stronger than necessary for some practical settings at the cost of efficiency.

In this work, we propose the notion of predicate extension, which transforms the predicate used in a PE scheme to include one additional attribute, in both the keys and the ciphertexts. Using predicate extension, we can generically obtain CCA-security and signatures from a CPA-secure PE scheme. For the CCA-security transform, we observe that predicate extension implies a two-step approach to achieving CCA-security. This insight broadens the applicability of existing transforms for specific subclasses of PE to cover all PE. We also propose a new transform that incurs slightly less overhead than existing transforms. Furthermore, we show that predicate extension allows us to create a new type of signatures, which we call PE-based signatures. PE-based signatures are weaker than typical predicate signatures in the sense that they do not provide privacy for the signer. Nevertheless, such signatures may be more suitable for some practical settings owing to their efficiency or reduced interactivity. Lastly, to show that predicate extensions may facilitate a more efficient way to achieve CCA-security generically than existing methods, we propose a novel predicate-extension transformation for a large class of pairing-based PE, covered by the pair and predicate encodings frameworks. In particular, this yields the most efficient generic CCA-conversion for ciphertext-policy ABE.

##### A Survey of Two Verifiable Delay Functions Using Proof of Exponentiation

Dan Boneh, Benedikt Bünz, Ben Fisch

A verifiable delay function (VDF) is an important tool used for adding delay in decentralized applications. This paper surveys and compares two beautiful verifiable delay functions, one due to Pietrzak, and the other due to Wesolowski, In addition, we provide a new computational proof of security for one of them, present an attack on an incorrect implementation of the other, and compare the complexity assumptions needed for both schemes.

##### On the Efficiency of Generic, Quantum Cryptographic Constructions

Keita Xagawa

One of the central questions in cryptology is how efficient generic constructions of cryptographic primitives can be. Gennaro, Gertner, Katz, and Trevisan [SIAM J. of Compt., 2005] studied the lower bounds of the number of invocations of a (trapdoor) one-way permutation in order to construct cryptographic schemes, e.g., pseudorandom number generators, digital signatures, and public-key and symmetric-key encryption.

Recently, quantum machines have been explored to _construct_ cryptographic primitives other than quantum key distribution. This paper studies the efficiency of _quantum_ black-box constructions of cryptographic primitives when the communications are _classical_. Following Gennaro et al., we give the lower bounds of the number of invocations of an underlying quantumly-computable quantum-one-way permutation when the _quantum_ construction of pseudorandom number generator and symmetric-key encryption is weakly black-box. Our results show that the quantum black-box constructions of pseudorandom number generator and symmetric-key encryption do not improve the number of invocations of an underlying quantumly-computable quantum-one-way permutation.

##### Fast polynomial multiplication using matrix multiplication accelerators with applications to NTRU on Apple M1/M3 SoCs

Décio Luiz Gazzoni Filho, Guilherme Brandão, Julio López

Efficient polynomial multiplication routines are critical to the performance of lattice-based post-quantum cryptography (PQC). As PQC standards only recently started to emerge, CPUs still lack specialized instructions to accelerate such routines. Meanwhile, deep learning has grown immeasurably in importance. Its workloads call for teraflops-level of processing power for linear algebra operations, mainly matrix multiplication. Computer architects have responded by introducing ISA extensions, coprocessors and special-purpose cores to accelerate such operations. In particular, Apple ships an undocumented matrix-multiplication coprocessor, AMX, in hundreds of millions of mobile phones, tablets and personal computers. Our work repurposes AMX to implement polynomial multiplication and applies it to the NTRU cryptosystem, setting new speed records on the Apple M1 and M3 systems-on-chip (SoCs): polynomial multiplication, key generation, encapsulation and decapsulation are sped up by $1.54$–$3.07\times$, $1.08$–$1.33\times$, $1.11$–$1.50\times$ and $1.20$–$1.98\times$, respectively, over the previous state-of-the-art.

##### A Prime-Order Group with Complete Formulas from Even-Order Elliptic Curves

Thomas Pornin

This paper describes a generic methodology for obtaining unified, and then complete formulas for a prime-order group abstraction homomorphic to a subgroup of an elliptic curve with even order. The method is applicable to any curve with even order, in finite fields of both even and odd characteristic; it is most efficient on curves with order equal to 2 modulo 4, dubbed "double-odd curves". In large characteristic fields, we obtain doubling formulas with cost as low as 1M + 5S, and the resulting group allows building schemes such as signatures that outperform existing fast solutions, e.g. Ed25519. In binary fields, the obtained formulas are not only complete but also faster than previously known incomplete formulas; we can sign and verify in as low as 18k and 27k cycles on x86 CPUs, respectively.

##### CCA Security with Short AEAD Tags

Mustafa Khairallah

The size of the authentication tag represents a significant overhead for applications that are limited by bandwidth or memory. Hence, some authenticated encryption designs have a smaller tag than the required privacy level, which was also suggested by the NIST lightweight cryptography standardization project. In the ToSC 2022, two papers have raised questions about the IND-CCA security of AEAD schemes in this situation. These papers show that (a) online AE cannot provide IND-CCA security beyond the tag length, and (b) it is possible to have IND-CCA security beyond the tag length in a restricted Encode-then-Encipher framework. In this paper, we address some of the remaining gaps in this area. Our main result is to show that, for a fixed stretch, Pseudo-Random Injection security implies IND-CCA security as long as the minimum ciphertext size is at least as large as the required IND-CCA security level. We also show that this bound is tight and that any AEAD scheme that allows empty plaintexts with a fixed stretch cannot achieve IND-CCA security beyond the tag length. Next, we look at the weaker notion of MRAE security, and show that two-pass schemes that achieve MRAE security do not achieve IND-CCA security beyond the tag size. This includes SIV and rugged PRPs.

##### Computing isogenies between finite Drinfeld modules

Benjamin Wesolowski

We prove that isogenies between Drinfeld F[x]-modules over a finite field can be computed in polynomial time. This breaks Drinfeld analogs of isogeny-based cryptosystems.

##### Differential-Linear Cryptanalysis of GIFT family and GIFT-based Ciphers

Shichang Wang, Meicheng Liu, Shiqi Hou, Dongdai Lin

At CHES 2017, Banik et al. proposed a lightweight block cipher GIFT consisting of two versions GIFT-64 and GIFT-128. Recently, there are lots of authenticated encryption schemes that adopt GIFT-128 as their underlying primitive, such as GIFT-COFB and HyENA. To promote a comprehensive perception of the soundness of the designs, we evaluate their security against differential-linear cryptanalysis.

For this, automatic tools have been developed to search differential-linear approximation for the ciphers based on S-boxes. With the assistance of the automatic tools, we find 13-round differential-linear approximations for GIFT-COFB and HyENA. Based on the distinguishers, 18-round key-recovery attacks are given for the message processing phase and initialization phase of both ciphers. Moreover, the resistance of GIFT-64/128 against differential-linear cryptanalysis is also evaluated. The 12-round and 17-round differential-linear approximations are found for GIFT-64 and GIFT-128 respectively, which lead to 18-round and 19-round key-recovery attacks respectively. Here, we stress that our attacks do not threaten the security of these ciphers.

##### Understanding binary-Goppa decoding

Daniel J. Bernstein

This paper reviews, from bottom to top, a polynomial-time algorithm to correct $t$ errors in classical binary Goppa codes defined by squarefree degree-$t$ polynomials. The proof is factored through a proof of a simple Reed–Solomon decoder, and the algorithm is simpler than Patterson's algorithm. All algorithm layers are expressed as Sage scripts backed by test scripts. All theorems are formally verified. The paper also covers the use of decoding inside the Classic McEliece cryptosystem, including reliable recognition of valid inputs.

##### Simple Two-Message OT in the Explicit Isogeny Model

Emmanuela Orsini, Riccardo Zanotto

In this work we study algebraic and generic models for group actions, and extend them to the universal composability (UC) framework of Canetti (FOCS 2001). We revisit the constructions of Duman et al. (PKC 2023) integrating the type-safe model by Zhandry (Crypto 2022), adapted to the group action setting, and formally define an algebraic action model (AAM). This model restricts the power of the adversary in a similar fashion to the algebraic group model (AGM). By imposing algebraic behaviour to the adversary and environment of the UC framework, we construct the UC-AAM. Finally, we instantiate UC-AAM with isogeny-based assumptions, in particular the CSIDH action with twists, obtaining the explicit isogeny model, UC-EI; we observe that, under certain assumptions, this model is "closer" to standard UC than the UC-AGM, even though there still exists an important separation. We demonstrate the utility of our definitions by proving UC-EI security for the passive-secure oblivious transfer protocol described by Lai et al. (Eurocrypt 2021), hence providing the first concretely efficient two-message isogeny-based OT protocol in the random oracle model against malicious adversaries.

##### Feldman's Verifiable Secret Sharing for a Dishonest Majority

Yi-Hsiu Chen, Yehuda Lindell

Verifiable secret sharing (VSS) protocols enable parties to share secrets while guaranteeing security (in particular, that all parties hold valid and consistent shares) even if the dealer or some of the participants are malicious. Most work on VSS focuses on the honest majority case, primarily since it enables one to guarantee output delivery (e.g., a corrupted recipient cannot prevent an honest dealer from sharing their value). Feldman's VSS is a well known and popular protocol for this task and relies on the discrete log hardness assumption. In this paper, we present a variant of Feldman's VSS for the dishonest majority setting and formally prove its security. Beyond the basic VSS protocol, we present a publicly-verifiable version, as well as show how to securely add participants to the sharing and how to refresh an existing sharing (all secure in the presence of a dishonest majority). We prove that our protocols are UC secure, for appropriately defined ideal functionalities.

##### Post-Quantum Ready Key Agreement for Aviation

Marcel Tiepelt, Christian Martin, Nils Maeurer

Transitioning from classically to quantum secure key agreement protocols may require to exchange fundamental components, for example, exchanging Diffie-Hellman-like key exchange with a key encapsulation mechanism (KEM). Accordingly, the corresponding security proof can no longer rely on the Diffie-Hellman assumption, thus invalidating the security guarantees. As a consequence, the security properties have to be re-proven under a KEM-based security notion.

We initiate the study of the LDACS key agreement protocol (Edition 01.01.00 from 25.04.2023), which is soon-to-be-standardized by the International Civil Aviation Organization. The protocol's cipher suite features Diffie-Hellman as well as a KEM-based key agreement protocol to provide post-quantum security. While the former results in an instantiation of an ISO key agreement inheriting all security properties, the security achieved by the latter is ambiguous. We formalize the computational security using the systematic notions of de Saint Guilhem, Fischlin and Warinshi (CSF '20), and prove the exact security that the KEM-based variant achieves in this model; primarily entity authentication, key secrecy and key authentication. To further strengthen our “pen-and-paper” findings, we model the protocol and its security guarantees using Tamarin, providing an automated proof of the security against a Dolev-Yao attacker.

##### Broadcast Encryption using Sum-Product decomposition of Boolean functions

Aurélien Dupin, Simon Abelard

The problem of Broadcast Encryption (BE) consists in broadcasting an encrypted message to a large number of users or receiving devices in such a way that the emitter of the message can control which of the users can or cannot decrypt it.

Since the early 1990s, the design of BE schemes has received significant interest and many different concepts were proposed. A major breakthrough was achieved by Naor, Naor and Lotspiech (CRYPTO 2001) by partitioning cleverly the set of authorized users and associating a symmetric key to each subset. Since then, while there have been many advances in public-key based BE schemes, mostly based on bilinear maps, little was made on symmetric cryptography.

In this paper, we design a new symmetric-based BE scheme, named $\Sigma\Pi$BE, that relies on logic optimization and consensual security assumptions. It is competitive with the work of Naor et al. and provides a different tradeoff: the bandwidth requirement is significantly lowered at the cost of an increase in the key storage.

##### How to Make Rational Arguments Practical and Extractable

Matteo Campanelli, Chaya Ganesh, Rosario Gennaro

We investigate proof systems where security holds against rational parties instead of malicious ones. Our starting point is the notion of rational arguments, a variant of rational proofs (Azar and Micali, STOC 2012) where security holds against rational adversaries that are also computationally bounded.

Rational arguments are an interesting primitive because they generally allow for very efficient protocols, and in particular sublinear verification (i.e. where the Verifier does not have to read the entire input). In this paper we aim at narrowing the gap between literature on rational schemes and real world applications. Our contribution is two-fold.

We provide the first construction of rational arguments for the class of polynomial computations that is practical (i.e., it can be applied to real-world computations on reasonably common hardware) and with logarithmic communication. Techniques-wise, we obtain this result through a compiler from information-theoretic protocols and rational proofs for polynomial evaluation. The latter could be of independent interest.

As a second contribution, we propose a new notion of extractability for rational arguments. Through this notion we can obtain arguments where knowledge of a witness is incentivized (rather than incentivizing mere soundness). We show how our aforementioned compiler can also be applied to obtain efficient extractable rational arguments for $\mathsf{NP}$.

##### Towards Practical Transciphering for FHE with Setup Independent of the Plaintext Space

Pierrick Méaux, Jeongeun Park, Hilder V. L. Pereira

Fully Homomorphic Encryption (FHE) is a powerful tool to achieve non-interactive privacy preserving protocols with optimal computation/communication complexity. However, the main disadvantage is that the actual communication cost (bandwidth) is high due to the large size of FHE ciphertexts. As a solution, a technique called transciphering (also known as Hybrid Homomorphic Encryption) was introduced to achieve almost optimal bandwidth for such protocols. However, all existing works require clients to fix a precision for the messages or a mathematical structure for the message space beforehand. It results in unwanted constraints on the plaintext size or underlying structure of FHE based applications.

In this article, we introduce a new approach for transciphering which does not require fixed message precision decided by the client, for the first time. In more detail, a client uses any kind of FHE-friendly symmetric cipher for $\{0,1\}$ to send its input data encrypted bit-by-bit, then the server can choose a precision $p$ depending on the application and homomorphically transforms the encrypted bits into FHE ciphertexts encrypting integers in $\mathbb{Z}_p$. To illustrate our new technique, we evaluate a transciphering using FiLIP cipher and adapt the most practical homomorphic evaluation technique [CCS'22] to keep the practical latency. As a result, our proof-of-concept implementation for $p$ from $2^2$ to $2^8$ takes only from $13$ ms to $137$ ms.

##### X-Wing The Hybrid KEM You've Been Looking For

Manuel Barbosa, Deirdre Connolly, João Diogo Duarte, Aaron Kaiser, Peter Schwabe, Karolin Varner, Bas Westerbaan

X-Wing is a hybrid key-encapsulation mechanism based on X25519 and ML-KEM-768. It is designed to be the sensible choice for most applications. The concrete choice of X25519 and ML-KEM-768 allows X-Wing to achieve improved efficiency compared to using a generic KEM combiner. In this paper, we introduce the X-Wing hybrid KEM construction and provide a proof of security. We show (1) that X-Wing is a classically IND-CCA secure KEM if the strong Diffie-Hellman assumption holds in the X25519 nominal group, and (2) that X-Wing is a post-quantum IND-CCA secure KEM if ML-KEM-768 is itself an IND-CCA secure KEM and SHA3-256 is secure when used as a pseudorandom function. The first result is proved in the ROM, whereas the second one holds in the standard model. Loosely speaking, this means X-Wing is secure if either X25519 or ML-KEM-768 is secure. We stress that these security guarantees and optimizations are only possible due to the concrete choices that were made, and it may not apply in the general case.

##### New Attacks on LowMC Using Partial Sets in the Single-Data Setting

Subhadeep Banik, Andrea Caforio, Serge Vaudenay

The LowMC family of block ciphers was proposed by Albrecht et al. in Eurocrypt 2015, specifically targeting adoption in FHE and MPC applications due to its low multiplicative complexity. The construction operates a 3-bit quadratic S-box as the sole non-linear transformation in the algorithm. In contrast, both the linear layer and round key generation are achieved through multiplications of full rank matrices over GF(2). The cipher is instantiable using a diverse set of default configurations, some of which have partial non-linear layers i.e., in which the S-boxes are not applied over the entire internal state of the cipher.

The significance of cryptanalysing LowMC was elevated by its inclusion into the NIST PQC digital signature scheme PICNIC in which a successful key recovery using a single plaintext/ciphertext pair is akin to retrieving the secret signing key. The current state-of-the-art attack in this setting is due to Dinur at Eurocrypt 2021, in which a novel way of enumerating roots of a Boolean system of equation is morphed into a key-recovery procedure that undercuts an ordinary exhaustive search in terms of time complexity for the variants of the cipher up to five rounds.

In this work, we demonstrate that this technique can efficiently be enriched with a specific linearization strategy that reduces the algebraic degree of the non-linear layer as put forward by Banik et al. at IACR ToSC 2020(4). This amalgamation yields new attacks on certain instances of LowMC up to seven rounds.

##### A provably masked implementation of BIKE Key Encapsulation Mechanism

Loïc Demange, Mélissa Rossi

BIKE is a post-quantum key encapsulation mechanism (KEM) selected for the 4th round of the NIST's standardization campaign. It relies on the hardness of the syndrome decoding problem for quasi-cyclic codes and on the indistinguishability of the public key from a random element, and provides the most competitive performance among round 4 candidates, which makes it relevant for future real-world use cases. Analyzing its side-channel resistance has been highly encouraged by the community and several works have already outlined various side-channel weaknesses and proposed ad-hoc countermeasures. However, in contrast to the well-documented research line on masking lattice-based algorithms, the possibility of generically protecting code-based algorithms by masking has only been marginally studied in a 2016 paper by Chen et al. in SAC 2015. At this stage of the standardization campaign, it is important to assess the possibility of fully masking BIKE scheme and the resulting cost in terms of performances.

In this work, we provide the first high-order masked implementation of a code-based algorithm. We had to tackle many issues such as finding proper ways to handle large sparse polynomials, masking the key-generation algorithm or keeping the benefit of the bitslicing. In this paper, we present all the gadgets necessary to provide a fully masked implementation of BIKE, we discuss our different implementation choices and we propose a full proof of masking in the Ishai Sahai and Wagner (Crypto 2003) model.

More practically, we also provide an open C-code masked implementation of the key-generation, encapsulation and decapsulation algorithms with extensive benchmarks. While the obtained performance is slower than existing masked lattice-based algorithms, we show that masking at order 1, 2, 3, 4 and 5 implies a performance penalty of x5.8, x14.2, x24.4, x38 and x55.6 compared to order 0 (unmasked and unoptimized BIKE). This scaling is encouraging and no Boolean to Arithmetic conversion has been used.

##### Verifiable FHE via Lattice-based SNARKs

Shahla Atapoor, Karim Baghery, Hilder V. L. Pereira, Jannik Spiessens

Fully Homomorphic Encryption (FHE) is a prevalent cryptographic primitive that allows for computation on encrypted data. In various cryptographic protocols, this enables outsourcing computation to a third party while retaining the privacy of the inputs to the computation. However, these schemes make an honest-but-curious assumption about the adversary. Previous work has tried to remove this assumption by combining FHE with Verifiable Computation (VC). Recent work has increased the flexibility of this approach by introducing integrity checks for homomorphic computations over rings. However, efficient FHE for circuits of large multiplicative depth also requires non-ring computations called maintenance operations, i.e. modswitching and keyswitching, which cannot be efficiently verified by existing constructions. We propose the first efficiently verifiable FHE scheme that allows for arbitrary depth homomorphic circuits by utilizing the double-CRT representation in which FHE schemes are typically computed, and using lattice-based SNARKs to prove components of this computation separately, including the maintenance operations. Therefore, our construction can theoretically handle bootstrapping operations. We also present the first implementation of a verifiable computation on encrypted data for a computation that contains multiple ciphertext-ciphertext multiplications. Concretely, we verify the homomorphic computation of an approximate neural network containing three layers and >100 ciphertexts in less than 1 second while maintaining reasonable prover costs.

##### Simple Three-Round Multiparty Schnorr Signing with Full Simulatability

Yehuda Lindell

In a multiparty signing protocol, also known as a threshold signature scheme, the private signing key is shared amongst a set of parties and only a quorum of those parties can generate a signature. Research on multiparty signing has been growing in popularity recently due to its application to cryptocurrencies. Most work has focused on reducing the number of rounds to two, and as a result: (a) are not fully simulatable in the sense of MPC real/ideal security definitions, and/or (b) are not secure under concurrent composition, and/or (c) utilize non-standard assumptions of different types in their proofs of security. In this paper, we describe a simple three-round multiparty protocol for Schnorr signatures that is secure for any number of corrupted parties; i.e., in the setting of a dishonest majority. The protocol is fully simulatable, secure under concurrent composition, and proven secure in the standard model or random-oracle model (depending on the instantiations of the commitment and zero-knowledge primitives). The protocol realizes an ideal Schnorr signing functionality with perfect security in the ideal commitment and zero-knowledge hybrid model (and thus the only assumptions needed are for realizing these functionalities).

In our presentation, we do not assume that all parties begin with the message to be signed, the identities of the participating parties and a unique common session identifier, since this is often not the case in practice. Rather, the parties achieve consensus on these parameters as the protocol progresses.

##### Computing 2-isogenies between Kummer lines

Damien Robert, Nicolas Sarkis

We use theta groups to study $2$-isogenies between Kummer lines, with a particular focus on the Montgomery model. This allows us to recover known formulas, along with more efficient forms for translated isogenies, which require only $2S+2m_0$ for evaluation. We leverage these translated isogenies to build a hybrid ladder for scalar multiplication on Montgomery curves with rational $2$-torsion, which cost $3M+6S+2m_0$ per bit, compared to $5M+4S+1m_0$ for the standard Montgomery ladder.

##### On the Two-sided Permutation Inversion Problem

Gorjan Alagic, Chen Bai, Alexander Poremba, Kaiyan Shi

In the permutation inversion problem, the task is to find the preimage of some challenge value, given oracle access to the permutation. This fundamental problem in query complexity appears in many contexts, particularly cryptography. In this work, we examine the setting in which the oracle allows for quantum queries to both the forward and the inverse direction of the permutation—except that the challenge value cannot be submitted to the latter. Within that setting, we consider three options for the inversion algorithm: whether it can get quantum advice about the permutation, whether the query algorithm can restrict the distribution with which the challenge input is sampled, and whether it must produce the entire preimage (search) or only the first bit (decision). We prove several theorems connecting the hardness of the resulting variations of the permutation inversion problem and establish lower bounds for them. Our results show that, perhaps surprisingly, the permutation inversion problem does not become significantly easier when the adversary is granted oracle access to the inverse—provided it cannot query the challenge itself.

##### Survey: Recovering cryptographic keys from partial information, by example

Gabrielle De Micheli, Nadia Heninger

Side-channel attacks targeting cryptography may leak only partial or indirect information about the secret keys. There are a variety of techniques in the literature for recovering secret keys from partial information. In this work, we survey several of the main families of partial key recovery algorithms for RSA, (EC)DSA, and (elliptic curve) Diffie-Hellman, the classical public-key cryptosystems in common use today. We categorize the known techniques by the structure of the information that is learned by the attacker, and give simplified examples for each technique to illustrate the underlying ideas.

##### Secure Multi-Party Linear Algebra with Perfect Correctness

Jules Maire, Damien Vergnaud

We present new secure multi-party computation protocols for linear algebra over a finite field, which improve the state-of-the-art in terms of security. We look at the case of unconditional security with perfect correctness, i.e., information-theoretic security without errors. We notably propose an expected constant-round protocol for solving systems of m linear equations in n variables over Fq with expected complexity O(k n^2.5 + k m) (where complexity is measured in terms of the number of secure multiplications required) with k > m(m+n)+1. The previous proposals were not error-free: known protocols can indeed fail and thus reveal information with probability Omega(poly(m)/q). Our protocols are simple and rely on existing computer-algebra techniques, notably the Preparata-Sarwate algorithm, a simple but poorly known “baby-step giant-step” method for computing the characteristic polynomial of a matrix, and techniques due to Mulmuley for error-free linear algebra in positive characteristic.

##### Preliminary Cryptanalysis of the Biscuit Signature Scheme

Charles Bouillaguet, Julia Sauvage

Biscuit is a recent multivariate signature scheme based on the MPC-in-the-Head paradigm. It has been submitted to the NIST competition for additional signature schemes. Signatures are derived from a zero-knowledge proof of knowledge of the solution of a structured polynomial system. This extra structure enables efficient proofs and compact signatures. This short note demonstrates that it also makes these polynomial systems easier to solve than random ones. As a consequence, the original parameters of Biscuit failed to meet the required security levels and had to be upgraded.

##### New SAT-based Model for Quantum Circuit Decision Problem: Searching for Low-Cost Quantum Implementation

Jingwen Chen, Qun Liu, Yanhong Fan, Lixuan Wu, Boyun Li, Meiqin Wang

In recent years, quantum technology has been rapidly developed. As security analyses for symmetric ciphers continue to emerge, many require an evaluation of the resources needed for the quantum circuit implementation of the encryption algorithm. In this regard, we propose the quantum circuit decision problem, which requires us to determine whether there exists a quantum circuit for a given permutation f using M ancilla qubits and no more than K quantum gates within the circuit depth D. Firstly, we investigate heuristic algorithms and classical SAT-based models in previous works, revealing their limitations in solving the problem. Hence, we innovatively propose an improved SAT-based model incorporating three metrics of quantum circuits. The model enables us to find the optimal quantum circuit of an arbitrary 3 or 4-bit S-box under a given optimization goal based on SAT solvers, which has proved the optimality of circuits constructed by the tool, LIGHTER-R. Then, by combining different criteria in the model, we find more compact quantum circuit implementations of S-boxes such as RECTANGLE and GIFT. For GIFT S-box, our model provides the optimal quantum circuit that only requires 8 gates with a depth of 31. Furthermore, our model can be generalized to linear layers and improve the previous SAT-based model proposed by Huang et al. in ASIACRYPT 2022 by adding the criteria on the number of qubits and the circuit depth.

##### Towards the Impossibility of Quantum Public Key Encryption with Classical Keys from One-Way Functions

Samuel Bouaziz–Ermann, Alex B. Grilo, Damien Vergnaud, Quoc-Huy Vu

There has been a recent interest in proposing quantum protocols whose security relies on weaker computational assumptions than their classical counterparts. Importantly to our work, it has been recently shown that public-key encryption (PKE) from one-way functions (OWF) is possible if we consider quantum public keys. Notice that we do not expect classical PKE from OWF given the impossibility results of Impagliazzo and Rudich (STOC'89).

However, the distribution of quantum public keys is a challenging task. Therefore, the main question that motivates our work is if quantum PKE from OWF is possible if we have classical public keys. Such protocols are impossible if ciphertexts are also classical, given the impossibility result of Austrin et al.(CRYPTO'22) of quantum enhanced key-agreement (KA) with classical communication.

In this paper, we focus on black-box separation for PKE with classical public key and quantum ciphertext from OWF under the polynomial compatibility conjecture, first introduced in Austrin et al.. More precisely, we show the separation when the decryption algorithm of the PKE does not query the OWF. We prove our result by extending the techniques of Austrin et al. and we show an attack for KA in an extended classical communication model where the last message in the protocol can be a quantum state.