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#### 25 May 2023

###### Masahito Ishizaka, Kazuhide Fukushima

ePrint Report
In homomorphic signatures for subset predicates (HSSB), each message (to be signed) is a set. Any signature on a set $M$ allows us to derive a signature on any subset $M'\subseteq M$. Its superset version, which should be called homomorphic signatures for superset predicates (HSSP), allows us to derive a signature on any superset $M'\supseteq M$. In this paper, we propose homomorphic signatures for subset and superset mixed predicates (HSSM) as a simple combination of HSSB and HSSP. In HSSM, any signature on a message of a set-pair $(M, W)$ allows us to derive a signature on any $(M', W')$ such that $M'\subseteq M$ and $W'\supseteq W$. We propose an original HSSM scheme which is unforgeable under the decisional linear assumption and completely context-hiding. We show that HSSM has various applications, which include disclosure-controllable HSSB, disclosure-controllable redactable signatures, (key-delegatable) superset/subset predicate signatures, and wildcarded identity-based signatures.

###### Wutichai Chongchitmate, Yuval Ishai, Steve Lu, Rafail Ostrovsky

ePrint Report
Private set intersection (PSI) is one of the most extensively studied instances of secure computation. PSI allows two parties to compute the intersection of their input sets without revealing anything else. Other useful variants include PSI-Payload, where the output includes payloads associated with members of the intersection, and PSI-Sum, where the output includes the sum of the payloads instead of individual ones.

In this work, we make two related contributions. First, we construct simple and efficient protocols for PSI and PSI-Payload from a ring version of oblivious linear function evaluation (ring-OLE) that can be efficiently realized using recent ring-LPN based protocols. A standard OLE over a field F allows a sender with $a,b \in \mathbb{F}$ to deliver $ax+b$ to a receiver who holds $x \in \mathbb{F}$. Ring-OLE generalizes this to a ring $\mathcal{R}$, in particular, a polynomial ring over $\mathbb{F}$. Our second contribution is an efficient general reduction of a variant of PSI-Sum to PSI-Payload and secure inner product.

Our protocols have better communication cost than state-of-the-art PSI protocols, especially when requiring security against malicious parties and when allowing input-independent preprocessing. Compared to previous maliciously secure PSI protocols that have a similar com- putational cost, our online communication is 2x better for small sets (28 − 212 elements) and 20% better for large sets (220 − 224). Our protocol is also simpler to describe and implement. We obtain even bigger improvements over the state of the art (4-5x better running time) for our variant of PSI-Sum.

In this work, we make two related contributions. First, we construct simple and efficient protocols for PSI and PSI-Payload from a ring version of oblivious linear function evaluation (ring-OLE) that can be efficiently realized using recent ring-LPN based protocols. A standard OLE over a field F allows a sender with $a,b \in \mathbb{F}$ to deliver $ax+b$ to a receiver who holds $x \in \mathbb{F}$. Ring-OLE generalizes this to a ring $\mathcal{R}$, in particular, a polynomial ring over $\mathbb{F}$. Our second contribution is an efficient general reduction of a variant of PSI-Sum to PSI-Payload and secure inner product.

Our protocols have better communication cost than state-of-the-art PSI protocols, especially when requiring security against malicious parties and when allowing input-independent preprocessing. Compared to previous maliciously secure PSI protocols that have a similar com- putational cost, our online communication is 2x better for small sets (28 − 212 elements) and 20% better for large sets (220 − 224). Our protocol is also simpler to describe and implement. We obtain even bigger improvements over the state of the art (4-5x better running time) for our variant of PSI-Sum.

###### Vasyl Ustimenko, Tymoteusz Chojecki, Michal Klisowski

ePrint Report
Algebraic Constructions of Extremal Graph Theory
were efficiently used for the construction of Low Density Parity Check Codes for satellite communication, constructions of
stream ciphers and Postquantum Protocols of Noncommutative
cryptography and corresponding El Gamal type cryptosystems.
We shortly observe some results in these applications and present
idea of the usage of algebraic graphs for the development
of Multivariate Public Keys (MPK). Some MPK schemes are
presented at theoretical level, implementation of one of them is discussed.

###### Sherman S. M. Chow, Christoph Egger, Russell W. F. Lai, Viktoria Ronge, Ivy K. Y. Woo

ePrint Report
Anonymous systems (e.g. anonymous cryptocurrencies and updatable anonymous credentials) often follow a construction template where an account can only perform a single anonymous action, which in turn potentially spawns new (and still single-use) accounts (e.g. UTXO with a balance to spend or session with a score to claim). Due to the anonymous nature of the action, no party can be sure which account has taken part in an action and, therefore, must maintain an ever-growing list of potentially unused accounts to ensure that the system keeps running correctly. Consequently, anonymous systems constructed based on this common template are seemingly not sustainable.

In this work, we study the sustainability of ring-based anonymous systems, where a user performing an anonymous action is hidden within a set of decoy users, traditionally called a ``ring''.

On the positive side, we propose a general technique for ring-based anonymous systems to achieve sustainability. Along the way, we define a general model of decentralised anonymous systems (DAS) for arbitrary anonymous actions, and provide a generic construction which provably achieves sustainability. As a special case, we obtain the first construction of anonymous cryptocurrencies achieving sustainability without compromising availability. We also demonstrate the generality of our model by constructing sustainable decentralised anonymous social networks.

On the negative side, we show empirically that Monero, one of the most popular anonymous cryptocurrencies, is unlikely to be sustainable without altering its current ring sampling strategy. The main subroutine is a sub-quadratic-time algorithm for detecting used accounts in a ring-based anonymous system.

In this work, we study the sustainability of ring-based anonymous systems, where a user performing an anonymous action is hidden within a set of decoy users, traditionally called a ``ring''.

On the positive side, we propose a general technique for ring-based anonymous systems to achieve sustainability. Along the way, we define a general model of decentralised anonymous systems (DAS) for arbitrary anonymous actions, and provide a generic construction which provably achieves sustainability. As a special case, we obtain the first construction of anonymous cryptocurrencies achieving sustainability without compromising availability. We also demonstrate the generality of our model by constructing sustainable decentralised anonymous social networks.

On the negative side, we show empirically that Monero, one of the most popular anonymous cryptocurrencies, is unlikely to be sustainable without altering its current ring sampling strategy. The main subroutine is a sub-quadratic-time algorithm for detecting used accounts in a ring-based anonymous system.

###### Manas Wadhwa, Anubhab Baksi, Kai Hu, Anupam Chattopadhyay, Takanori Isobe, Dhiman Saha

ePrint Report
This paper presents ``SASQUATCH'', an open-source tool, that aids in finding an unknown substitution box (SBox) given its properties. The inspiration of our work can be directly attributed to the DCC 2022 paper by Lu, Mesnager, Cui, Fan and Wang. Taking their work as the foundation (i.e., converting the problem of SBox search to a satisfiability modulo theory instance and then invoking a solver), we extend in multiple directions (including -- but not limiting to -- coverage of more options, imposing time limit, parallel execution for multiple SBoxes, non-bijective SBox), and package everything within an easy-to-use interface. We also present ASIC benchmarks for some of the SBoxes.

###### Artem Grigor, Vincenzo Iovino, Giuseppe Visconti

ePrint Report
A natural approach to anonymous voting over Ethereum assumes that there is an off-chain aggregator that performs the following task. The aggregator receives valid signatures of YES/NO preferences from eligible voters and uses them to compute a zk-SNARK proof of the fact that the majority of voters have cast a preference for YES or NO. Then, the aggregator sends to the smart contract the zk-SNARK proof, the smart contract verifies the proof and can trigger an action (e.g., a transfer of funds). It is believed that as the zk-SNARK proof guarantees anonymity, the privacy of the voters is preserved by attackers not colluding with the aggregator. Moreover, if the SNARK proof verification is efficient the GAS cost will be independent on the number of participating voters and signatures submitted by voters to the aggregator.
In this paper we show that this naive approach to run referenda over Ethereum can incur severe security problems. We propose both mitigations and hardness results for achieving voting procedures in
which the proofs submitted on-chain are either ZK or succinct.

###### Shahla Atapoor, Karim Baghery, Daniele Cozzo, Robi Pedersen

ePrint Report
A Distributed Key Generation (DKG) protocol is an essential component of threshold cryptography. DKGs enable a group of parties to generate a secret and public key pair in a distributed manner so that the secret key is protected from being exposed, even if a certain number of parties are compromised. Robustness further guarantees that the construction of the key pair is always successful, even if malicious parties try to sabotage the computation. In this paper, we construct two efficient robust DKG protocols in the CSIDH setting that work with Shamir secret sharing. Both the proposed protocols are proven to be actively secure in the quantum random oracle model and use an Information Theoretically (IT) secure Verifiable Secret Sharing (VSS) scheme that is built using bivariate polynomials. As a tool, we construct a new piecewise verifiable proof system for structured public keys, that could be of independent interest. In terms of isogeny computations, our protocols outperform the previously proposed DKG protocols CSI-RAShi and Structured CSI-RAShi. As an instance, using our DKG protocols, 4 parties can sample a PK of size 4kB, for CSI-FiSh and CSI-SharK, respectively, 3.4 and 1.7 times faster than the current alternatives. On the other hand, since we use an IT-secure VSS, the fraction of corrupted parties is limited to less than a third and the communication cost of our schemes scales slightly worse with an increasing number of parties. For a low number of parties, our scheme still outperforms the alternatives in terms of communication.

###### Jung Hee Cheon, Hyeongmin Choe, Dongyeon Hong, MinJune Yi

ePrint Report
Recently, NIST has announced Kyber, a lattice-based key encapsulation mechanism (KEM), as a post-quantum standard.
However, it is not the most efficient scheme among the NIST's KEM finalists.
Saber enjoys more compact sizes and faster performance, and Mera et al. (TCHES '21) further pushed its efficiency, proposing a shorter KEM, Sable.
As KEM are frequently used on the Internet, such as in TLS protocols, it is essential to achieve high efficiency while maintaining sufficient security.

In this paper, we further push the efficiency limit of lattice-based KEMs by proposing SMAUG, a new post-quantum KEM scheme submitted to the Korean Post-Quantum Cryptography (KPQC) competition, whose IND-CCA2 security is based on the combination of MLWE and MLWR problems. We adopt several recent developments in lattice-based cryptography, targeting the textit{smallest} and the \textit{fastest} KEM while maintaining high enough security against various attacks, with a full-fledged use of sparse secrets. Our design choices allow SMAUG to balance the decryption failure probability and ciphertext sizes without utilizing error correction codes, whose side-channel resistance remains open.

With a constant-time C reference implementation, SMAUG achieves ciphertext sizes up to 12% and 9% smaller than Kyber and Saber, with much faster running time, up to 103% and 58%, respectively. Compared to Sable, SMAUG has the same ciphertext sizes but a larger public key, which gives a trade-off between the public key size versus performance; SMAUG has 39%-55% faster encapsulation and decapsulation speed in the parameter sets having comparable security.

In this paper, we further push the efficiency limit of lattice-based KEMs by proposing SMAUG, a new post-quantum KEM scheme submitted to the Korean Post-Quantum Cryptography (KPQC) competition, whose IND-CCA2 security is based on the combination of MLWE and MLWR problems. We adopt several recent developments in lattice-based cryptography, targeting the textit{smallest} and the \textit{fastest} KEM while maintaining high enough security against various attacks, with a full-fledged use of sparse secrets. Our design choices allow SMAUG to balance the decryption failure probability and ciphertext sizes without utilizing error correction codes, whose side-channel resistance remains open.

With a constant-time C reference implementation, SMAUG achieves ciphertext sizes up to 12% and 9% smaller than Kyber and Saber, with much faster running time, up to 103% and 58%, respectively. Compared to Sable, SMAUG has the same ciphertext sizes but a larger public key, which gives a trade-off between the public key size versus performance; SMAUG has 39%-55% faster encapsulation and decapsulation speed in the parameter sets having comparable security.

###### Vasyl Ustimenko, Aneta Wróblewska

ePrint Report
We introduce large groups of quadratic transformations of a vector space over the finite fields defined via symbolic computations with the usage of
algebraic constructions of Extremal Graph Theory. They can serve as platforms for the protocols of Noncommutative Cryptography with security based on the complexity of word decomposition problem in noncommutative polynomial transformation group.
The modifications of these symbolic computations in the case of large fields of characteristic two allow us to define quadratic bijective multivariate public keys such that the inverses of public maps has a large polynomial degree. Another family of public keys is defined over arbitrary commutative ring with unity.
We suggest the usage of constructed protocols for the private delivery of quadratic encryption maps instead of the public usage of these transformations, i.e. the idea of temporal multivariate rules with their periodical change.

###### Koustabh Ghosh, Joan Daemen

ePrint Report
In this paper, we study the differential properties of integer multiplication between two $w$-bit integers, resulting in a $2w$-bit integer. Our objective is to gain insights into its resistance against differential cryptanalysis and asses its suitability as a source of non-linearity in symmetric key primitives.

###### Julie Ha, Chloe Cachet, Luke Demarest, Sohaib Ahmad, Benjamin Fuller

ePrint Report
Biometric databases are being deployed with few cryptographic protections. Because of the nature of biometrics, privacy breaches affect users for their entire life.
This work introduces Private Eyes, the first zero-leakage biometric database. The only leakage of the system is unavoidable: 1) the log of the dataset size and 2) the fact that a query occurred. Private Eyes is built from symmetric searchable encryption. Proximity queries are the required functionality: given a noisy reading of a biometric, the goal is to retrieve all stored records that are close enough according to a distance metric.
Private Eyes combines locality sensitive-hashing or LSHs (Indyk and Motwani, STOC 1998) and encrypted maps. One searches for the disjunction of the LSHs of a noisy biometric reading. The underlying encrypted map needs to efficiently answer disjunction queries.
We focus on the iris biometric. Iris biometric data requires a large number of LSHs, approximately 1000. The most relevant prior work is in zero-leakage k-nearest-neighbor search (Boldyreva and Tang, PoPETS 2021), but that work is designed for a small number of LSHs.
Our main cryptographic tool is a zero-leakage disjunctive map designed for the setting when most clauses do not match any records. For the iris, on average at most 6% of LSHs match any stored value.
To aid in evaluation, we produce a synthetic iris generation tool to evaluate sizes beyond available iris datasets. This generation tool is a simple generative adversarial network. Accurate statistics are crucial to optimizing the cryptographic primitives so this tool may be of independent interest.
Our scheme is implemented and open-sourced. For the largest tested parameters of 5000 stored irises, search requires 26 rounds of communication and 26 minutes of single-threaded computation.

###### Ghada Arfaoui, Thibaut Jacques, Marc Lacoste, Cristina Onete, Léo Robert

ePrint Report
In multi-tenant cloud environments, physical resources are shared between various parties (called tenants) through the use of virtual machines (VMs). Tenants can verify the state of their VMs by means of deep-attestation: a process by which a (physical or virtual) Trusted Platform Module --TPM -- generates attestation quotes about the integrity state of the VMs. Unfortunately, most existing deep-attestation solutions are either: limited to single-tenant environments, in which tenant {privacy is irrelevant; are inefficient in terms of {linking VM attestations to hypervisor attestations; or provide privacy and/or linking, but at the cost of modifying the TPM hardware.

In this paper, we propose a privacy preserving TPM-based deep-attestation solution in multi-tenant environments, which provably guarantees: (i) Inter-tenant privacy: a tenant is unaware of whether or not the physical machine hosting its VMs also contains other VMs (belonging to other tenants); (ii) Configuration privacy: the hypervisor's configuration, used in the attestation process, remains private with respect to the tenants requiring a hypervisor attestation; and (iii) Layer linking: our protocol enables tenants to link hypervisors with the VMs, thus obtaining a guarantee that their VMs are running on specific physical machines.

Our solution relies on vector commitments and ZK-SNARKs. We build on the security model of Arfaoui et al. and provide both formalizations of the properties we require and proofs that our scheme does, in fact attain them. Our protocol is scalable, and our implementation results prove that it is viable, even for a large number of VMs hosted on a single platform.

In this paper, we propose a privacy preserving TPM-based deep-attestation solution in multi-tenant environments, which provably guarantees: (i) Inter-tenant privacy: a tenant is unaware of whether or not the physical machine hosting its VMs also contains other VMs (belonging to other tenants); (ii) Configuration privacy: the hypervisor's configuration, used in the attestation process, remains private with respect to the tenants requiring a hypervisor attestation; and (iii) Layer linking: our protocol enables tenants to link hypervisors with the VMs, thus obtaining a guarantee that their VMs are running on specific physical machines.

Our solution relies on vector commitments and ZK-SNARKs. We build on the security model of Arfaoui et al. and provide both formalizations of the properties we require and proofs that our scheme does, in fact attain them. Our protocol is scalable, and our implementation results prove that it is viable, even for a large number of VMs hosted on a single platform.

###### Dimitri Mankowski, Thom Wiggers, Veelasha Moonsamy

ePrint Report
The ubiquitous use of smartphones has contributed to more and more users conducting their online browsing activities through apps, rather than web browsers. In order to provide a seamless browsing experience to the users, apps rely on a variety of HTTP-based APIs and third-party libraries, and make use of the TLS protocol to secure the underlying communication. With NIST's recent announcement of the first standards for post-quantum algorithms, there is a need to better understand the constraints and requirements of TLS usage by Android apps in order to make an informed decision for migration to the post-quantum world.

In this paper, we performed an analysis of TLS usage by highest-ranked apps from Google Play Store to assess the resulting overhead for adoption of post-quantum algorithms. Our results show that apps set up large numbers of TLS connections with a median of 94, often to the same hosts. At the same time, many apps make little use of resumption to reduce the overhead of the TLS handshake. This will greatly magnify the impact of the transition to post-quantum cryptography, and we make recommendations for developers, server operators and the mobile operating systems to invest in making more use of these mitigating features or improving their accessibility. Finally, we briefly discuss how alternative proposals for post-quantum TLS handshakes might reduce the overhead.

In this paper, we performed an analysis of TLS usage by highest-ranked apps from Google Play Store to assess the resulting overhead for adoption of post-quantum algorithms. Our results show that apps set up large numbers of TLS connections with a median of 94, often to the same hosts. At the same time, many apps make little use of resumption to reduce the overhead of the TLS handshake. This will greatly magnify the impact of the transition to post-quantum cryptography, and we make recommendations for developers, server operators and the mobile operating systems to invest in making more use of these mitigating features or improving their accessibility. Finally, we briefly discuss how alternative proposals for post-quantum TLS handshakes might reduce the overhead.

###### Vasyl Ustimenko, Tymoteusz Chojecki

ePrint Report
Classical Multivariate Cryptography (MP) is searching for special families of functions of kind ^nF=T_1FTT_2 on the vector space V= (F_q)^n where F is a quadratic or cubical polynomial map of the space to itself, T_1 and T^2 are affine transformations and T is the piece of information such that the knowledge of the triple T_1, T_2, T allows the computation of reimage x of given nF(x) in polynomial time O(n^ᾳ). Traditionally F is given by the list of coefficients C(^nF) of its monomial terms ordered lexicographically. We consider the Inverse Problem of MP of finding T_1, T_2, T for F given in its standard form. The solution of inverse problem is harder than finding the procedure to compute the reimage of ^nF in time O(n^ᾳ). For general quadratic or cubic maps nF this is NP hard problem. In the case of special family some arguments on its inclusion to class NP has to be given.

###### Quentin L. Meunier, Abdul Rahman Taleb

ePrint Report
Side-Channel Attacks are powerful attacks which can recover secret information in a cryptographic device by analysing physical quantities such as power consumption. Masking is a common countermeasure to these attacks which can be applied in software and hardware, and consists in splitting the secrets in several parts. Masking schemes and their implementations are often not trivial, and require the use of automated tools to check for their correctness.
In this work, we propose a new practical tool named VerifMSI which extends an existing verification tool called LeakageVerif targeting software schemes. Compared to LeakageVerif, VerifMSI includes hardware constructs, namely gates and registers, what allows to take glitch propagation into account. Moreover, it includes a new representation of the inputs, making it possible to verify three existing security properties (Non-Interference, Strong Non-Interference, Probe Isolating Non-Interference) as well as a newly defined one called Relaxed Non-Interference, compared to the unique Threshold Probing Security verified in LeakageVerif. Finally, optimisations have been integrated in VerifMSI in order to speed up the verification.
We evaluate VerifMSI on a set of 9 benchmarks from the literature, focusing on the hardware descriptions, and show that it performs well both in terms of accuracy and scalability.

###### Bo-Yin Yang, Wei-Jeng Wang, Shang-Yi Yang, Char-Shin Miou, Chen-Mou Cheng

ePrint Report
Solving multivariate polynomial systems over finite fields is an important
problem in cryptography. For random F2 low-degree systems with equally many
variables and equations, enumeration is more efficient than advanced solvers for all
practical problem sizes. Whether there are others remained an open problem.
We here study and propose an exhaustive-search algorithm for low degrees systems
over F3 which is suitable for parallelization. We implemented it on Graphic Processing
Units (GPUs) and commodity CPUs. Its optimizations and differences from the F2
case are also analyzed.
We can solve 30+ quadratic equations in 30 variables on an NVIDIA GeForce GTX
980 Ti in 14 minutes; a cubic system takes 36 minutes. This well outperforms
existing solvers. Using these results, we compare Gröbner Bases vs. enumeration for
polynomial systems over small fields as the sizes go up.

#### 22 May 2023

###### Graz, Austria, 1 September - 4 September 2023

School
Event date: 1 September to 4 September 2023

###### Warszawa, Polska, 31 July - 3 August 2023

School
Event date: 31 July to 3 August 2023

###### Anubhab Baksi

ePrint Report
In the design of GIFT, half round key XOR is used. This leads to the undesired consequence that the security against the differential/linear attacks are overestimated. This comes from the observation that; in the usual DDT/LAT based analysis of the differential/linear attacks, the inherent assumption is the full round key is XORed at each round.

###### Yang Yu, Huiwen Jia, Xiaoyun Wang

ePrint Report
Lattice gadgets and the associated algorithms are the essential building blocks of lattice-based cryptography. In the past decade, they have been applied to build versatile and powerful cryptosystems. However, the practical optimizations and designs of gadget-based schemes generally lag their theoretical constructions.
For example, the gadget-based signatures have elegant design and capability of extending to more advanced primitives, but they are far less efficient than other lattice-based signatures.

This work aims to improve the practicality of gadget-based cryptosystems, with a focus on hash-and-sign signatures. To this end, we develop a compact gadget framework in which the used gadget is a square matrix instead of the short and fat one used in previous constructions. To work with this compact gadget, we devise a specialized gadget sampler, called semi-random sampler, to compute the approximate preimage. It first deterministically computes the error and then randomly samples the preimage. We show that for uniformly random targets, the preimage and error distributions are simulatable without knowing the trapdoor. This ensures the security of the signature applications. Compared to the Gaussian-distributed errors in previous algorithms, the deterministic errors have a smaller size, which lead to a substantial gain in security and enables a practically working instantiation.

As the applications, we present two practically efficient gadget-based signature schemes based on NTRU and Ring-LWE respectively. The NTRU-based scheme offers comparable efficiency to Falcon and Mitaka and a simple implementation without the need of generating the NTRU trapdoor. The LWE-based scheme also achieves a desirable overall performance. It not only greatly outperforms the state-of-the-art LWE-based hash-and-sign signatures, but also has an even smaller size than the LWE-based Fiat-Shamir signature scheme Dilithium. These results fill the long-term gap in practical gadget-based signatures.

This work aims to improve the practicality of gadget-based cryptosystems, with a focus on hash-and-sign signatures. To this end, we develop a compact gadget framework in which the used gadget is a square matrix instead of the short and fat one used in previous constructions. To work with this compact gadget, we devise a specialized gadget sampler, called semi-random sampler, to compute the approximate preimage. It first deterministically computes the error and then randomly samples the preimage. We show that for uniformly random targets, the preimage and error distributions are simulatable without knowing the trapdoor. This ensures the security of the signature applications. Compared to the Gaussian-distributed errors in previous algorithms, the deterministic errors have a smaller size, which lead to a substantial gain in security and enables a practically working instantiation.

As the applications, we present two practically efficient gadget-based signature schemes based on NTRU and Ring-LWE respectively. The NTRU-based scheme offers comparable efficiency to Falcon and Mitaka and a simple implementation without the need of generating the NTRU trapdoor. The LWE-based scheme also achieves a desirable overall performance. It not only greatly outperforms the state-of-the-art LWE-based hash-and-sign signatures, but also has an even smaller size than the LWE-based Fiat-Shamir signature scheme Dilithium. These results fill the long-term gap in practical gadget-based signatures.