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01 April 2024
Jehyuk Jang, Jamie Judd
The advancement of succinct non-interactive argument of knowledge (SNARK) with constant proof size has significantly enhanced the efficiency and privacy of verifiable computation. Verifiable computation finds applications in distributed computing networks, particularly in scenarios where nodes cannot be generally trusted, such as blockchains. However, fully harnessing the efficiency of SNARK becomes challenging when the computing targets in the network change frequently, as the SNARK verification can involve some untrusted preprocess of the target, which is expected to be reproduced by other nodes. This problem can be addressed with two approaches: One relieves the reproduction overhead by reducing the dimensionality of preprocessing data; The other utilizes verifiable machine computation, which eliminates the dependency on preprocess at the cost of increased overhead to SNARK proving and verification. In this paper, we propose a new SNARK with constant proof size applicable to both approaches. The proposed SNARK combines the efficiency of Groth16 protocol, albeit lacking universality for new problems, and the universality of PlonK protocol, albeit with significantly larger preprocessing data dimensions. Consequently, we demonstrate that our proposed SNARK maintains the efficiency and the universality while significantly reducing the dimensionality of preprocessing data. Furthermore, our SNARK can be seamlessly applied to the verifiable machine computation, requiring a proof size smaller about four to ten times than other related works.
Olive Chakraborty, Aymen Boudguiga
Nowadays Federated learning (FL) is established as one of the best techniques for collaborative machine learning. It allows a set of clients to train a common model without disclosing their sensitive and private
dataset to a coordination server. The latter is in charge of the model aggregation. However, FL faces some problems, regarding the security of updates, integrity of computation and the availability of a server.
In this paper, we combine some new ideas like clients’ reputation with techniques like secure aggregation using Homomorphic Encryption and verifiable secret sharing using Multi-Party Computation techniques to design a decentralized FL system that addresses the issues of incentives, security and availability amongst others. One of the original contributions of this work is the new leader election protocol which uses a secure shuffling and is based on a proof of reputation. Indeed, we propose to select an aggregator among the clients participating to
the FL training using their reputations. That is, we estimate the reputation of each client at every FL iteration and then we select the next round aggregator from the set of clients with the best reputations. As such, we remove misbehaving clients (e.g., byzantines) from the list of clients eligible for the role of aggregation server.
Victor Youdom Kemmoe, Anna Lysyanskaya
A cryptographic accumulator is a compact data structure for representing a set of elements coming from some domain. It allows for a compact proof of membership and, in the case of a universal accumulator, non-membership of an element x in the data structure. A dynamic accumulator, furthermore, allows elements to be added to and deleted from the accumulator.
Previously known RSA-based dynamic accumulators were too slow in practice because they required that an element in the domain be represented as a prime number. Accumulators based on settings other than RSA had other drawbacks such as requiring a prohibitively large common reference string or a trapdoor, or not permitting deletions.
In this paper, we construct RSA-based dynamic universal accumulators that do not require that the accumulated elements be represented as primes. We also show how to aggregate membership and non-membership witnesses and batch additions and deletions. We demonstrate that the efficiency gains compared to previously known RSA-based accumulators are substantial, and, for the first time, make cryptographic accumulators a viable candidate for a certificate revocation mechanism as part of a WebPKI-type system.
Benjamin E. Diamond, Jim Posen
We introduce a polylogarithmic-verifier polynomial commitment scheme for multilinears over towers of binary fields. To achieve this, we adapt an idea of Zeilberger, Chen and Fisch's BaseFold ('23) to the setting of binary towers, using FRI (ICALP '18)'s binary-field variant. In the process, we reinterpret Lin, Chung and Han (FOCS '14)'s novel polynomial basis so as to make apparent its compatibility with FRI. We moreover introduce a "packed" version of our protocol, which supports—with no embedding overhead during its commitment phase—multilinears over tiny fields (including that with just two elements). Our protocol leverages a new multilinear FRI-folding technique, and exploits the recent tensor proximity gap of Diamond and Posen (Commun. Cryptol. '24). We achieve concretely small proofs for enormous binary multilinears, shrinking the proofs of Diamond and Posen ('23) by an order of magnitude.
Two Levels are Better than One: Dishonest Majority MPC with $\widetilde{O}(|C|)$ Total Communication
Alexander Bienstock, Kevin Yeo
In recent years, there has been tremendous progress in improving the communication complexity of dishonest majority MPC. In the sub-optimal corruption threshold setting, where $t<(1-\varepsilon)\cdot n$ for some constant $0<\varepsilon\leq 1/2$, the recent works Sharing Transformation (Goyal $\textit{et al.}$, CRYPTO'22) and SuperPack (Escudero $\textit{et al.}$, EUROCRYPT'23) presented protocols with information-theoretic online phases achieving $O(1)$ communication per multiplication gate, across all parties. However, the former assumes that their offline phase is instantiated by a trusted party, while the latter instantiates their offline phase with $\Omega(n)$ communication per multiplication gate assuming oblivious linear evaluation (OLE) correlations.
In this work, we present a dishonest majority MPC protocol for $t< (1-\varepsilon)\cdot n$ with $\widetilde{O}(1)$ total communication per multiplication gate across both the offline and online phases, or $\widetilde{O}(|C|)$ total communication for any arithmetic circuit $C$. To do so, we securely instantiate the offline phase of Sharing Transformation, assuming some OLE correlations. The major bottleneck in instantiating the offline phases of both Sharing Transformation and SuperPack is generating random packed beaver triples of the form $[\boldsymbol{a}], [\boldsymbol{b}], [\boldsymbol{c}]$, for random $\boldsymbol{a},\boldsymbol{b}\in\mathbb{F}^k$, and $\boldsymbol{c}=\boldsymbol{a}*\boldsymbol{b}\in\mathbb{F}^k$, where $k=\Omega(n)$ is the $\textit{packing parameter}$. We overcome this barrier by presenting a packed beaver triple protocol with $\widetilde{O}(n)$ total communication, or $\widetilde{O}(1)$ communication per underlying triple.
Our packed beaver triple protocol consists of two levels of randomness extraction. The first level uses a relaxation of super-invertible matrices that we introduce, called $\textit{weakly}$ super-invertible matrices, in which sub-matrices have sufficiently high (but not necessarily full) rank. This weakening enables matrix constructions with only $O(n)$ non-zero entries, which is a primary reason for the efficiency of our protocol. Our second level of extraction is based on the $\textit{triple extraction}$ protocol of (Choudhury and Patra, Trans. Inform. Theory '17).
In this work, we present a dishonest majority MPC protocol for $t< (1-\varepsilon)\cdot n$ with $\widetilde{O}(1)$ total communication per multiplication gate across both the offline and online phases, or $\widetilde{O}(|C|)$ total communication for any arithmetic circuit $C$. To do so, we securely instantiate the offline phase of Sharing Transformation, assuming some OLE correlations. The major bottleneck in instantiating the offline phases of both Sharing Transformation and SuperPack is generating random packed beaver triples of the form $[\boldsymbol{a}], [\boldsymbol{b}], [\boldsymbol{c}]$, for random $\boldsymbol{a},\boldsymbol{b}\in\mathbb{F}^k$, and $\boldsymbol{c}=\boldsymbol{a}*\boldsymbol{b}\in\mathbb{F}^k$, where $k=\Omega(n)$ is the $\textit{packing parameter}$. We overcome this barrier by presenting a packed beaver triple protocol with $\widetilde{O}(n)$ total communication, or $\widetilde{O}(1)$ communication per underlying triple.
Our packed beaver triple protocol consists of two levels of randomness extraction. The first level uses a relaxation of super-invertible matrices that we introduce, called $\textit{weakly}$ super-invertible matrices, in which sub-matrices have sufficiently high (but not necessarily full) rank. This weakening enables matrix constructions with only $O(n)$ non-zero entries, which is a primary reason for the efficiency of our protocol. Our second level of extraction is based on the $\textit{triple extraction}$ protocol of (Choudhury and Patra, Trans. Inform. Theory '17).
Neyire Deniz Sarier
In [1], two generic constructions for biometric-based non-transferable Attribute Based Credentials (biometric ABC) are presented, which offer different trade-offs between efficiency and trust assumptions. In this paper, we focus on the second scheme denoted as BioABC-ZK that tries to remove the strong (and unrealistic) trust assumption on the Reader R, and show that BioABC-ZK has a security flaw for a colluding R and Verifier V. Besides, BioABC-ZK lacks GDPR-compliance, which requires secure processing of biometrics, for instance in form of Fuzzy Extractors, as opposed to (i) storing the reference biometric template aBio in the user's mobile phone and (ii) processing of biometrics using an external untrusted R, whose foreign manufacturers are unlikely to adjust their products according to GDPR. The contributions of this paper are threefold. First, we review efficient biometric ABC schemes to identify the privacy-by-design criteria for them. In view of these principles, we propose a new architecture for biometric ABC of [2] by adapting the recently introduced core/helper setting of [3]. Briefly, a user in our modified setting is composed of a constrained core device (a SIM card) inside a helper device (a smart phone with dual SIM and face recognition feature), which -as opposed to [1]- does not need to store aBio. This way, the new design provides Identity Privacy without the need for an external R and/or a dedicated hardware per user such as a biometric smart card reader or a tamper proof smart card as in current hardware-bound credential systems. Besides, the new system maintains minimal hardware requirements on the SIM card -only responsible for storing ABC and helper data-, which results in easy adoption and usability without loosing efficiency, if recently introduced key derivation scheme of [4] and the modified ABC scheme of [2] are employed together. As a result, a total overhead of 500 milliseconds to a showing of a comparable non-biometric ABC is obtained instead of the 2.1 seconds in [1] apart from the removal of computationally expensive pairings. Finally, as different from [1], auditing is achieved via Blockchain instead of proving in zero-knowledge the actual biometric matching by the user to reveal malicious behavior of R and V.
Kwangsu Lee
Anonymous identity-based encryption (AIBE) is an extension of identity-based encryption (IBE) that enhances the privacy of a ciphertext by providing ciphertext anonymity. In this paper, we introduce the concept of revocable IBE with anonymous revocation (RIBE-AR), which is capable of issuing an update key and hiding the revoked set of the update key that efficiently revokes private keys of AIBE. We first define the security models of RIBE-AR and propose an efficient RIBE-AR scheme in bilinear groups. Our RIBE-AR scheme is similar to the existing RIBE scheme in terms of efficiency, but is the first RIBE scheme to provide additional ciphertext anonymity and revocation privacy. We show that our RIBE-AR scheme provides the selective message privacy, selective identity privacy, and selective revocation privacy.
Scott Fluhrer
Here is a potential way to create a SLH-DSA-like\cite{DraftFIPS205} key generation/signer that aspires to be resistant to DPA side channel attacks.
We say that it is “SLH-DSA-like”, because it does not follow the FIPS 205 method of generating signatures (in particular, it does not have the same mapping from private key, messages, opt\_rand to signatures), however it does generate public keys and signatures that are compatible with the standard signature verification method, and with the same security (with a small security loss against side channel attacks). In our tests, this idea performed 1.7 times slower compared to an unprotected version.
Jonas Meers, Doreen Riepel
Ciphertext-independent updatable encryption (UE) allows to rotate encryption keys and update ciphertexts via a token without the need to first download the ciphertexts. Although, syntactically, UE is a symmetric-key primitive, ciphertext-independent UE with forward secrecy and post-compromise security is known to imply public-key encryption (Alamati, Montgomery and Patranabis, CRYPTO 2019).
Constructing post-quantum secure UE turns out to be a difficult task. While lattices offer the necessary homomorphic properties, the introduced noise allows only a bounded number of updates. Group actions have become an important alternative, however, their structure is limited. The only known UE scheme by Leroux and Roméas (IACR ePrint 2022/739) uses effective triple orbital group actions which uses additional algebraic structure of CSIDH. Using an ideal cipher, similar to the group-based scheme $\mathsf{SHINE}$ (Boyd et al., CRYPTO 2020), requires the group action to be mappable, a property that natural isogeny-based group actions do not satisfy. At the same time, other candidates based on non-commutative group actions suffer from linearity attacks.
For these reasons, we explicitly ask how to construct UE from group actions that are not mappable. As a warm-up, we present $\mathsf{BIN}\text{-}\mathsf{UE}$ which uses a bit-wise approach and is CPA secure based on the well-established assumption of weak pseudorandomness and in the standard model. We then construct the first actively secure UE scheme from post-quantum assumptions. Our scheme $\mathsf{COM}\text{-}\mathsf{UE}$ extends $\mathsf{BIN}\text{-}\mathsf{UE}$ via the Tag-then-Encrypt paradigm. We prove CCA security in the random oracle model based on a stronger computational assumption. We justify the hardness of our new assumption in the algebraic group action model.
Constructing post-quantum secure UE turns out to be a difficult task. While lattices offer the necessary homomorphic properties, the introduced noise allows only a bounded number of updates. Group actions have become an important alternative, however, their structure is limited. The only known UE scheme by Leroux and Roméas (IACR ePrint 2022/739) uses effective triple orbital group actions which uses additional algebraic structure of CSIDH. Using an ideal cipher, similar to the group-based scheme $\mathsf{SHINE}$ (Boyd et al., CRYPTO 2020), requires the group action to be mappable, a property that natural isogeny-based group actions do not satisfy. At the same time, other candidates based on non-commutative group actions suffer from linearity attacks.
For these reasons, we explicitly ask how to construct UE from group actions that are not mappable. As a warm-up, we present $\mathsf{BIN}\text{-}\mathsf{UE}$ which uses a bit-wise approach and is CPA secure based on the well-established assumption of weak pseudorandomness and in the standard model. We then construct the first actively secure UE scheme from post-quantum assumptions. Our scheme $\mathsf{COM}\text{-}\mathsf{UE}$ extends $\mathsf{BIN}\text{-}\mathsf{UE}$ via the Tag-then-Encrypt paradigm. We prove CCA security in the random oracle model based on a stronger computational assumption. We justify the hardness of our new assumption in the algebraic group action model.
Jingwei Hu, Yuhong Fang, Wangchen Dai
This paper introduces a high-performance and scalable hardware architecture designed for the Number-Theoretic Transform (NTT), a fundamental component extensively utilized in lattice-based encryption and fully homomorphic encryption schemes.
The underlying rationale behind this research is to harness the advantages of the hypercube topology. This topology serves to significantly diminish the volume of data exchanges required during each iteration of the NTT, reducing it to a complexity of $\Omega(\log N)$. Concurrently, it enables the parallelization of $N$ processing elements. This reduction in data exchange operations is of paramount importance. It not only facilitates the establishment of interconnections among the $N$ processing elements but also lays the foundation for the development of a high-performance NTT design. This is particularly valuable when dealing with large values of $N$.
The underlying rationale behind this research is to harness the advantages of the hypercube topology. This topology serves to significantly diminish the volume of data exchanges required during each iteration of the NTT, reducing it to a complexity of $\Omega(\log N)$. Concurrently, it enables the parallelization of $N$ processing elements. This reduction in data exchange operations is of paramount importance. It not only facilitates the establishment of interconnections among the $N$ processing elements but also lays the foundation for the development of a high-performance NTT design. This is particularly valuable when dealing with large values of $N$.
István Vajda
The income of companies working on data markets steadily grows year by year. Private function evaluation (PFE) is a valuable tool in solving corresponding security problems. The task of Controlled Private Function Evaluation and its relaxed version was introduced in [Horvath et.al., 2019]. In this article, we propose and examine several different approaches for such tasks with computational and information theoretical security against static corruption adversary. The latter level of security implies quantum-security. We also build known techniques and constructions into our solution where they fit into our tasks. The main cryptographic primitive, naturally related to the task is 1-out-of-n oblivious transfer. We use Secure Multiparty Computation techniques and in one of the constructions functional encryption primitive. The analysis of the computational complexity of the constructions shows that the considered tasks can efficiently be implemented, however it depends on the range of parameter values (e.g. size of database, size of the set of permitted function), the execution environment (e.g. concurrency) and of course on the level of security.
Thomas Espitau, Shuichi Katsumata, Kaoru Takemure
Threshold signatures have recently seen a renewed interest due to applications in cryptocurrency while NIST has released a call for multi-party threshold schemes, with a deadline for submission expected for the first half of 2025. So far, all lattice-based threshold signatures requiring less than two-rounds are based on heavy tools such as (fully) homomorphic encryption (FHE) and homomorphic trapdoor commitments (HTDC). This is not unexpected considering that most efficient two-round signatures from classical assumptions either rely on idealized model such as algebraic group models or on one-more type assumptions, none of which we have a nice analogue in the lattice world.
In this work, we construct the first efficient two-round lattice-based threshold signature without relying on FHE or HTDC. It has an offline-online feature where the first round can be preprocessed without knowing message or the signer sets, effectively making the signing phase non-interactive. The signature size is small and shows great scalability. For example, even for a threshold as large as 1024 signers, we achieve a signature size roughly 11 KB. At the heart of our construction is a new lattice-based assumption called the algebraic one-more learning with errors (AOMMLWE) assumption. We believe this to be a strong inclusion to our lattice toolkits with an independent interest. We establish the selective security of AOMMLWE based on the standard MLWE and MSIS assumptions, and provide an in depth analysis of its adaptive security, which our threshold signature is based on.
In this work, we construct the first efficient two-round lattice-based threshold signature without relying on FHE or HTDC. It has an offline-online feature where the first round can be preprocessed without knowing message or the signer sets, effectively making the signing phase non-interactive. The signature size is small and shows great scalability. For example, even for a threshold as large as 1024 signers, we achieve a signature size roughly 11 KB. At the heart of our construction is a new lattice-based assumption called the algebraic one-more learning with errors (AOMMLWE) assumption. We believe this to be a strong inclusion to our lattice toolkits with an independent interest. We establish the selective security of AOMMLWE based on the standard MLWE and MSIS assumptions, and provide an in depth analysis of its adaptive security, which our threshold signature is based on.
Tung Chou, Ruben Niederhagen, Lars Ran, Simona Samardjiska
This paper shows novel techniques to reduce the signature size of the code-based signature schemes MEDS and ALTEQ, by a large factor. For both schemes, the signature size is dominated by the responses for rounds with nonzero challenges, and we reduce the signature size by reducing the size of these responses. For MEDS, each of the responses consists of $m^2 + n^2$ field elements,while in our new protocol each response consists of only $2k$ ($k$ is usually chosen to be close to $m$ and $n$) field elements. For ALTEQ, each of the responses consists of $n^2$ field elements, while in our new protocol each response consists of about $\sqrt{2} n^{3/2}$ field elements. In both underlying $\Sigma$-protocols of the schemes, the prover generates a random isometry and sends the corresponding isometry to the verifier as the response. Instead of doing this, in our new protocols, the prover derives an isometry from some random code words and their presumed (full or partial) images. The prover sends the corresponding code words and images to the verifier as the response, so that the verifier can derive an isometry in the same way. Interestingly, it turns out that each response takes much fewer field elements to represent in this way.
István Vajda
In the common random string model, the parties executing a protocol have access to a uniformly random bit string. It is known that under standard intractability assumptions, we can realize any ideal functionality with universally composable (UC) security if a trusted common random string (CrS) setup is available. It was always a question of where this CrS should come from since the parties provably could not compute it themselves. Trust assumptions are required, so minimizing the level of such trust is a fundamentally important task. Our goal is to design a CrS setup protocol under a weakened trust assumption. We present an HW-token-based CrS setup for 2-party cryptographic protocols using a single token only. Our protocol is a UC-secure realization of ideal common random string functionality FCrS. We show the multiple-session security of the protocol and we also consider the multi-party extension of it.
Charalampos Papamanthou, Shravan Srinivasan, Nicolas Gailly, Ismael Hishon-Rezaizadeh, Andrus Salumets, Stjepan Golemac
We propose Reckle trees, a new vector commitment based on succinct RECursive arguments and MerKLE trees. Reckle trees' distinguishing feature is their support for succinct batch proofs that are updatable - enabling new applications in the blockchain setting where a proof needs to be computed and efficiently maintained over a moving stream of blocks. Our technical approach is based on embedding the computation of the batch hash inside the recursive Merkle verification via a hash-based accumulator called canonical hashing. Due to this embedding, our batch proofs can be updated in logarithmic time, whenever a Merkle leaf (belonging to the batch or not) changes, by maintaining a data structure that stores previously-computed recursive proofs. Assuming enough parallelism, our batch proofs are also computable in $O(\log n)$ parallel time - independent of the size of the batch. As a natural extension of Reckle trees, we also introduce Reckle+ trees. Reckle+ trees provide updatable and succinct proofs for certain types of Map/Reduce computations. In this setting, a prover can commit to a memory $\mathsf{M}$ and produce a succinct proof for a Map/Reduce computation over a subset $I$ of $\mathsf{M}$. The proof can be efficiently updated whenever $I$ or $\mathsf{M}$ changes.
We present and experimentally evaluate two applications of Reckle+ trees, dynamic digest translation and updatable BLS aggregation. In dynamic digest translation we are maintaining a proof of equivalence between Merkle digests computed with different hash functions, e.g., one with a SNARK-friendly Poseidon and the other with a SNARK-unfriendly Keccak. In updatable BLS aggregation we maintain a proof for the correct aggregation of a $t$-aggregate BLS key, derived from a $t$-subset of a Merkle-committed set of individual BLS keys. Our evaluation using Plonky2 shows that Reckle trees and Reckle+ trees have small memory footprint, significantly outperform previous approaches in terms of updates and verification time, enable applications that were not possible before due to huge costs involved (Reckle trees are up to 200 times faster), and have similar aggregation performance with previous implementations of batch proofs.
We present and experimentally evaluate two applications of Reckle+ trees, dynamic digest translation and updatable BLS aggregation. In dynamic digest translation we are maintaining a proof of equivalence between Merkle digests computed with different hash functions, e.g., one with a SNARK-friendly Poseidon and the other with a SNARK-unfriendly Keccak. In updatable BLS aggregation we maintain a proof for the correct aggregation of a $t$-aggregate BLS key, derived from a $t$-subset of a Merkle-committed set of individual BLS keys. Our evaluation using Plonky2 shows that Reckle trees and Reckle+ trees have small memory footprint, significantly outperform previous approaches in terms of updates and verification time, enable applications that were not possible before due to huge costs involved (Reckle trees are up to 200 times faster), and have similar aggregation performance with previous implementations of batch proofs.
30 March 2024
University of Exeter, Department of Computer Science, Exeter, England, UK
As part of a US funded project, we have an exciting opportunity for a PostDoc in
the Security and Trust of Advanced Systems Group at the University of Exeter
(UK) to work applying formal methods to enterprise systems:
We will use formal methods (e.g., model checking, SMT solving, interactive
theorem proving), to analyze business-process-driven (enterprise) systems (e.g.,
business logic and workflows described a BPMN models). A particular focus will
be the analysis of complex compositions of workflows within one organization as
well as across multiple organizations.
In particular, we will develop novel techniques to detect faults and
vulnerabilities (that can be exploited by both internal and external attackers)
in complex business-process-driven systems, contributing to protecting critical
workflows such as manufacturing or logistics.
In such environments, attackers can exploit such faults and vulnerabilities to
cause all kinds of harm such as direct financial losses or causing the
production of safety or security critical products to stop. Overall, the project
aims to develop automated techniques for assessing the risk of business process
or workflows as well as finding and mitigating such attacks.
Closing date for applications:
Contact: Achim D. Brucker
More information: https://jobs.exeter.ac.uk/hrpr_webrecruitment/wrd/run/etrec179gf.open?WVID=171839ediw&LANG=USA&VACANCY_ID=386422ijTy
Queensland University of Technology
We are seeking a Associate Professor/Professor Information Security to join School of Computer Science, Faculty of Science, Academic Division.
We are seeking an Associate Professor or Professor to lead and make strategic contributions to teaching and research in the field of Information Security. The position holder will lead, promote and foster an inclusive high performance and high impact research and teaching team that achieves excellent outcomes for the school and faculty. The successful applicant will be joining a school which conducts fundamental and applied research into creating better, faster, more secure, and more accessible computing and interactive systems.
Closing date for applications:
Contact: Paul Roe (p.roe@qut.edu.au)
27 March 2024
Cameron Foreman, Richie Yeung, Florian J. Curchod
Random number generators (RNGs) are notoriously hard to build and test, especially in a cryptographic setting. Although one cannot conclusively determine the quality of an RNG by testing the statistical properties of its output alone, running numerical tests is both a powerful verification tool and the only universally applicable method. In this work, we present and make available a comprehensive statistical testing environment (STE) that is based on existing statistical test suites. The STE can be parameterised to run lightweight (i.e. fast) all the way to intensive testing, which goes far beyond what is required by certification bodies. With it, we benchmark the statistical properties of several RNGs, comparing them against each other. We then present and implement a variety of post-processing methods, in the form of randomness extractors, which improve the RNG's output quality under different sets of assumptions and analyse their impact through numerical testing with the STE.
Christian Badertscher, Monosij Maitra, Christian Matt, Hendrik Waldner
Policy-compliant signatures (PCS) are a recently introduced primitive by Badertscher et
al. [TCC 2021] in which a central authority distributes secret and public keys associated with sets of attributes (e.g., nationality, affiliation with a specific department, or age) to its users. The authority also enforces a policy determining which senders can sign messages for which receivers based on a joint check of their attributes. For example, senders and receivers must have the same nationality, or only senders that are at least 18 years old can send to members of the computer science department. PCS further requires attribute-privacy – nothing about the users’ attributes is revealed from their public keys and signatures apart from whether the attributes satisfy the policy or not. The policy in a PCS scheme is fixed once and for all during the setup. Therefore, a policy update requires a redistribution of all keys. This severely limits the practicality of PCS. In this work, we introduce the notion of updatable policy-compliant signatures (UPCS) extending PCS with a mechanism to efficiently update the policy without redistributing keys to all participants.
We define the notion of UPCS and provide the corresponding security definitions. We then provide a generic construction of UPCS based on digital signatures, a NIZK proof system, and a so-called secret-key two-input partially-hiding predicate encryption (2-PHPE) scheme. Unfortunately, the only known way to build the latter for general two-input predicates is using indistinguishability obfuscation. We show that the reliance on the heavy tool of 2-PHPE is inherent to build UPCS by proving that non-interactive UPCS implies 2-PHPE.
To circumvent the reliance on 2-PHPE, we consider interactive UPCS, which allows the sender and receiver to interact during the message signing procedure. In this setting, we present two schemes: the first one requires only a digital signature scheme, a NIZK proof system, and secure two-party computation. This scheme works for arbitrary policies, but requires sender and receiver to engage in a two-party computation protocol for each policy update. Our second scheme additionally requires a (single-input) predicate-encryption scheme but, in turn, only requires a single interaction between sender and receiver, independent of the updates. In contrast to 2-PHPE, single-input predicate encryption for certain predicate classes is known to exist (e.g., from pairings) under more concrete and well-understood assumptions.
Carsten Baum, Ward Beullens, Shibam Mukherjee, Emmanuela Orsini, Sebastian Ramacher, Christian Rechberger, Lawrence Roy, Peter Scholl
The use of MPC-in-the-Head (MPCitH)-based zero-knowledge proofs of knowledge (ZKPoK) to prove knowledge of a preimage of a one-way function (OWF) is a popular approach towards constructing efficient post-quantum digital signatures. Starting with the Picnic signature scheme, many optimized MPCitH signatures using a variety of (candidate) OWFs have been proposed. Recently, Baum et al. (CRYPTO 2023) showed a fundamental improvement to MPCitH, called VOLE-in-the-Head (VOLEitH), which can generically reduce the signature size by at least a factor of two without decreasing computational performance or introducing new assumptions. Based on this, they designed the FAEST signature which uses AES as the underlying OWF. However, in comparison to MPCitH, the behavior of VOLEitH when using other OWFs is still unexplored.
In this work, we improve a crucial building block of the VOLEitH and MPCitH approaches, the so-called all-but-one vector commitment, thus decreasing the signature size of VOLEitH and MPCitH signature schemes. Moreover, by introducing a small Proof of Work into the signing procedure, we can improve the parameters of VOLEitH (further decreasing signature size) without compromising the computational performance of the scheme. Based on these optimizations, we propose three VOLEitH signature schemes FAESTER, KuMQuat, and MandaRain based on AES, MQ, and Rain, respectively. We carefully explore the parameter space for these schemes and implement each, showcasing their performance with benchmarks. Our experiments show that these three signature schemes outperform MPCitH-based competitors that use comparable OWFs, in terms of both signature size and signing/verification time.
In this work, we improve a crucial building block of the VOLEitH and MPCitH approaches, the so-called all-but-one vector commitment, thus decreasing the signature size of VOLEitH and MPCitH signature schemes. Moreover, by introducing a small Proof of Work into the signing procedure, we can improve the parameters of VOLEitH (further decreasing signature size) without compromising the computational performance of the scheme. Based on these optimizations, we propose three VOLEitH signature schemes FAESTER, KuMQuat, and MandaRain based on AES, MQ, and Rain, respectively. We carefully explore the parameter space for these schemes and implement each, showcasing their performance with benchmarks. Our experiments show that these three signature schemes outperform MPCitH-based competitors that use comparable OWFs, in terms of both signature size and signing/verification time.