Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

A tale of SNARKs: quantum resilience, knowledge extractability and data privacy

Anca Nitulescu

Published Apr 1, 2019• 0 citations
Publisher

Abstract

The contributions detailed in this thesis focus on the design and the analysis of Succinct non-interactive arguments of knowledge, known as SNARKs. SNARKs enable a party with large computational resources to prove to a weaker party that a particular statement is true in an efficient way without further interaction and under a minimal communication requirement. Our results deal with three different aspects of SNARK protocols: the postquantum security of SNARKs, the composability of SNARKs with other cryptographic primitives and the confidentiality of the inputs in the computations verified by SNARKs. First, we propose a new framework that allows the instantiation of a quantumresilient SNARK scheme from lattice assumptions. We also study the notion of extractability that is part of the soundness definition for SNARKs. We remark some limitations of this definition and we address this problem, by introducing and studying a new notion, O-SNARKs. Finally, to achieve data privacy in delegated computation, we study the possibility of constructing SNARKs that enables verification of computations over encrypted data.

DOI
10.70675/613f26dez1fcfz4bb3zb710ze245a8b88a2a

Related papers

Shorter ZK-SNARKs from square span programs over ideal lattices

Xi Lin, Heyang Cao, Feng-Hao Liu +2 more

Abstract Zero-knowledge succinct non-interactive arguments of knowledge (zk-SNARKs) are cryptographic protocols that offer efficient and privacy-preserving means of verifying NP language relations and have drawn considerable attention for their appealing applications, e.g., verifiable computation and anonymous payment protocol. Compared with the pre-quantum case, the practicability of this primitive in the post-quantum setting is still unsatisfactory, especially for the space complexity. To tackle this issue, this work seeks to enhance the efficiency and compactness of lattice-based zk-SNARKs, including proof length and common reference string (CRS) length. In this paper, we develop the framework of square span program-based SNARKs and design new zk-SNARKs over cyclotomic rings. Compared with previous works, our construction is without parallel repetition and achieves shorter proof and CRS lengths than previous lattice-based zk-SNARK schemes. Particularly, the proof length of our scheme is around $$23.3\%$$ 23.3 % smaller than the recent shortest lattice-based zk-SNARKs by Ishai et al. (in: Proceedings of the 2021 ACM SIGSAC conference on computer and communications security, pp 212–234, 2021), and the CRS length is $$3.6\times$$ 3.6 × smaller. Our constructions follow the framework of Gennaro et al. (in: Proceedings of the 2018 ACM SIGSAC conference on computer and communications security, pp 556–573, 2018), and adapt it to the ring setting by slightly modifying the knowledge assumptions. We develop concretely small constructions by using module-switching and key-switching procedures in a novel way.

Cybersecurity•Mar 19, 2024•4 citations

Post-quantum zk-SNARKs from QAPs

Ken Naganuma, Masayuki Yoshino, Noboru Kunihiro +3 more

In recent years, the zero-knowledge succinct non-interactive argument of knowledge (zk-SNARK) have drawn significant attention as privacy-enhancing technologies in various domains. A post-quantum designated verifier type zk-SNARK for Boolean circuits was proposed by Gennaro et al. in ACM CCS '18. However, this scheme does not include arithmetic circuits and they claim that a construction of post zk-SNARKs for arithmetic circuits as open problem. In this paper we give answers to this problem. Our first proposal is based on the data structure used in Pinocchio, a previous study, and can be easily implemented using the existing Pinocchio-based systems. In our second proposal, which also employs QAPs, the zero-knowledge proof comprises three learning with errors (LWE) ciphertexts, and the size of the proof is smaller compared with that of the first proposal. Our second proposal is also more efficient than the first one or all other known post-quantum zk-SNARKs.

International Journal of Information and Computer Security•Jan 1, 2024•0 citations

Post-quantum zk-SNARKs from QAPs

Yukinori Matsuoka, Mineaki Okazaki, Atsuo Inoue +3 more

In recent years, the zero-knowledge succinct non-interactive argument of knowledge (zk-SNARK) have drawn significant attention as privacy-enhancing technologies in various domains. A post-quantum designated verifier type zk-SNARK for Boolean circuits was proposed by Gennaro et al. in ACM CCS '18. However, this scheme does not include arithmetic circuits and they claim that a construction of post zk-SNARKs for arithmetic circuits as open problem. In this paper we give answers to this problem. Our first proposal is based on the data structure used in Pinocchio, a previous study, and can be easily implemented using the existing Pinocchio-based systems. In our second proposal, which also employs QAPs, the zero-knowledge proof comprises three learning with errors (LWE) ciphertexts, and the size of the proof is smaller compared with that of the first proposal. Our second proposal is also more efficient than the first one or all other known post-quantum zk-SNARKs.

International Journal of Information and Computer Security•Jan 1, 2024•0 citations

Quantum Security of Zero Knowledge Protocols

Morcos Doueihy, Jean-Paul

A Zero-Knowledge Proof basically is a protocol between two parties, the Prover and the Verifier, that allows the Prover to convince the Verifier about the truthness of a non trivial statement without revealing any additional information. Zero Knowledge Proofs have found a lot of practical applications covering most of the protocols concerning about data privacy and protocol verification. Examples of that are anonymous cash or electronic voting. The possibility to have real quantum computers with a reasonable size in a near future is forcing the cryptographic community to devise new methods to provide security that resist quantum attacks. Most of the zero-knowledge protocols used nowadays are based on computational problems like the discrete logarithm problem that can no longer be considered hard, since there are known efficient ways to solve them with quantum algorithms. Cryptographic research about the quantum security of zero knowledge proofs started nearly 20 years ago in a very theoretical approach, but not many papers on that topic appeared since then. The goal of this thesis is writing a survey including the main concepts about quantum secure zero-knowledge protocols, the state-of-the-art both from the theoretical and practical approaches, and an exploration of their potential application areas. The survey will be a good starting document for further students willing to do research in this topic.

•Sep 10, 2024•0 citations

A Survey of Post-Quantum Oblivious Protocols

Altana Felixovna Khutsaeva, Леевик Антон Георгиевич, Sergey Valentinovich Bezzateev

Modern distributed computing systems and applications with strict privacy requirements demand robust data confidentiality. A primary challenge involves enabling parties to exchange data or perform joint computations. These interactions must avoid revealing private information about the data. Protocols with the obliviousness property, known as oblivious protocols, address this issue. They ensure that no party learns more than necessary. This survey analyzes the security and performance of post-quantum oblivious protocols, with a focus on oblivious transfer and oblivious pseudorandom functions. The evaluation assesses resilience against malicious adversaries in the Universal Composability framework. Efficiency is quantified through communication and computational overhead. It identifies optimal scenarios for these protocols. This paper also surveys related primitives, such as oblivious signatures and data structures, along with their applications. Key findings highlight the inherent trade-offs between computational cost and communication complexity in post-quantum oblivious constructions. Open challenges and future research directions are outlined. Emphasis is placed on quantum-resistant designs and formal security proofs in stronger adversarial models.

Cryptography•Sep 27, 2025•2 citations

New frontiers in secure computation

Rafail Ostrovsky, Amit Sahai, Abhishek Jain

The notion of secure computation is central to cryptography. Introduced in the seminal works of Yao [FOCS'82, FOCS'86] and Goldreich, Micali and Wigderson [STOC'87], secure multiparty computation allows a group of (mutually) distrustful parties to jointly compute any functionality over their individual private inputs in such a manner that the honest parties obtain the correct outputs and no group of malicious parties learn anything beyond their inputs and the prescribed outputs. General feasibility results for secure computation were given by Yao [FOCS'86] and Goldreich et al. [STOC'87] more than two decades ago. Subsequent to these works, designing secure computation protocols that can tolerate more powerful adversaries and satisfy stronger notions of security has been a very active area of research. In this dissertation, we study two such new frontiers in the area of secure computation. In the first part of this dissertation, we initiate a study of designing leakage-resilient interactive protocols. Specifically, we consider the scenario where an adversary, in addition to corrupting a subset of parties, can leak (potentially via physical attacks) arbitrary information from the secret state of any honest party. This is in contrast to the standard notion of secure computation where it is assumed that the adversary only has black-box'' access to the honest parties. In particular, we formalize a meaningful definition of leakage-resilient zero knowledge proof systems and provide constructions that satisfy our notion. We also discuss various applications of our results. The second part of this dissertation concerns with the general question of whether it is possible to securely run cryptographic protocols over an insecure network environment such as the Internet. It is well-known that the standard notion of secure computation is only relevant to the stand-alone setting where a single protocol is being executed in isolation; as such it does not guarantee security when multiple protocol sessions may be executed concurrently under the control of an adversary who is present across all sessions. We consider the open problem of constructing secure password-based authenticated key exchange protocols in such a setting in the plain model (i.e., without assuming any trusted infrastructure or random oracles). We give the first construction of such a protocol based on standard cryptographic assumptions. Our results are in fact much more general, and extend to other functionalities w.r.t. a (necessarily) weakened notion of concurrently secure computation. The results presented in this dissertation stem from two papers which are joint works with Sanjam Garg and Amit Sahai, and with Vipul Goyal and Rafail Ostrovsky, respectively.

•Jan 1, 2012•0 citations
The contributions detailed in this thesis focus on the design and the analysis of Succinct non-interactive arguments of knowledge, known as SNARKs. SNARKs enable a party with large computational resources to prove to a weaker party that a particular statement is true in an efficient way without further interaction and under a minimal communication requirement. Our results deal with three different aspects of SNARK protocols: the postquantum security of SNARKs, the composability of SNARKs with other cryptographic primitives and the confidentiality of the inputs in the computations verified by SNARKs. First, we propose a new framework that allows the instantiation of a quantumresilient SNARK scheme from lattice assumptions. We also study the notion of extractability that is part of the soundness definition for SNARKs. We remark some limitations of this definition and we address this problem, by introducing and studying a new notion, O-SNARKs. Finally, to achieve data privacy in delegated computation, we study the possibility of constructing SNARKs that enables verification of computations over encrypted data.
Abstract Zero-knowledge succinct non-interactive arguments of knowledge (zk-SNARKs) are cryptographic protocols that offer efficient and privacy-preserving means of verifying NP language relations and have drawn considerable attention for their appealing applications, e.g., verifiable computation and anonymous payment protocol. Compared with the pre-quantum case, the practicability of this primitive in the post-quantum setting is still unsatisfactory, especially for the space complexity. To tackle this issue, this work seeks to enhance the efficiency and compactness of lattice-based zk-SNARKs, including proof length and common reference string (CRS) length. In this paper, we develop the framework of square span program-based SNARKs and design new zk-SNARKs over cyclotomic rings. Compared with previous works, our construction is without parallel repetition and achieves shorter proof and CRS lengths than previous lattice-based zk-SNARK schemes. Particularly, the proof length of our scheme is around 23.3%23.3\%23.3% 23.3 % smaller than the recent shortest lattice-based zk-SNARKs by Ishai et al. (in: Proceedings of the 2021 ACM SIGSAC conference on computer and communications security, pp 212–234, 2021), and the CRS length is 3.6×3.6\times3.6× 3.6 × smaller. Our constructions follow the framework of Gennaro et al. (in: Proceedings of the 2018 ACM SIGSAC conference on computer and communications security, pp 556–573, 2018), and adapt it to the ring setting by slightly modifying the knowledge assumptions. We develop concretely small constructions by using module-switching and key-switching procedures in a novel way.
In recent years, the zero-knowledge succinct non-interactive argument of knowledge (zk-SNARK) have drawn significant attention as privacy-enhancing technologies in various domains. A post-quantum designated verifier type zk-SNARK for Boolean circuits was proposed by Gennaro et al. in ACM CCS '18. However, this scheme does not include arithmetic circuits and they claim that a construction of post zk-SNARKs for arithmetic circuits as open problem. In this paper we give answers to this problem. Our first proposal is based on the data structure used in Pinocchio, a previous study, and can be easily implemented using the existing Pinocchio-based systems. In our second proposal, which also employs QAPs, the zero-knowledge proof comprises three learning with errors (LWE) ciphertexts, and the size of the proof is smaller compared with that of the first proposal. Our second proposal is also more efficient than the first one or all other known post-quantum zk-SNARKs.
In recent years, the zero-knowledge succinct non-interactive argument of knowledge (zk-SNARK) have drawn significant attention as privacy-enhancing technologies in various domains. A post-quantum designated verifier type zk-SNARK for Boolean circuits was proposed by Gennaro et al. in ACM CCS '18. However, this scheme does not include arithmetic circuits and they claim that a construction of post zk-SNARKs for arithmetic circuits as open problem. In this paper we give answers to this problem. Our first proposal is based on the data structure used in Pinocchio, a previous study, and can be easily implemented using the existing Pinocchio-based systems. In our second proposal, which also employs QAPs, the zero-knowledge proof comprises three learning with errors (LWE) ciphertexts, and the size of the proof is smaller compared with that of the first proposal. Our second proposal is also more efficient than the first one or all other known post-quantum zk-SNARKs.
A Zero-Knowledge Proof basically is a protocol between two parties, the Prover and the Verifier, that allows the Prover to convince the Verifier about the truthness of a non trivial statement without revealing any additional information. Zero Knowledge Proofs have found a lot of practical applications covering most of the protocols concerning about data privacy and protocol verification. Examples of that are anonymous cash or electronic voting. The possibility to have real quantum computers with a reasonable size in a near future is forcing the cryptographic community to devise new methods to provide security that resist quantum attacks. Most of the zero-knowledge protocols used nowadays are based on computational problems like the discrete logarithm problem that can no longer be considered hard, since there are known efficient ways to solve them with quantum algorithms. Cryptographic research about the quantum security of zero knowledge proofs started nearly 20 years ago in a very theoretical approach, but not many papers on that topic appeared since then. The goal of this thesis is writing a survey including the main concepts about quantum secure zero-knowledge protocols, the state-of-the-art both from the theoretical and practical approaches, and an exploration of their potential application areas. The survey will be a good starting document for further students willing to do research in this topic.
Modern distributed computing systems and applications with strict privacy requirements demand robust data confidentiality. A primary challenge involves enabling parties to exchange data or perform joint computations. These interactions must avoid revealing private information about the data. Protocols with the obliviousness property, known as oblivious protocols, address this issue. They ensure that no party learns more than necessary. This survey analyzes the security and performance of post-quantum oblivious protocols, with a focus on oblivious transfer and oblivious pseudorandom functions. The evaluation assesses resilience against malicious adversaries in the Universal Composability framework. Efficiency is quantified through communication and computational overhead. It identifies optimal scenarios for these protocols. This paper also surveys related primitives, such as oblivious signatures and data structures, along with their applications. Key findings highlight the inherent trade-offs between computational cost and communication complexity in post-quantum oblivious constructions. Open challenges and future research directions are outlined. Emphasis is placed on quantum-resistant designs and formal security proofs in stronger adversarial models.
The notion of secure computation is central to cryptography. Introduced in the seminal works of Yao [FOCS'82, FOCS'86] and Goldreich, Micali and Wigderson [STOC'87], secure multiparty computation allows a group of (mutually) distrustful parties to jointly compute any functionality over their individual private inputs in such a manner that the honest parties obtain the correct outputs and no group of malicious parties learn anything beyond their inputs and the prescribed outputs. General feasibility results for secure computation were given by Yao [FOCS'86] and Goldreich et al. [STOC'87] more than two decades ago. Subsequent to these works, designing secure computation protocols that can tolerate more powerful adversaries and satisfy stronger notions of security has been a very active area of research. In this dissertation, we study two such new frontiers in the area of secure computation. In the first part of this dissertation, we initiate a study of designing leakage-resilient interactive protocols. Specifically, we consider the scenario where an adversary, in addition to corrupting a subset of parties, can leak (potentially via physical attacks) arbitrary information from the secret state of any honest party. This is in contrast to the standard notion of secure computation where it is assumed that the adversary only has black-box'' access to the honest parties. In particular, we formalize a meaningful definition of leakage-resilient zero knowledge proof systems and provide constructions that satisfy our notion. We also discuss various applications of our results. The second part of this dissertation concerns with the general question of whether it is possible to securely run cryptographic protocols over an insecure network environment such as the Internet. It is well-known that the standard notion of secure computation is only relevant to the stand-alone setting where a single protocol is being executed in isolation; as such it does not guarantee security when multiple protocol sessions may be executed concurrently under the control of an adversary who is present across all sessions. We consider the open problem of constructing secure password-based authenticated key exchange protocols in such a setting in the plain model (i.e., without assuming any trusted infrastructure or random oracles). We give the first construction of such a protocol based on standard cryptographic assumptions. Our results are in fact much more general, and extend to other functionalities w.r.t. a (necessarily) weakened notion of concurrently secure computation. The results presented in this dissertation stem from two papers which are joint works with Sanjam Garg and Amit Sahai, and with Vipul Goyal and Rafail Ostrovsky, respectively.