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A Provably Secure Group Signature Scheme from Code-Based Assumptions.

Martianus Frederic Ezerman, Hyung Tae Lee, San Ling, Khoa Nguyen, Huaxiong Wang

Published Jan 1, 2015• 0 citations
OpenAlex

Abstract

Abstract. We solve an open question in code-based cryptography by introducing the first provably secure group signature scheme from code-based assumptions. Specifically, the scheme satisfies the CPA-anonymity and traceability requirements in the random oracle model, assuming the hardness of the McEliece problem, the Learning Parity with Noise prob-lem, and a variant of the Syndrome Decoding problem. Our construction produces smaller key and signature sizes than the existing post-quantum group signature schemes from lattices, as long as the cardinality of the underlying group does not exceed the population of the Netherlands ( ≈ 224 users). The feasibility of the scheme is supported by implementa-tion results. Additionally, the techniques introduced in this work might be of independent interest: a new verifiable encryption protocol for the randomized McEliece encryption and a new approach to design formal security reductions from the Syndrome Decoding problem.

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Abstract Verifiably encrypted signature (VES) schemes are extensively utilized in fair exchange which combine the features of encryption and signature, aiming to provide a solution that can not only verify the validity of signatures but also safeguard the privacy of signatures. With the development of quantum algorithms and quantum computing, it is necessary to construct a VES protocol that can resist attack of quantum computing. At the same time, some new security properties can also be added to the VES protocol to enhance its security. To reach this goal, we propose a state-of-the-art lattice-based verifiably encrypted group signature (VEGS) scheme. In the random oracle model, the VEGS scheme is provably secure under the assumptions of learning with error (LWE) and inhomogeneous small integer solution (ISIS). Our scheme provides five security properties, namely unforgeability, opacity, extractability, anonymity and traceability. The three properties unforgeability, opacity and extractability are the properties that the VES protocol needs to meet, and the anonymity and traceability properties are additional security properties brought by combining with the group signature.

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ML-GS: Module Lattice-Based Group Signature Scheme

Deng Pan, Yatao Yang, Weitao Sun +2 more

Abstract With the rapid growth of online users, protecting user privacy in access control scenarios has become a critical challenge in the field of information security. Group signatures serve as a fundamental cryptographic primitive that enables users to sign on behalf of a group, providing anonymity while supporting traceability of signers. However, traditional group signature schemes, which rely on number-theoretic assumptions vulnerable to quantum algorithms, face significant security threats in the advent of quantum computing. In this paper, we propose a module lattice-based group signature scheme (ML-GS). ML-GS leverages FIPS 204 standard, a recently standardized signature scheme by the National Institute of Standards Technology (NIST), and integrates a dualrejection-sampling signature mechanism with the K-PKE encryption scheme from FIPS 203 standard, forming a “sign-hybrid-encrypt” hybrid structure to ensure both efficiency and traceability. In the key generation phase, we introduce a module Gaussian preimage sampling algorithm that reduces public key size and supports dynamic user enrollment. The security of ML-GS is formally proven in the random oracle model under the Module Learning with Error (MLWE) and Module Short Integer Solution (MSIS) assumptions. Experimental results demonstrate that, compared to existing scheme with equivalent security level, the ML-GS scheme achieves significant improvements in both time and storage overhead.

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Abstract. Support of membership revocation is a desirable functionality for any group signature scheme. Among the known revocation approaches, verifier-local revocation (VLR) seems to be the most flexible one, because it only requires the verifiers to possess some up-to-date revocation information, but not the signers. All of the contemporary VLR group signatures operate in the bilinear map setting, and all of them will be insecure once quantum computers become a reality. In this work, we introduce the first lattice-based VLR group signature, and thus, the first such scheme that is believed to be quantum-resistant. In comparison with existing lattice-based group signatures, our scheme has several noticeable advantages: support of membership revocation, logarithmic-size signatures, and weaker security assumption. In the random oracle model, our scheme is proved to be secure based on the hardness of the SIVPÕ(n1.5) problem in general lattices- an assumption that is as weak as those of state-of-the-art lattice-based standard signatures. Moreover, our construction works without relying on encryption schemes, which is an intriguing feature for group signatures.

•Jan 1, 2014•3 citations
Abstract. We solve an open question in code-based cryptography by introducing the first provably secure group signature scheme from code-based assumptions. Specifically, the scheme satisfies the CPA-anonymity and traceability requirements in the random oracle model, assuming the hardness of the McEliece problem, the Learning Parity with Noise prob-lem, and a variant of the Syndrome Decoding problem. Our construction produces smaller key and signature sizes than the existing post-quantum group signature schemes from lattices, as long as the cardinality of the underlying group does not exceed the population of the Netherlands ( ≈ 224 users). The feasibility of the scheme is supported by implementa-tion results. Additionally, the techniques introduced in this work might be of independent interest: a new verifiable encryption protocol for the randomized McEliece encryption and a new approach to design formal security reductions from the Syndrome Decoding problem.
Abstract Verifiably encrypted signature (VES) schemes are extensively utilized in fair exchange which combine the features of encryption and signature, aiming to provide a solution that can not only verify the validity of signatures but also safeguard the privacy of signatures. With the development of quantum algorithms and quantum computing, it is necessary to construct a VES protocol that can resist attack of quantum computing. At the same time, some new security properties can also be added to the VES protocol to enhance its security. To reach this goal, we propose a state-of-the-art lattice-based verifiably encrypted group signature (VEGS) scheme. In the random oracle model, the VEGS scheme is provably secure under the assumptions of learning with error (LWE) and inhomogeneous small integer solution (ISIS). Our scheme provides five security properties, namely unforgeability, opacity, extractability, anonymity and traceability. The three properties unforgeability, opacity and extractability are the properties that the VES protocol needs to meet, and the anonymity and traceability properties are additional security properties brought by combining with the group signature.
Abstract With the rapid growth of online users, protecting user privacy in access control scenarios has become a critical challenge in the field of information security. Group signatures serve as a fundamental cryptographic primitive that enables users to sign on behalf of a group, providing anonymity while supporting traceability of signers. However, traditional group signature schemes, which rely on number-theoretic assumptions vulnerable to quantum algorithms, face significant security threats in the advent of quantum computing. In this paper, we propose a module lattice-based group signature scheme (ML-GS). ML-GS leverages FIPS 204 standard, a recently standardized signature scheme by the National Institute of Standards Technology (NIST), and integrates a dualrejection-sampling signature mechanism with the K-PKE encryption scheme from FIPS 203 standard, forming a “sign-hybrid-encrypt” hybrid structure to ensure both efficiency and traceability. In the key generation phase, we introduce a module Gaussian preimage sampling algorithm that reduces public key size and supports dynamic user enrollment. The security of ML-GS is formally proven in the random oracle model under the Module Learning with Error (MLWE) and Module Short Integer Solution (MSIS) assumptions. Experimental results demonstrate that, compared to existing scheme with equivalent security level, the ML-GS scheme achieves significant improvements in both time and storage overhead.
In this work, we construct a dual version of statistically binding commitment scheme by Jain et al. (Asiacrypt 2012) with shorter commitment size under hardness of syndrome decoding. Then, we point out that perfectly binding variants of the above schemes follow directly from the Randomized McEliece and Niederreiter public key encryption schemes, assuming indistinguishability of permuted Goppa codes, as well as hardness of the exact learning parity with noise (xLPN) problem (for the McEliece scheme) and hardness of syndrome decoding (for the Niederreiter scheme). Our key observation here is that perfect binding (as opposed to statistical binding) requires exact knowledge of minimal distance of the underlying code. Finally, we provide security evaluation of our proposals, and compare their performance with that of existing schemes.
Group signature is a cryptographic primitive where any member can anonymously sign a message on behalf of the population they belong to. Several group signatures were proposed based on number-theoretic assumptions. All these schemes are insecure in the presence of quantum computers. Group signatures based on lattice assumptions are believed to be quantum-resistant. In the past few years, group signatures based on lattice assumptions have been proposed and most of them are proved to be secure in random-oracle model. This paper presents a lattice-based group signature scheme without using random-oracle. Our scheme is based on correlation-intractable function ensembles for all evasive relations which are constructed recently based on well-defined assumptions. Security of our scheme is proved based on correlation-intractable function ensembles and hardness of Short Integer Solution and Learning With Errors problem.
With the development of quantum computation, quantum computers will break the almost classical cryptography. It is imminent to design post-quantum cryptography algorithm that could resist quantum adversaries. Lattice-based problem has been verified that could resist quantum attacks. Our goal is to design a signature and try to prove it is secure in the quantum random oracle model. Our new signature scheme is redesigned based on the signature proposed by Lyu, but that scheme only proved secure in the random oracle model. The difference between the two signature is that we introduce the middle-product operation. So our signature is based on middle-product LWE hard assumption, which enjoys a security proof from PL WE. Then we combine the secure chameleon hash function and our new scheme, prove that our new combined signature is still secure in the quantum random oracle model.
Abstract. Support of membership revocation is a desirable functionality for any group signature scheme. Among the known revocation approaches, verifier-local revocation (VLR) seems to be the most flexible one, because it only requires the verifiers to possess some up-to-date revocation information, but not the signers. All of the contemporary VLR group signatures operate in the bilinear map setting, and all of them will be insecure once quantum computers become a reality. In this work, we introduce the first lattice-based VLR group signature, and thus, the first such scheme that is believed to be quantum-resistant. In comparison with existing lattice-based group signatures, our scheme has several noticeable advantages: support of membership revocation, logarithmic-size signatures, and weaker security assumption. In the random oracle model, our scheme is proved to be secure based on the hardness of the SIVPÕ(n1.5) problem in general lattices- an assumption that is as weak as those of state-of-the-art lattice-based standard signatures. Moreover, our construction works without relying on encryption schemes, which is an intriguing feature for group signatures.