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IET Information Security

Leakage‐resilient lattice‐based partially blind signatures

Dimitrios Papachristoudis, Dimitrios Hristu‐Varsakelis, Foteini Baldimtsi, George Stephanides

Published Jul 29, 2019• 18 citations
Publisher

Abstract

Blind signature schemes (BSS) play a pivotal role in privacy‐oriented cryptography. However, with BSS, the signed message remains unintelligible to the signer, giving them no guarantee that the blinded message he signed actually contained valid information. Partially BSS (PBSS) were introduced to address precisely this problem. In this study, the authors present the first leakage‐resilient, lattice‐based PBSS in the literature. The proposed construction is provably secure in the random oracle model and offers quasi‐linear complexity w.r.t. key/signature sizes and signing speed. In addition, it offers statistical partial blindness and its unforgeability is based on the computational hardness of worst‐case ideal lattice problems for approximation factors in in dimension n . The proposed scheme benefits from the subexponential hardness of ideal lattice problems and remains secure even if a fraction of the signer's secret key leaks to an adversary via arbitrary side‐channels. Several extensions of the security model, such as honest‐user unforgeability and selective failure blindness, are also considered and concrete parameters for instantiation are proposed.

DOI
10.1049/iet-ifs.2019.0156

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Blind signature schemes (BSS) play a pivotal role in privacy‐oriented cryptography. However, with BSS, the signed message remains unintelligible to the signer, giving them no guarantee that the blinded message he signed actually contained valid information. Partially BSS (PBSS) were introduced to address precisely this problem. In this study, the authors present the first leakage‐resilient, lattice‐based PBSS in the literature. The proposed construction is provably secure in the random oracle model and offers quasi‐linear complexity w.r.t. key/signature sizes and signing speed. In addition, it offers statistical partial blindness and its unforgeability is based on the computational hardness of worst‐case ideal lattice problems for approximation factors in in dimension n . The proposed scheme benefits from the subexponential hardness of ideal lattice problems and remains secure even if a fraction of the signer's secret key leaks to an adversary via arbitrary side‐channels. Several extensions of the security model, such as honest‐user unforgeability and selective failure blindness, are also considered and concrete parameters for instantiation are proposed.
Blind signature schemes (BSS) play a pivotal role in privacy-oriented cryptography. However, with BSS, the signed message remains unintelligible to the signer, giving them no guarantee that the blinded message he signed actually contained valid information. Partially BSS (PBSS) were introduced to address precisely this problem. In this study, the authors present the first leakage-resilient, lattice-based PBSS in the literature. The proposed construction is provably secure in the random oracle model and offers quasi-linear complexity w.r.t. key/signature sizes and signing speed. In addition, it offers statistical partial blindness and its unforgeability is based on the computational hardness of worst-case ideal lattice problems for approximation factors in O ~ ( n 4 ) in dimension n. The proposed scheme benefits from the subexponential hardness of ideal lattice problems and remains secure even if a ( 1 − o ( 1 ) ) fraction of the signer's secret key leaks to an adversary via arbitrary side-channels. Several extensions of the security model, such as honest-user unforgeability and selective failure blindness, are also considered and concrete parameters for instantiation are proposed.
Blind signature allows a user to get a signature of a signer on an arbitrary message, and the verifier can convince that the signature is indeed signed by the signer without leaking any information about the message. This property is necessary when the user’s privacy needs protection, such as a bank bill, a trade secret, etc. As an alternative of public key infrastructure, the identity-based system can simplify the key management procedures in certificate-based public key systems. Inspired by the requirement of identity-based blind signature in the post quantum world, we research on identity-based blind signature based on hard lattice problems under the random Oracle model. We propose a construction built upon the blind signature by Rückert, and it is proved to be one-more unforgeable against selective identity and chosen message attacks (sID-CMA) and unconditionally blind. The proposed scheme has 2 moves, and its security can be reduced to the small integer solution (SIS) problem.
A proxy blind signature scheme is a special form of blind signature which allowed a designated person called proxy signer to sign on behalf of original signers without knowing the content of the message. It combines the advantages of proxy signature and blind signature. Up to date, most proxy blind signature schemes rely on hard number theory problems, discrete logarithm, and bilinear pairings. Unfortunately, the above underlying number theory problems will be solvable in the postquantum era. Lattice‐based cryptography is enjoying great interest these days, due to implementation simplicity and provable security reductions. Moreover, lattice‐based cryptography is believed to be hard even for quantum computers. In this paper, we present a new identity‐based proxy blind signature scheme from lattices without random oracles. The new scheme is proven to be strongly unforgeable under the standard hardness assumption of the short integer solution problem (SIS) and the inhomogeneous small integer solution problem (ISIS). Furthermore, the secret key size and the signature length of our scheme are invariant and much shorter than those of the previous lattice‐based proxy blind signature schemes. To the best of our knowledge, our construction is the first short lattice‐based identity‐based proxy blind signature scheme in the standard model.
Motivated by the need to have secure blind signatures even in the presence of quantum computers, we present two efficient blind signature schemes based on hard worst-case lattice problems. Both schemes are provably secure in the random oracle model and unconditionally blind. The first scheme is based on preimage samplable functions that were introduced at STOC 2008 by Gentry, Peikert, and Vaikuntanathan. The scheme is stateful and runs in 3 moves. The second scheme builds upon the PKC 2008 identification scheme of Lyubashevsky. It is stateless, has 4 moves, and its security is based on the hardness of worst-case problems in ideal lattices.
Blind signatures were first introduced by David Chaum. They allow a user to have a message signed by a signer without revealing the message itself. This property is particularly useful in applications such as electronic voting and digital cash, where user anonymity is important. In a blind signature scheme, the user blinds their message before sending it to the signer, who signs the blinded message. The user then unblinds the signed message to obtain a valid signature that can be verified publicly, ensuring that the signer cannot trace the signed message back to the original unblinded version. A good analogy is placing the message inside an envelope and having the envelope signed. Once the envelope is opened, the signature remains valid for the enclosed message, ensuring that the content remains confidential. Such constructions provide anonymity and privacy to the user but given a practical quantum computer, the security of traditional crypto-systems providing such features will be broken. To address this, the development of quantum-resistant cryptographic protocols is essential for maintaining the security of digital transactions and data. Aligning with the same goal, this work aims to thoroughly review the background of lattice-based blind signatures. We start with the foundations of digital signatures in the classical settings and then move on to lattice-based constructions.
Blind signatures are a central tool for privacy-preserving protocols. They allow users to obtain signatures from a signer without the signer seeing the signed message. For instance, it enables electronic cash: signatures correspond to coins which can be issued by the bank in a privacy-preserving manner via blind signing. To mitigate the risk of key compromise, threshold blind signatures allow the distribution of the signing key amongst N parties. While recent works have focused on improving the security of this primitive in the classical setting, no construction is known to date in the post-quantum setting. We present the first construction of a threshold blind signature secure in the post-quantum setting, based on lattices. We prove its security under an interactive variant of the SIS assumption introduced in [Agrawal et al., CCS’22]. Our construction has a reasonable overhead of a factor of roughly 1.4 X to 2.5 X in signature size over comparable non-threshold blind signatures over lattices under heuristic but natural assumptions.