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International Journal of Information Technology

A lattice-based ring signature scheme with gradual revelation of non-signers

Ramakant Kumar, Sahadeo Padhye

Published Dec 3, 2024• 2 citations
Publisher
DOI
10.1007/s41870-024-02275-1

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In a ring signature scheme, a user selects an arbitrary ring to be able to sign a message on behalf of the ring without revealing the signer’s identity. Whistle-blowers especially find this useful. To date, various ring signature schemes have been proposed, all considered to be secure as existentially unforgeable with respect to insider corruption; that is, an adversary who chooses ring-message pairs for which he requests signatures, corrupts honest users, and obtains their signing keys can not produce forgeries for new ring-message pairs. Lattice-based ring signature schemes offer lower computational overhead and security from quantum attacks. In this paper, we offer a lattice-based scheme. We begin by showing that the existing ring signature schemes are not sufficiently secure, because existential unforgeability still permits a signer to potentially produce a new signature on previously signed messages. Furthermore, we show that existing ring signature schemes from lattices are not even existentially unforgeable with respect to insider corruption. We then improve previous schemes by applying, for the first time, the concept of strong unforgeability with respect to insider corruption to a ring signature scheme in lattices. This offers more security than any previous ring signature scheme: adversaries cannot produce new signatures for any ring-message pair, including previously signed ring-message pairs.

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In cryptography, a ring signature is anonymous as it hides the signer’s identity among other users. When generating the signature, the users are arranged as a ring. Compared with group signatures, a ring signature scheme needs no group manager or special setup and supports flexibility of group choice. However, the anonymity provided by ring signatures can be used to conceal a malicious signer and put other ring members under suspicion. At the other extreme, it does not allow the actual signer to prove their identity and gain recognition for their actions. A deniable ring signature is designed to overcome these disadvantages. It can initially protect the signer, but if necessary, it enables other ring members to deny their involvement, and allows the real signer to prove who made the signed action. Many real-world applications can benefit from such signatures. Inspired by the requirement for them to remain viable in the post-quantum age, this work proposes a new non-interactive deniable ring signature scheme based on lattice assumptions. Our scheme is proved to be anonymous, traceable and non-frameable under quantum attacks.
A ring signature scheme (RSS) provides a method to digitally sign a document anonymously on the behalf of a set of possible signers. It is generally used to leak secret information. But an ordinary/general RSS can not be used for anonymous bidding, revealing secrets and later getting reward scenarios. We can use convertible/verifiable RSS to achieve these goals. A convertible RSS is an RSS where the original signer has the potency to convert it into a general/ordinary signature, if required. Here, we construct the first lattice-based (LB) convertible RSS. This scheme gives way to the signer to unfold his identity, if required (Reward, Bidding). We use bimodal Gaussian and rejection sampling in the scheme. We show that our convertible RSS is unforgeable against insider corruption, anonymous against full key exposure, and non-convertible against non-signers. The designed scheme is quantum secure as the underlying short integer solution (SIS) problem over lattice is conjectured to be hard.
In a ring signature scheme, a user selects an arbitrary ring to be able to sign a message on behalf of the ring without revealing the signer’s identity. Whistle-blowers especially find this useful. To date, various ring signature schemes have been proposed, all considered to be secure as existentially unforgeable with respect to insider corruption; that is, an adversary who chooses ring-message pairs for which he requests signatures, corrupts honest users, and obtains their signing keys can not produce forgeries for new ring-message pairs. Lattice-based ring signature schemes offer lower computational overhead and security from quantum attacks. In this paper, we offer a lattice-based scheme. We begin by showing that the existing ring signature schemes are not sufficiently secure, because existential unforgeability still permits a signer to potentially produce a new signature on previously signed messages. Furthermore, we show that existing ring signature schemes from lattices are not even existentially unforgeable with respect to insider corruption. We then improve previous schemes by applying, for the first time, the concept of strong unforgeability with respect to insider corruption to a ring signature scheme in lattices. This offers more security than any previous ring signature scheme: adversaries cannot produce new signatures for any ring-message pair, including previously signed ring-message pairs.