Abstract
We present the first linkable ring signature scheme with both unconditional anonymity and forward-secure key update: a powerful tool which has direct applications in elegantly addressing a number of simultaneous constraints in remote electronic voting. We propose a comprehensive security model, and construct a scheme based on the hardness of finding discrete logarithms, and (for forward security) inverting bilinear or multilinear maps of moderate degree to match the time granularity of forward security. We prove efficient security reductions—which, of independent interest, apply to, and are much tighter than, linkable ring signatures without forward security, thereby vastly improving the provable security of these legacy schemes. If efficient multilinear maps should ever admit a secure realisation, our contribution would elegantly address a number of problems heretofore unsolved in the important application of (multi-election) practical Internet voting. Even if multilinear maps are never obtained, our minimal two-epoch construction instantiated from bilinear maps can be combinatorially boosted to synthesise a polynomial time granularity, which would be sufficient for Internet voting and more.
Highlights
Ring signatures, and especially linkable ring signatures, garner much interest in the applied cryptographic community for their promise to simplify certain aspects of the notoriously hard problem of remote electronic voting, which has conflicting and often frustrating security requirements.In particular, linkability [1] or the closely related notion of traceability [2], make it easy to detect when the same signer has signed twice on the same matter, thereby preventing double spending in an electronic cash system, double voting in the same election
We present the first linkable ring signature with unconditional anonymity and forward-secure key update, which is a tool that enables significantly more simple and secure remote electronic voting, even within the framework of existing electronic voting protocols, and opens the door to a number of simplified general anonymous authentication protocols for online systems
Without forward security or key update, our results are inspired by the linkable ring scheme from [1]—which we incidentally vastly improve via much tighter security reductions
Summary
Especially linkable ring signatures, garner much interest in the applied cryptographic community for their promise to simplify certain aspects of the notoriously hard problem of remote electronic voting, which has conflicting and often frustrating security requirements. At present, most proposed electronic voting schemes use cryptography which is likely to allow adversaries to break the privacy of the voters at some point in the future To address these issues, an offline key update mechanism would allow the potentially costly registration of a voter’s public key to happen once, whereafter the corresponding private key can be refreshed or updated multiple times, efficiently and non-interactively, for use in subsequent elections. An offline key update mechanism would allow the potentially costly registration of a voter’s public key to happen once, whereafter the corresponding private key can be refreshed or updated multiple times, efficiently and non-interactively, for use in subsequent elections In this context, forward security refers to the notion that the leakage or compromise of an updated private key will not compromise one’s privacy in a past election—or let an attacker forge signatures. We deliberately choose to focus on the problem of achieving unconditional anonymity against outsiders, but only computational forward security against insiders in the sense of unforgeability and anonymity after key update
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