Publication

On the Security of Two-Round Multi-Signatures

Bryan Alexander Ford, Manu Drijvers, Kasra Edalatnejadkhamene
2019
Conference Papers

Abstract

A multi-signature scheme allows a group of signers to collaboratively sign a message, creating a single signature that convinces a verifier that every individual signer approved the message. The increased interest in technologies to decentralize trust has triggered the proposal of highly efficient two-round Schnorr-based multi-signature schemes designed to scale up to thousands of signers, namely BCJ by Bagherzandi et al. (CCS 2008), MWLD by Ma et al. (DCC 2010), CoSi by Syta et al. (S&P 2016), and MuSig by Maxwell et al. (ePrint 2018). In this work, we point out serious security issues in all currently known two-round multi-signature schemes (without pairings). First, we prove that none of the schemes can be proved secure without radically departing from currently known techniques. Namely, we show that if the one-more discrete-logarithm problem is hard, then no algebraic reduction exists that proves any of these schemes secure under the discrete-logarithm or one-more discrete-logarithm problem. We point out subtle flaws in the published security proofs of the above schemes (except CoSi, which was not proved secure) to clarify the contradiction between our result and the existing proofs. Next, we describe practical sub exponential attacks on all schemes, providing further evidence to their insecurity. Being left without two-round multi-signature schemes, we present rnBCJ, a variant of the BCJ scheme that we prove secure under the discrete-logarithm assumption in the random-oracle model. Our experiments show that rni3CJ barely affects scalability compared to CoSi, allowing 16384 signers to collaboratively sign a message in about 2 seconds, making it a highly practical and provably secure alternative for large-scale deploy tents.

Official source

https://infoscience.epfl.ch/entities/publication/7627fcac-17de-4ecf-b7c1-59e0cc8f2dcc

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Bryan Alexander Ford, Manu Drijvers, Kasra Edalatnejadkhamene
2019
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/7627fcac-17de-4ecf-b7c1-59e0cc8f2dcc

About this result

Related concepts (30)

Discrete logarithm

In mathematics, for given real numbers a and b, the logarithm logb a is a number x such that bx = a. Analogously, in any group G, powers bk can be defined for all integers k, and the discrete logarithm logb a is an integer k such that bk = a. In number theory, the more commonly used term is index: we can write x = indr a (mod m) (read "the index of a to the base r modulo m") for rx ≡ a (mod m) if r is a primitive root of m and gcd(a,m) = 1. Discrete logarithms are quickly computable in a few special cases.

Elliptic-curve cryptography

Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC allows smaller keys compared to non-EC cryptography (based on plain Galois fields) to provide equivalent security. Elliptic curves are applicable for key agreement, digital signatures, pseudo-random generators and other tasks. Indirectly, they can be used for encryption by combining the key agreement with a symmetric encryption scheme.

Secure communication

Secure communication is when two entities are communicating and do not want a third party to listen in. For this to be the case, the entities need to communicate in a way that is unsusceptible to eavesdropping or interception. Secure communication includes means by which people can share information with varying degrees of certainty that third parties cannot intercept what is said.

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