Cryptology ePrint Archive: Report 2019/830

The Simplest Multi-key Linearly Homomorphic Signature Scheme

Diego F. Aranha and Elena Pagnin

Abstract: We consider the problem of outsourcing computation on data authenticated by different users. Our aim is to describe and implement the simplest possible solution to provide data integrity in cloud-based scenarios. Concretely, our multi-key linearly homomorphic signature scheme (mklhs) allows users to upload signed data on a server, and at any later point in time any third party can query the server to compute a linear combination of data authenticated by different users and check the correctness of the returned result. Our construction generalizes Boneh et al.'s linearly homomorphic signature scheme (PKC'09) to the multi-key setting and relies on basic tools of pairing-based cryptography. Compared to existing multi-key homomorphic signature schemes, our mklhs is a conceptually simple and elegant direct construction, which trades-off privacy for efficiency. The simplicity of our approach leads us to a very efficient construction that enjoys significantly shorter signatures and higher performance than previous proposals. Finally, we implement mklhs using two different pairing-friendly curves at the 128-bit security level, a Barreto-Lynn-Scott curve and a Barreto-Naehrig curve. Our benchmarks illustrate interesting performance trade-offs between these parameters, involving the cost of exponentiation and hashing in pairing groups. We provide a discussion on such trade-offs that can be useful to other implementers of pairing-based protocols.

Category / Keywords: cryptographic protocols / Multi-key homomorphic signatures, cryptographic pairings, efficient software implementation

Original Publication (in the same form): LATINCRYPT 2019

Date: received 17 Jul 2019

Contact author: elena at cs au dk, dfaranha@eng au dk

Available format(s): PDF | BibTeX Citation

Version: 20190718:065826 (All versions of this report)

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