Title: A Unique Signature Scheme Based on Candidate Multilinear Maps

Year of Publication: Nov - 2014
Page Numbers: 36-43
Authors: Han Wang, Zhuojun Liu
Conference Name: The International Conference on Electrical, Electronics, Computer Engineering and their Applications (EECEA2014)
- Malaysia


The graded encoding scheme introduced by Gentry, Garg and Halevi (GGH scheme) is considered as an important candidate multilinear map, which has many applications in cryptography. On the other hand, the unique signature (also called invariant signature or deterministic signature) is a significant kind of digital signatures. In this article, we first present a variant of the GGH scheme which we call GGH-II graded encoding scheme, and give a hardness assumption-GGH multilinear computational Diffie-Hellman assumption (GGH-MCDH assumption). Moreover, we show that the GGH-MCDH assumption resist the arithmetic straight-line programs attack. Then, we give a unique signature scheme using the GGH-II scheme and show the consistence and uniqueness of the unique signature scheme by the properties of ideal lattices. We also prove that the unique signature is secure under the GGH-MCDH assumption, while the previous unique signatures are based on RSA assumption or DH-DDH assumption.