Two-Dimensional Representation of Cover Free Families and Its Applications: Short Signatures and More

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Abstract

Very recently, Hofheinz, Jager, and Kiltz proposed novel digital signature schemes that yield significantly shorter signatures. However, in contrast to such remarkably short signatures, the size of the public key is still huge, making it desirable for this to be reduced. In this paper, we present a two-dimensional representation technique for cover free families, and show that this technique is quite useful for reducing the public key size in various cryptographic primitives. As immediate applications, we give constructions of the k-resilient identity-based key encapsulation mechanism (KEM), q-bounded CCA-secure KEM, and m-time signature which yield shorter public keys than previous schemes. Moreover, by applying our technique, we propose a (fully-fledged) signature scheme with the public key approximately 1/100 the size of that in the Hofheinz-Jager-Kiltz scheme with the same signature size and security assumption.