Welcome to the resource topic for
**2023/180**

**Title:**

Asymmetric Trapdoor Pseudorandom Generators: Definitions, Constructions, and Applications to Homomorphic Signatures with Shorter Public Keys

**Authors:**
Jinpeng Hou, Yansong Gao, Mang Su, Willy Susilo, Jie Chen, Anmin Fu

**Abstract:**

We introduce a new primitive called the asymmetric trapdoor pseudorandom generator (ATPRG), which belongs to pseudorandom generators with two additional trapdoors (a public trapdoor and a secret trapdoor) or backdoor pseudorandom generators with an additional trapdoor (a secret trapdoor). Specifically, ATPRG can only generate public pseudorandom numbers pr_1,\dots,pr_n for the users having no knowledge of the public trapdoor and the secret trapdoor; so that this function is the same as pseudorandom generators. However, the users having the public trapdoor can use any public pseudorandom number pr_i to recover the whole pr sequence; so that this function is the same as backdoor pseudorandom generators. Further, the users having the secret trapdoor can use pr sequence to generate a sequence sr_1,\dots,sr_n of the secret pseudorandom numbers.

As for applications of ATPRG, we construct the first homomorphic signature scheme (in the standard model) whose public key size is only O(T) independent of the dataset size. As a comparison, the shortest size of the existing public key is O(\sqrt{N}+\sqrt{T}), proposed by Catalano et al. (CRYPTOâ€™15), where N is the dataset size and T is the dimension of the message. In other words, we provide the first homomorphic signature scheme with O(1)-sized public keys for the one-dimension messages.

**ePrint:**
https://eprint.iacr.org/2023/180

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