Title: Improved RSA lossy trapdoor function and applications

Authors: Nanyuan Cao; Zhenfu Cao; Xiaolei Dong; Haijiang Wang

Addresses: School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, China ' School of Computer Science and Software Engineering, East China Normal University, Shanghai, China ' School of Computer Science and Software Engineering, East China Normal University, Shanghai, China ' School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, China

Abstract: Kakvi and Kiltz (EUROCRYPT'12) proposed the first tight security reduction for RSA full domain hash signature scheme (RSA-FDH) with public exponent e < N^1/4 in the random oracle (RO) model, and they left an open problem which called for a tightly secure RSA-FDH for N^1/4 < e < N. In this paper, we consider the improved RSA (iRSA) trapdoor functions, introduced by Cao (Science in China'01), are functions that the security can be strictly proved to be equivalent to the factoring. We show that iRSA-FDH has a tight security reduction for e < N. Technically we construct iRSA lossy trapdoor functions, and then we apply the lossiness of the iRSA trapdoor functions to obtain tight security reductions for iRSA-FDH in the RO model. Finally, we propose a tightly secure blind signature scheme based on our iRSA lossy trapdoor functions in the RO model.

Keywords: RSA; lossy trapdoor function; LTDF; full domain hash; FDH; tight reduction; blind signatures.

DOI: 10.1504/IJICS.2021.114703

International Journal of Information and Computer Security, 2021 Vol.14 No.3/4, pp.229 - 241

Received: 23 Feb 2018
Accepted: 20 Mar 2018
Published online: 04 May 2021 *

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