Explicit expression for decryption in a generalisation of the Paillier scheme

Obi, O O, Ali, F H and Stipidis, E (2007) Explicit expression for decryption in a generalisation of the Paillier scheme. IET Information Security, 1 (4). pp. 163-166. ISSN 1751-8709

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Abstract

The Paillier scheme encryption, (m,r) c=g^m r^N mod N^2 where m is in Z_N, r is in Z_N ^*, N=pq (p,q being strong primes) and g is an element of Z_N^2^*, of order a multiple of N, is decrypted by, m mod N=L(c^ mod N^2)/ L(g^ mod N^2),where L is defined on all u in Z_N^2 ^* , such that u mod N=1, by L(u)=(u-1)/N. In the generalization of the scheme due to Damgard and Jurik, the modulus N^2 is replaced by N^(1+s), 1s< p,q but an explicit expression for decryption was not given. Rather a way, the only known way so far, was found for decryption, by first encoding the cyphertext and then using an algorithm of a quadratic order of complexity in s to extract the plaintext part by part therefrom. In this work we fill this gap. We present an explicit expression for decryption in this setting, which is more straight forward, linear in s in complexity and hence more efficient, and reduces to the original Paillier L function for s=1.

Item Type: Article
Schools and Departments: School of Engineering and Informatics > Engineering and Design
Depositing User: Obowoware Oghenefumehuvie Obi
Date Deposited: 06 Feb 2012 20:01
Last Modified: 30 Mar 2012 12:21
URI: http://sro.sussex.ac.uk/id/eprint/23582
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