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Explicit expression for decryption in a generalisation of the Paillier scheme

journal contribution
posted on 2023-06-08, 00:58 authored by O O Obi, Falah AliFalah Ali, E Stipidis
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.

History

Publication status

  • Published

Journal

IET Information Security

ISSN

1751-8709

Issue

4

Volume

1

Page range

163-166

Pages

4.0

Department affiliated with

  • Engineering and Design Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-02-06

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