Threshold Properties of Prime Power Subgroups with Application to Secure Integer Comparisons

Rhys Carlton; Aleksander Essex; Krzysztof Kapulkin

Paper 2018/224

Threshold Properties of Prime Power Subgroups with Application to Secure Integer Comparisons

Rhys Carlton, Aleksander Essex, and Krzysztof Kapulkin

Abstract

We present a semantically secure somewhat homomorphic public-key cryptosystem working in sub-groups of $Z_{n}^{*}$ of prime power order. Our scheme introduces a novel threshold homomorphic property, which we use to build a two-party protocol for secure integer comparison. In contrast to related work which encrypts and acts on each bit of the input separately, our protocol compares multiple input bits simultaneously within a single ciphertext. Compared to the related protocol of Damgård et al.~we present results showing this approach to be both several times faster in computation and lower in communication complexity.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. RSA Conference Cryptographers’ Track 2018
Keywords: RSA homomorphic encryption homomorphic threshold secure integer comparison
Contact author(s): kkapulki @ uwo ca
History: 2018-03-01: received
Short URL: https://ia.cr/2018/224
License: CC BY

BibTeX

@misc{cryptoeprint:2018/224,
      author = {Rhys Carlton and Aleksander Essex and Krzysztof Kapulkin},
      title = {Threshold Properties of Prime Power Subgroups with Application to Secure Integer Comparisons},
      howpublished = {Cryptology {ePrint} Archive, Paper 2018/224},
      year = {2018},
      url = {https://eprint.iacr.org/2018/224}
}