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

  • Rhys Carlton
  • Aleksander EssexEmail author
  • Krzysztof Kapulkin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10808)


We present a semantically secure somewhat homomorphic public-key cryptosystem working in sub-groups of \(\mathbb {Z}_{n}^{*}\) 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. [9, 10] we present results showing this approach to be both several times faster in computation and lower in communication complexity.


Public-key encryption Homomorphic encryption Homomorphic threshold Secure integer comparison 


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Western UniversityLondonCanada

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