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RNS-Based Public-Key Cryptography (RSA and ECC)

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Embedded Systems Design with Special Arithmetic and Number Systems

Abstract

As computer arithmetic advances for computation-bound systems like public-key cryptographic processors become increasingly incremental, researchers tend to focus their quest for advanced performance on alternative number system representations. The stake is not only to further boost up performance but also to explore new cryptanalytic properties offered by such representations. Among various options available, the ancient Residue Number System (RNS) stands out as the main player. This chapter focuses on RNS-based system design for public-key cryptography and highlights important concepts of residue arithmetic application in two of the most popular public-key cryptosystems, namely the RSA and Elliptic Curve Cryptography (ECC). Starting from basic arithmetic operations and algorithms and progressing to state-of-the-art hardware implementations and useful cryptanalytic properties, the reader will hopefully obtain a holistic overview of the implications, challenges, and unexplored issues of this emerging field.

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Acknowledgements

Our warmest thanks to Mrs. Elli Kyrmanidou (PhD candidate in LMU Munich) for editing the chapter.

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Authors and Affiliations

  1. NOKIA Bell Labs, Werinherstr. 91, Munich, Germany

    Dimitris Schinianakis

  2. University of Patras, Patras, Greece

    Thanos Stouraitis

  3. KUSTAR, Abu Dhabi, United Arab Emirates

    Thanos Stouraitis

Authors
  1. Dimitris Schinianakis
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  2. Thanos Stouraitis
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Corresponding author

Correspondence to Dimitris Schinianakis .

Editor information

Editors and Affiliations

  1. Department of Computer Engineering, Islamic Azad University, Kerman Branch, Kerman, Iran

    Amir Sabbagh Molahosseini

  2. INESC-ID, Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal

    Leonel Seabra de Sousa

  3. School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Singapore

    Chip-Hong Chang

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Schinianakis, D., Stouraitis, T. (2017). RNS-Based Public-Key Cryptography (RSA and ECC). In: Molahosseini, A., de Sousa, L., Chang, CH. (eds) Embedded Systems Design with Special Arithmetic and Number Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-49742-6_12

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  • DOI: https://doi.org/10.1007/978-3-319-49742-6_12

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-49742-6

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