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New rank codes based encryption scheme using partial circulant matrices

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Abstract

We propose a new rank metric code based encryption based on the hard problem of rank syndrome decoding problem. We consider a generator matrix for Gabidulin codes in the form of k-partial circulant matrix. We distort the matrix G by adding it with another random k-partial circulant matrix and multiplying the product with a random circulant matrix. We also convert our encryption into an IND-CCA2 secured encryption scheme under assumption of Rank Syndrome Decoding problem. Our encryption has the smallest key size (of 4.306 KB) at 256-bit security level as compared to all the other rank code based encryption schemes with zero decryption failure and hidden structure for the decodable codes.

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Acknowledgements

We are grateful to the anonymous reviewers for their careful reading of our manuscript and their many insightful comments and suggestions which have greatly improved this manuscript.

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Authors and Affiliations

  1. Temasek Laboratories, National University of Singapore, 5A Engineering Drive 1, #09-02, Singapore, 117411, Singapore

    Terry Shue Chien Lau & Chik How Tan

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  1. Terry Shue Chien Lau
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  2. Chik How Tan
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Correspondence to Terry Shue Chien Lau.

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Communicated by G. Lunardon.

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Lau, T.S.C., Tan, C.H. New rank codes based encryption scheme using partial circulant matrices. Des. Codes Cryptogr. 87, 2979–2999 (2019). https://doi.org/10.1007/s10623-019-00659-0

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