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Cryptography 2018, 2(4), 32;

A New Technique in Rank Metric Code-Based Encryption

Temasek Laboratories, National University of Singapore, T-Lab Building, 5A, Engineering Drive 1, #09-02, Singapore 117411, Singapore
This paper is an extended version of our paper published in 23rd Australasian Conference on Information Security and Privacy (ACISP 2018).
These authors contributed equally to this work.
Author to whom correspondence should be addressed.
Received: 29 August 2018 / Revised: 7 October 2018 / Accepted: 11 October 2018 / Published: 15 October 2018
(This article belongs to the Special Issue Public Key Cryptography)
Full-Text   |   PDF [371 KB, uploaded 31 October 2018]


We propose a rank metric codes based encryption based on the hard problem of rank syndrome decoding problem. We propose a new encryption with a public key matrix by considering the adding of a random distortion matrix over F q m of full column rank n. We show that IND-CPA security is achievable for our encryption under assumption of the Decisional Rank Syndrome Decoding problem. Furthermore, we also prove some bounds for the number of matrices of a fixed rank with entries over a finite field. Our proposal allows the choice of the error terms with rank up to r 2 , where r is the error-correcting capability of a code. Our encryption based on Gabidulin codes has public key size of 13 . 68 KB, which is 82 times smaller than the public key size of McEliece Cryptosystem based on Goppa codes. For similar post-quantum security level of 2 140 bits, our encryption scheme has a smaller public key size than the key size suggested by LOI17 Encryption. View Full-Text
Keywords: code-based cryptography; McEliece; public key encryption; provable security code-based cryptography; McEliece; public key encryption; provable security
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Lau, T.S.C.; Tan, C.H. A New Technique in Rank Metric Code-Based Encryption. Cryptography 2018, 2, 32.

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