PolarRLCE: A New Code-Based Cryptosystem Using Polar Codes

Jingang Liu,Yongge Wang,Zongxiang Yi,Zhiqiang Lin

doi:10.1155/2019/3086975

Jingang Liu, Yongge Wang + Show 2 more

Open Access

https://doi.org/10.1155/2019/3086975

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Abstract

Security challenges brought about by the upcoming 5G era should be taken seriously. Code-based cryptography leverages difficult problems in coding theory and is one of the main techniques enabling cryptographic primitives in the postquantum scenario. In this work, we propose the first efficient secure scheme based on polar codes (i.e., polarRLCE) which is inspired by the RLCE scheme, a candidate for the NIST postquantum cryptography standardization in the first round. In addition to avoiding some weaknesses of the RLCE scheme, we show that, with the proper choice of parameters, using polar codes, it is possible to design an encryption scheme to achieve the intended security level while retaining a reasonably small public key size. In addition, we also present a KEM version of the polarRLCE scheme that can attain a negligible decryption failure rate within the corresponding security parameters. It is shown that our proposal enjoys an apparent advantage to decrease the public key size, especially on the high-security level.

Highlights

Cryptography is essential for the security of online communication
Current cryptographic protocols, such as RSA and Di e–Hellman, are proven to be vulnerable under quantum algorithms. is fact pushed cryptographic research to focus on postquantum solutions, i.e., nding new primitives based on more well-suited mathematical problems that may still be di cult to solve for a quantum computer
We have proposed a new variant of the codebased encryption scheme by exploring polar codes, benefitting the lower encoding and decoding complexity

Summary

Introduction

Cryptography is essential for the security of online communication. many commonly used cryptosystems will be completely broken once large quantum computers exist. The conservative and well-understood choices for code-based cryptography are the McEliece cryptosystem [4] and its dual variant by Niederreiter [5] using binary Goppa codes They su er from the disadvantage of having large public key size, in spite of the fast encryption and decryption operations. E advantage of the RLCE scheme is that its security does not depend on any specific structure of underlying linear codes, instead, it is based on the NP-hardness of decoding random linear codes In such a manner, previous attacks regarding GRS codes based on the technique of filtration distinguisher no longer work. We combine the idea of the RLCE scheme by inserting random columns, propose the first efficient secure scheme based on polar codes (i.e., polarRLCE), which can avoid the attack of [24].

Preliminaries

Our Proposed Scheme of polarRLCE

Security Analysis

Conclusion