Classic McEliece: key encapsulation based on codes

Introduction

At the end of the third round of the NIST standardization process, the CRYSTALS-Kyber key encapsulation method aimed at replacing the current ECDH scheme was selected.

NIST then defined a fourth round of selection, to differentiate the security assumptions underlying the standardized schemes.

This round, still in progress, aims to analyze three key code-based encapsulation schemes, Classic McEliece, BIKE and HQC, among which Classic McEliece represents the most conservative choice in terms of security.

The cryptosystem at the foundation of Classic McEliece is the public-key cipher proposed by Niederreiter in 1986, a dual version of the one proposed by McEliece in 1978.

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The authors

Veronica Cristiano, a bachelor’s degree in Mathematics from the University of Pisa and a master’s degree in Mathematics with a specialization in Cryptography at the University of Trento, joined the Telsy Cryptography research group in mid-2021.

Giuseppe D’Alconzo, graduated in Mathematics with a specialization in Cryptography at the University of Trento, in 2019 he carried out an internship at Telsy, dealing with Multiparty Computation and Attribute-Based Encryption. He is currently a PhD student in Pure and Applied Mathematics at the Politecnico di Torino, with a “Post-Quantum Cryptography” scholarship within the UniversiTIM program and in collaboration with the Telsy Research Group.