A STUDY ON CRYSTALS-KYBER AND ITS MASKED IMPLEMENTATIONS

Date

2023-10

Author

Özeren, Sıla

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As we transition into the quantum computing era, the security of widely-used cryptographic algorithms is facing significant challenges. This is attributable to Shor's algorithm, enabling quantum computers to break conventional cryptosystems such as RSA, DSA, and elliptic curve cryptosystems. This thesis provides a comprehensive study on the CRYSTALS-Kyber key encapsulation mechanism (KEM), the only KEM algorithm that was a third-round finalist in NIST's PQC Standardization effort. We begin with a detailed examination of the foundational concepts of lattices, introducing the inherent hard problems in lattice cryptography, including Learning with Errors (LWE), Ring-LWE, and Module-LWE. We subsequently delve into the three components of Kyber.CPAPKE and detail the Fujisaki-Okamoto transform version of each algorithm necessary to achieve IND-CCA2 security. An extensive study is conducted on existing masking methods for the compression function in Kyber, and their shortcomings due to prime modulo design are highlighted. We propose two methods for masking this compression function: one integrating a look-up-table, and the other utilizing a double-and-check method. Additionally, we introduce potential compression functions for various prime numbers.

Subject Keywords

post-quantum cryptography, lattice cryptography, CRYSTALS-KYBER, key encapsulation mechanism, side-channel attacks, masking countermeasures

URI

https://hdl.handle.net/11511/105430

Collections

Graduate School of Applied Mathematics, Thesis