CSCI 762 - An analysis of LAC, a lattice based post quantum encryption scheme.

Abstract

The threat of quantum computing is steadily becoming bigger and bigger. NIST have recognized this and are holding a competition to find the best cryptographic schemes most resilient towards attacks from quantum computers. For the first round of this competition they have 69 entries to check and test. This paper analyzes and discusses an entry in this competition, LAC, which has four Lattice based cryptosystem schemes which promise a high resistance to most known attacks while also providing high flexibility in parameters.

In particular this paper focuses on looking at all four of LACs sub-cryptosystems titled as LAC.CPA, LAC.CCA, LAC.KE, and LAC.AKE. LAC.CPA is a Public Key encryption scheme and LAC.KE, a passively secure key exchange protocol directly converted from LAC.CPA. LAC.CCA is a secure key encapsulation method that is based on LAC.CPA. LAC.AKE is an authenticated key exchange protocol based on LAC.CPA & LAC.CCA. This paper mainly covers the public key schema, followed by a brief discussion on all of the subsystems in how they’re designed, with their inputs and outputs. The correctness of the algorithms, and how well they perform compared to other, more current non-quantum safe algorithms. After describing the subsystems the Quantum resistance of the algorithms will be discussed, along with LACs advantages and disadvantages, followed by the Conclusion.

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