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Lecture notes in computer science

A Constructive Perspective on Key Encapsulation

Sandro Coretti, Ueli M. Maurer, Björn Tackmann

Published Jan 1, 2013• 8 citations
Publisher
DOI
10.1007/978-3-642-42001-6_16

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Driven by advances in the standardization of NIST’s Post-Quantum Cryptography (PQC) algorithms, research on constructing Password Authenticated Key Exchange (PAKE) protocols using Key Encapsulation Mechanisms (KEMs) has gained considerable attention. Several PAKE protocols have established precise security requirements for the underlying KEM. Arriaga et al. introduced a PAKE protocol called CHIC, which requires the KEM to achieve anonymity under plaintext-checkable attacks (ANO-1PCA). An anonymous KEM does not leak any information about which public key was used for encryption. It protects the identities and privacy of participants and is critical in preventing identity-guessing attacks, therefore, anonymity is also called key-privacy. The anonymity of NIST PQC Round-3 candidates has recently been analyzed, some of which satisfied ANO-CCA.Huguenin-Dumittan and Vaudenay proposed two efficient constructions, TCHand TH, to create KEM from public-key encryption (PKE) schemes. Jiang et al. introduced TRHbased on TH. These constructions can transform any OW-CPA PKE into an IND-qCCA KEM efficiently and avoid re-encryption. However, prior to this work, no research has been conducted to determine whether these constructions preserve or lift anonymity.In this paper, we proved that for any OW-CPA, DS-IND PKE, the construction KEMRH= TRH[PKE,H] achieves ANO1-CCA in the quantum random oracle model (QROM). We then construct a KEM called KyberRH, and provide an algorithm for the CHIC protocol using KyberRH.

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Driven by advances in the standardization of NIST’s Post-Quantum Cryptography (PQC) algorithms, research on constructing Password Authenticated Key Exchange (PAKE) protocols using Key Encapsulation Mechanisms (KEMs) has gained considerable attention. Several PAKE protocols have established precise security requirements for the underlying KEM. Arriaga et al. introduced a PAKE protocol called CHIC, which requires the KEM to achieve anonymity under plaintext-checkable attacks (ANO-1PCA). An anonymous KEM does not leak any information about which public key was used for encryption. It protects the identities and privacy of participants and is critical in preventing identity-guessing attacks, therefore, anonymity is also called key-privacy. The anonymity of NIST PQC Round-3 candidates has recently been analyzed, some of which satisfied ANO-CCA.Huguenin-Dumittan and Vaudenay proposed two efficient constructions, TCHand TH, to create KEM from public-key encryption (PKE) schemes. Jiang et al. introduced TRHbased on TH. These constructions can transform any OW-CPA PKE into an IND-qCCA KEM efficiently and avoid re-encryption. However, prior to this work, no research has been conducted to determine whether these constructions preserve or lift anonymity.In this paper, we proved that for any OW-CPA, DS-IND PKE, the construction KEMRH= TRH[PKE,H] achieves ANO1-CCA in the quantum random oracle model (QROM). We then construct a KEM called KyberRH, and provide an algorithm for the CHIC protocol using KyberRH.
Key encapsulation mechanisms play a main role in post-quantum cryptography, particularly in constructing encryption schemes. Understanding the design principles behind them is crucial not only for ensuring the efficient operation of the cryptographic protocols that employ them, but also for evaluating the security guarantees that these key encapsulation mechanisms provide. In this work, three lattice-based key encapsulation mechanism design paradigms are compared, and it is proved that asymmetric key consensus-based and encryption-based key encapsulation mechanisms are equivalent and that it is possible to construct a transformation from one approach to another.