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Lecture notes in computer science

Public-Key Cryptographic Primitives Provably as Secure as Subset Sum

Vadim Lyubashevsky, Adriana Palacio, Gil Segev

Published Jan 1, 2010• 90 citations
Publisher
DOI
10.1007/978-3-642-11799-2_23

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Abstract. We propose a semantically-secure public-key encryption scheme whose security is polynomialtime equivalent to the hardness of solving random instances of the subset sum problem. The subset sum assumption required for the security of our scheme is weaker than that of existing subset-sum based encryption schemes, namely the lattice-based schemes of Ajtai and Dwork (STOC ’97), Regev (STOC ’03, STOC ’05), and Peikert (STOC ’09). Additionally, our proof of security is simple and direct. We also present a natural variant of our scheme that is secure against key-leakage attacks, as well as an oblivious transfer protocol that is secure against semi-honest adversaries. 1

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Abstract. We propose a semantically-secure public-key encryption scheme whose security is polynomialtime equivalent to the hardness of solving random instances of the subset sum problem. The subset sum assumption required for the security of our scheme is weaker than that of existing subset-sum based encryption schemes, namely the lattice-based schemes of Ajtai and Dwork (STOC ’97), Regev (STOC ’03, STOC ’05), and Peikert (STOC ’09). Additionally, our proof of security is simple and direct. We also present a natural variant of our scheme that is secure against key-leakage attacks, as well as an oblivious transfer protocol that is secure against semi-honest adversaries. 1
Anonymity, robust synchronization, and perfect forward secrecy are the most important security properties of authenticated key agreement (AKA) protocols. Designing AKA protocols that simultaneously achieve these security properties and availability in the IoT environment is a challenging task. AKA protocols built using public key cryptographic primitives have advantages in achieving these critical security properties, but performing expensive public-key cryptographic operations is inefficient for resource-constrained IoT devices. The authentication protocols based on symmetric cryptographic primitives are often subject to various attacks. This paper proposes a secure lightweight AKA protocol with critical security properties (called CS-LAKA) for IoT environments without using public-key cryptographic primitives. LAKA cleverly achieves the security goals of anonymity, robust synchronization, and perfect forward secrecy by embedding dynamic identities in authenticators, and a few additional exchange messages are added. This enables LAKA to have both robust security and high efficiency. Subsequently, we perform a formal security analysis to prove that LAKA is secure, and compared with existing related schemes, LAKA has obvious advantages in terms of security, functionality and running performance.