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arXiv:2302.14860 · Lecture notes in computer science

Revocable Cryptography from Learning with Errors

Prabhanjan Ananth, Alexander Poremba, Vinod Vaikuntanathan

Published Jan 1, 2023• 15 citations
arXivHTMLPDF
DOI
10.1007/978-3-031-48624-1_4

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The emergence of quantum computing threatens many classical cryptographic schemes, leading to the innovations in public-key cryptography for postquantum cryptography primitives and protocols that resist to quantum attacks. Lattice-based cryptography is considered to be one of the promising mathematical approaches to achieving security resistant to quantum attacks, which could be built on the learning with errors (LWE) problem and its variants. The fundamental building blocks of protocols for public-key encryption (PKE) and key encapsulation mechanism (KEM) submitted to the National Institute of Standards and Technology (NIST) based on LWE and its variants are called key consensus (KC) and asymmetric key consensus (AKC) by Jin et al. They are powerful tools for constructing PKE schemes. In this work, we further demonstrate the power of KC/AKC by proposing two special types of PKE schemes, namely, revocable attribute-based encryption (RABE). To be specific, on the basis of AKC and PKE/KEM protocols submitted to the NIST based on LWE and its variants, combined with full-rank difference, trapdoor on lattices, sampling algorithms, leftover hash lemma, and binary tree structure, we propose two directly revocable ciphertext-policy attribute-based encryption (DR-ABE) schemes from LWE, which support flexible threshold access policies on multivalued attributes, achieving user-level and attribute-level user revocation, respectively. Specifically, the construction of the ciphertext is derived from AKC, and the revocation list is defined and embedded into the ciphertext by the message sender to revoke a user in the user-level revocable scheme or revoke some attributes of a certain user in the attribute-level revocable scheme. We also discuss how to outsource decryption and reduce the workload for the end user. Our schemes proved to be secure in the standard model, assuming the hardness of the LWE problem. The two schemes imply the versatility of KC/AKC.

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The emergence of quantum computing threatens many classical cryptographic schemes, leading to the innovations in public-key cryptography for postquantum cryptography primitives and protocols that resist to quantum attacks. Lattice-based cryptography is considered to be one of the promising mathematical approaches to achieving security resistant to quantum attacks, which could be built on the learning with errors (LWE) problem and its variants. The fundamental building blocks of protocols for public-key encryption (PKE) and key encapsulation mechanism (KEM) submitted to the National Institute of Standards and Technology (NIST) based on LWE and its variants are called key consensus (KC) and asymmetric key consensus (AKC) by Jin et al. They are powerful tools for constructing PKE schemes. In this work, we further demonstrate the power of KC/AKC by proposing two special types of PKE schemes, namely, revocable attribute-based encryption (RABE). To be specific, on the basis of AKC and PKE/KEM protocols submitted to the NIST based on LWE and its variants, combined with full-rank difference, trapdoor on lattices, sampling algorithms, leftover hash lemma, and binary tree structure, we propose two directly revocable ciphertext-policy attribute-based encryption (DR-ABE) schemes from LWE, which support flexible threshold access policies on multivalued attributes, achieving user-level and attribute-level user revocation, respectively. Specifically, the construction of the ciphertext is derived from AKC, and the revocation list is defined and embedded into the ciphertext by the message sender to revoke a user in the user-level revocable scheme or revoke some attributes of a certain user in the attribute-level revocable scheme. We also discuss how to outsource decryption and reduce the workload for the end user. Our schemes proved to be secure in the standard model, assuming the hardness of the LWE problem. The two schemes imply the versatility of KC/AKC.
A revocable identity-based encryption (IBE) scheme under learning with error (LWE) assumption from lattice is proposed; compared with the existing IBE schemes from lattices, two improvements are available in the new scheme. First, the revocation mechanism for identity of user (or thing) is added in the new scheme to manage the dynamic user (or thing) identity in the system, and making the IBE scheme from lattice becomes more practical than ever before. Second, the security of the new scheme is based on the LWE assumption from lattice, so our construction has a solid secure foundation. The scheme is proved to be secured against adaptive-ID attacks under LWE assumption from lattice in the standard model.
Abstract. In view of the expiration or reveal of user’s private credential (or private key) in a real-istic scenario, identity-based encryption (IBE) schemes with an efficient key revocation mechanism, or for short, revocable identity-based encryption (RIBE) schemes, become prominently significant. In this paper, we present an RIBE scheme from lattices by combining two Agrawal et al.’s IBE schemes with the subset difference (SD) method. Our scheme is secure against adaptive identity-time attacks in the standard model under the learning with errors (LWE) assumption. In particular, our scheme serves as one solution to the challenge posed by Chen et al. (ACISP ’12). 1