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Security and Communication Networks

Lattice‐based obfuscation for re‐encryption functions

Rong Cheng, Fangguo Zhang

Published Oct 20, 2014• 2 citations
Publisher

Abstract

Abstract Program obfuscation is a compiler that transfers a program into an unintelligible form while preserving the original functionality. Secure obfuscation for several particular function families has been raised out despite the general impossibility result presented by Barak et al. Re‐encryption function is a useful primitive, which transforms ciphertexts for one party into ciphertexts under another party's public key. Hohenberger et al. constructed a special re‐encryption function and securely obfuscated it in TCC'07, and the security is based on classical hardness assumption. In this paper, we construct a new re‐encryption function and securely obfuscate it based on the standard learning with error (LWE) assumption. LWE is proved to be reducible to standard lattice problems, which are conjectured immune to quantum cryptanalysis or ‘post‐quantum’. Besides, we discuss about the relations between these two cryptographic primitives in detail: proxy re‐encryption and obfuscation for re‐encryption functions. Copyright © 2014 John Wiley & Sons, Ltd.

DOI
10.1002/sec.1112

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Abstract Program obfuscation is a compiler that transfers a program into an unintelligible form while preserving the original functionality. Secure obfuscation for several particular function families has been raised out despite the general impossibility result presented by Barak et al. Re‐encryption function is a useful primitive, which transforms ciphertexts for one party into ciphertexts under another party's public key. Hohenberger et al. constructed a special re‐encryption function and securely obfuscated it in TCC'07, and the security is based on classical hardness assumption. In this paper, we construct a new re‐encryption function and securely obfuscate it based on the standard learning with error (LWE) assumption. LWE is proved to be reducible to standard lattice problems, which are conjectured immune to quantum cryptanalysis or ‘post‐quantum’. Besides, we discuss about the relations between these two cryptographic primitives in detail: proxy re‐encryption and obfuscation for re‐encryption functions. Copyright © 2014 John Wiley & Sons, Ltd.
Abstract Proxy re‐encryption (PRE) is a cryptographic primitive that allows a proxy to turn an Alice's ciphertext into a Bob's ciphertext on the same plaintext. At present, there are many different PRE schemes that have been proposed with different properties. However, all of them are based on the logarithm assumption and the large integer factorization assumption except for a bidirectional PRE scheme over lattices. In this paper, we construct the first multi‐use unidirectional PRE scheme based on lattices. In addition, the generation of the PRE key does not interact with two users, and the scheme can resist collusion attacks. Moreover, it is proved chosen plaintext attack secure in the standard model based on the Learning With Errors assumption. Finally, an identity‐based PRE is obtained from the basic construction. Copyright © 2015 John Wiley & Sons, Ltd.
The proxy re-encryption allows an intermediate proxy to convert a ciphertext for Alice into a ciphertext for Bob without seeing the original message and leaking out relevant information.Unlike many prior identity based proxy re-encryption schemes which are based on the number theoretic assumptions such as large integer factorization and discrete logarithm problem.In this paper, we first propose a novel identity based proxy re-encryption scheme which is based on the hardness of standard Learning With Error(LWE) problem and is CPA secure in the standard model.This scheme can be reduced to the worst-case lattice hard problem that is able to resist attacks from quantum algorithm.The key step in our construction is that the challenger how to answer the private query under a known trapdoor matrix.Our scheme enjoys properties of the non-interactivity, unidirectionality, anonymous and so on.In this paper, we utilize primitives include G-trapdoor for lattice and sample algorithms to realize simple and efficient re-encryption.
As an extension to conditional proxy re-encryption, fuzzy conditional proxy re-encryption allows for a proxy to re-encrypt a ciphertext only if it satisfies some t-out-of-d threshold condition. Therefore, it is more desirable in some applications where fine-grained control of the decryption delegation is required. In this paper, we construct the first lattice-based fuzzy conditional proxy re-encryption scheme as a post-quantum alternative to this primitive. In our construction, original ciphertexts and re-encryption ciphertexts have the same form, thus only one decryption algorithm is needed for both kinds of ciphertexts. We formalize its security model and prove that it is selective secure under the LWE assumption.
SUMMARY Signcryption is a cryptographic primitive that performs simultaneously both the functions of digital signature and public‐key encryption, at a cost significantly lower than that required by the traditional signature‐ then‐encryption approach. In this paper, we provide a positive answer to the question of if it is possible to construct signcryption based on lattice problems. More precisely, we design an efficient signcryption scheme that can send a message of length l one time. We prove that the proposed scheme has the indistinguishability against adaptive chosen ciphertext attacks under the learning with errors assumption and strong unforgeability against adaptive chosen messages attacks under the inhomogeneous small integer solution assumption in the random oracle model. Copyright © 2012 John Wiley & Sons, Ltd.
Proxy re-encryption (PRE) is an important cryptographic primitive used for private information sharing. However, the recent advance in quantum computer has potentially crippled its security, as the traditional decisional Diffie-Hellman (DDH)-based PRE is venerable to the quantum attack. Thus, learning with errors (LWE)-based PRE schemes, as a kind of latticebased construction with the inherent quantum-resistant property, has attracted special research interest. Unfortunately, the main drawback of lattice-based public key encryption scheme is noise management after multiplication evaluation. Many cryptographers have been devoted to controlling the expansion of noise. In this line of work, Dagdelen-Gajek-G̈opfert (DGG) put forth the notion of learning with errors in the exponent (LWEE) which is based on lattice and group-theoretic assumption, meanwhile demonstrated a paradigm for constructing efficient quantum resistance public key schemes. In this paper, on top of DGG, we construct a single-bit, single-hop and unidirectional LWEE- based PRE scheme with indistinguishable chosen plaintext attack (IND-CPA) security. To the best of our knowledge, our scheme is the first LWEE-based PRE scheme.
Proxy Re-encryption (PRE) is a useful cryptographic structure who enables a semi-trusted proxy to convert a ciphertext for Alice into a ciphertext for Bob without seeing the corresponding plaintext. Although there are many PRE schemes in recent years, few of them are set up based on lattice. Not only this, these lattice-based PRE schemes are all more complicated than the traditional PRE schemes. In this paper, through the study of the common lattice problems such as the Small integer solution (SIS) and the Learning with Errors (LWE), we analyze the feasibility of efficient lattice-based PRE scheme combined with the previous results. Finally, we propose an efficient lattice-based PRE scheme L-PRE without losing the hardness of lattice problems.