Learning With Errors Research Articles

Fully collusion resistant trace-and-revoke functional encryption for arbitrary identities

Functional Encryption (FE) has been extensively studied in the recent years, mainly focusing on the feasibility of constructing FE for general functionalities, as well as some realizations for restricted functionalities of practical interest, such as inner-product. However, little consideration has been given to the issue of key leakage on FE. The property of FE that allows multiple users to obtain the same functional keys from the holder of the master secret key raises an important problem: if some users leak their keys or collude to create a pirate decoder, how can we identify at least one of those users, given some information about the compromised keys or the pirate decoder? Moreover, how do we disable the decryption capabilities of those users (i.e. traitors)?Two recent works have offered potential solutions to the above traitor scenario. However, the two solutions satisfy weaker notions of security and traceability, can only tolerate bounded collusions (i.e., there is an a priori bound on the number of keys the pirate decoder obtains), or can only handle a polynomially large universe of possible identities. In this paper, we study trace-and-revoke mechanism on FE and provide the first construction of trace-and-revoke FE that supports arbitrary identities, is both fully collusion resistant and fully anonymous. Our construction relies on a generic transformation from revocable predicate functional encryption with broadcast (RPFE with broadcast, which is an extension of revocable predicate encryption with broadcast proposed by Kim and J. Wu at ASIACRYPT'2020) to trace-and-revoke FE. Since this construction admits a generic construction of trace-and-revoke inner-product FE (IPFE), we instantiate the trace-and-revoke IPFE from the well-studied Learning with Errors (LWE). This is achieved by proposing a new LWE-based attribute-based IPFE (ABIPFE) scheme to instantiate RPFE with broadcast.

From learning with errors (LWE) problem to CLWE problem

The main purpose of this paper is to introduce the learning with errors problem on cyclic algebras, i.e., the CLWE problem, and to fully discuss and utilize the well-proven LWE-related conclusions and assumptions in cryptography theory. Firstly, this paper provides the basic framework of Learning with Errors (LWE) problems for cyclic algebra samples. Then lattices generated by the two-sided ideal of cyclic algebra with natural order are applied to cryptography. Based on the above contents, the so-called CLWE problem is introduced to point out the dimensions and structures suitable for constructing cryptographic systems for explicit algebra, and the security of corroding problems is discussed in the CLWE samples. Finally, this paper also discusses some possible future research directions, some natural routes to further research the construction and application of CLWE problems, for example, how to choose parameters for a specific security level, so as to offer some references for future study.

Revocable-Attribute-Based Encryption with En-DKER from Lattices

Cloud computing offers abundant computing resources and scalable storage, but data leakage in the cloud storage environment is a common and critical concern due to inadequate protection measures. Revocable-attribute-based encryption (RABE) is introduced as an advanced form of identity-based encryption (IBE), which encrypts sensitive data while providing fine-grained access control and an effective user revocation mechanism. However, most existing RABE schemes are not resistant to quantum attacks and are limited in their application scenarios due to the revocation model. In this paper, we propose a RABE scheme constructed from lattices. Our scheme has several advantages, including a near-zero periodic workload for the key generation center (KGC), ensuring scalability as the number of users increases. Additionally, the encryptor is relieved from managing a revocation list. Moreover, our scheme guarantees the confidentiality and privacy of other ciphertexts even if the decryption key for a specific period is compromised. We validated the correctness of our scheme and demonstrated its security under the assumption of learning with errors (LWE), which is widely believed to be resistant to quantum attacks. Finally, we provide an application example of our RABE scheme in the electronic healthcare scenario.

HRA-secure attribute-based threshold proxy re-encryption from lattices

Proxy re-encryption (PRE) allows a semi-trust proxy with a re-encryption key to transform a ciphertext encrypted under one key to an encryption of the same message under another key. Attribute-based proxy re-encryption (AB-PRE) is a generalization of PRE which enables fine-grained access control and delegation of encrypted data. However, traditional AB-PRE suffers from the single point of failure as it relies on a single proxy to perform ciphertext transformations. To resolve this problem, this paper introduces a new primitive called attribute-based threshold proxy re-encryption (AB-TPRE), that utilizes multiple (N) proxies for the transformations. In AB-TPRE, the re-encryption key is split into N shares, with each proxy receiving one share to generate a transformed ciphertext share. Only when a threshold (t) number of transformed ciphertext shares are combined can the transformed ciphertext be correctly generated. Furthermore, to address the security risk of shares leakage, we introduce a share updatable property that allows the re-encryption key shares to be refreshed. We propose a construction of AB-TPRE from lattices, and prove its security against the honest re-encryption attacks under the learning with errors (LWE) assumption, which is assumed to be quantum secure since up to now there is no known quantum algorithm to solve LWE in polynomial time.

Post‐quantum secure two‐party computing protocols against malicious adversaries

SummarySecure two‐party computation allows a pair of parties to compute a function together while keeping their inputs private. Ultimately, each party receives only its own correct output. In this paper, a post‐quantum secure two‐party computation protocol is proposed that can be used to effectively block malicious parties. The protocol solves the problems of traditional protocols based on garbled circuits, which are vulnerable to quantum attacks, high communication costs and low computational efficiency. The input garbled keys of the circuit constructor is structured as a Learning with Error (LWE) equation, enabling the circuit constructor to employ a zero‐knowledge proof that demonstrates the uniformity of inputs across all circuits.In the key transfer phase, an LWE‐based batch single‐choice cut‐and‐choose oblivious transfer is proposed to avoid selective failure attacks. In addition, the protocol employs a penalty mechanism to detect if the circuit constructor has generated an incorrect circuit. We have compared the communication overhead of this protocol with three other secure two‐party computation protocols based on Cut‐and‐Choose technology. The analytical results show that this protocol has the best error probability and is resilient to quantum attacks under the malicious adversary model. In addition, with appropriate parameters, the protocol is able to reduce its communication bandwidth by an average of 40.41%.

KDM Security IBE Based on LWE beyond Affine Functions

Key-dependent message (KDM) security identity-based encryption (IBE) schemes aim to solve the security risks caused by the dependency between plaintext and secret keys in traditional IBE schemes. However, current KDM-IBE schemes are only secure with respect to affine functions, which limits their security level when a message is derived from the evaluation of a polynomial function using the secret key. To address this issue, in this study, we propose a novel approach to construct a KDM-IBE scheme with respect to polynomial or even arbitrary functions that achieves maximum security based on the learning with errors (LWE) assumption. Our approach overcomes two major technical barriers to constructing KDM-IBE schemes with respect to polynomial functions. Compared to existing KDM-IBE schemes, our proposed scheme ensures the secrecy of the key-related plaintext, even when it is obtained using arbitrary functions, not just affine functions. Thus, our approach provides a more robust solution to the security risks inherent in traditional IBE schemes.

A CP-ABE Scheme Based on Lattice LWE and Its Security Analysis

In recent years, the research on ciphertext-policy attribute-based encryption (CP-ABE) scheme design based on learning with errors (LWE) has been a challenging problem, and many researchers have made a lot of attempts at it. At EUROCRYPT 2021, Datta, Komargodski, and Waters proposed the first provably secure direct CP-ABE construction that supports NC1 circuit access structures. Improving on their work, we propose a CP-ABE scheme. Technically, we use the new lattice two-stage sampling technique of Lai, Liu, and Wang (EUROCRYPT 2021) in the key generation phase instead of the extended trapdoor sampling technique. In this way, we obtain a CP-ABE scheme, which is at least as secure as the original scheme under the same conditions, and has a shorter ciphertext; we provide an innovative design idea for designing CP-ABE schemes only based on LWE, although this is only a partial theoretical work.

Privacy-Preserving Multi-Source Image Retrieval in Edge Computing

Users outsource images to edge servers physically closer to their location for real time applications because of the low latency and low transmission overhead. Outsourcing to these edge servers however, increases the risks to data privacy. Almost all existing privacy preserving image retrieval schemes utilize a single cloud server to execute retrieval tasks and provide centralized image retrieval but at high computational costs, thus are not suitable for the distributed edge environments with limited computing resources. We propose a lightweight privacy-preserving multi-source image retrieval scheme adapted specifically for the distributed edge environment. We apply high efficiency orthogonal decomposition and learning with errors (LWE) strategy to encrypt image features and construct cipher indexes and trapdoors, guaranteeing the security of the data, while reducing computational costs. The orthogonality of data ensures that the accuracy of retrieval results is not compromised by the random numbers used in the scheme. In addition, the proxy re-encryption technology is adopted to support the retrieval of multi-source images encrypted by unique data owners with different keys. A detailed performance analysis and comprehensive experiments demonstrate that our scheme guarantees data security with very high retrieval accuracy and a low computational burden, consistent with the demands of edge environments.

An Efficient Identity-Based Encryption With Equality Test in Cloud Computing

Identity-based encryption with equality test (IBEET) provides a feasible way for cloud server partitioning or searching on ciphertexts in the cloud. In that case, the server can judge if two different ciphertexts encrypt the same plaintexts or not. In response to threats posed by quantum computers, lattice-based IBEET schemes have been proposed to make cloud service post-quantum secure. However, those schemes are inefficient and can hardly meet the needs of resource-constrained devices. In this paper, an efficient post-quantum IBEET scheme is introduced, which achieves testability by embedding the hash value of plaintext into testing trapdoor instead of encrypting it directly and doubling the size of ciphertext. We also prove that, with the Learning With Errors (LWE) problem assumption, the new scheme is one-way secure against selective identity and chosen ciphertext attacks (OW-sID-CCA) in quantum secure model. Furthermore, we evaluate the performance of the new construction and demonstrate its efficiency by showing that it only costs about half storage comparing with other lattice-based IBEET schemes. The execution time of encryption and decryption phrases in the new scheme reduce by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$50\%$</tex-math></inline-formula> , while the computational cost in test algorithm keeps the same. Therefore, the new proposed IBEET is much more practical for working in post-quantum cloud computing scenarios.

Efficient matrix key homomorphic encryption of medical images

A sure way of providing privacy to sensitive images is to encrypt them, especially when they are stored in a public cloud server. Homomorphic encryption enables arithmetic operations over encrypted data without access to the secret key. This facility can be well harnessed for secure outsourced image processing by exploiting the available computational capabilities of modern cloud servers. This paper presents a new homomorphic image encryption scheme that uses integer matrix keys. The homomorphic operations are carried out in the finite field Zp to avail the advantages of integer arithmetic and to limit the cipher text sizes to reasonable levels. Our method does not use any error vector as in learning with errors (LWE) to improve the security.

Lattices-Inspired CP-ABE from LWE Scheme for Data Access and Sharing Based on Blockchain

To address the quantum attacks on number theory-based ciphertext policy attribute-based encryption (CP-ABE), and to avoid private key leakage problems by relying on a trustworthy central authority, we propose a lattice-inspired CP-ABE scheme for data access and sharing based on blockchain in this paper. Firstly, a CP-ABE-based algorithm using learning with errors (LWE) assumption is constructed, which is selective security under linear independence restriction in the random oracle model. Secondly, the blockchain nodes can act as a distributed key management server to offer control over master keys used to generate private keys for different data users that reflect their attributes through launching transactions on the blockchain system. Finally, we develop smart contracts for proving the correctness of proxy re-encryption (PRE) and provide auditability for the whole data-sharing process. Compared with the traditional CP-ABE algorithm, the post-quantum CP-ABE algorithm can significantly improve the computation speed according to the result of the functional and experimental analysis. Moreover, the proposed blockchain-based CP-ABE scheme provides not only multi-cryptography collaboration to enhance the security of data access and sharing but also reduces average transaction response time and throughput.

Extending quantum key distribution through proxy re-encryption

Modern quantum key distribution (QKD) network designs are based on sending photons from one node to another and require free-space or dedicated fiber optic cables between nodes. The purpose of this is to co-generate secret key material on both sides of the quantum channel. In addition to this quantum link, there are several insecure classical channels that allow QKD algorithms to exchange book-keeping information and send symmetrically encrypted data. The attenuation of photons transmitted through fiber becomes too high to practically generate key material over fiber at distances of more than 100 km. Free-space transmission through the atmosphere or the vacuum of space can reduce attenuation, but at the cost of system complexity and sensitivity to other impairments, such as weather. To extend the effective range of QKD networks, we present a method that combines QKD algorithms with post-quantum, homomorphic key-switching to allow multiple parties to effectively share secret key material over longer distances through semi-trusted relay nodes. We define how such a system should work for arbitrary network topologies and provide proofs that our scheme is both correct and secure. We assess the feasibility of this solution by building and evaluating two implementations based on lattice-based cryptography: learning with errors.

Attribute-Based Verifiable Conditional Proxy Re-Encryption Scheme.

There are mostly semi-honest agents in cloud computing, so agents may perform unreliable calculations during the actual execution process. In this paper, an attribute-based verifiable conditional proxy re-encryption (AB-VCPRE) scheme using a homomorphic signature is proposed to solve the problem that the current attribute-based conditional proxy re-encryption (AB-CPRE) algorithm cannot detect the illegal behavior of the agent. The scheme implements robustness, that is the re-encryption ciphertext, can be verified by the verification server, showing that the received ciphertext is correctly converted by the agent from the original ciphertext, thus, meaning that illegal activities of agents can be effectively detected. In addition, the article demonstrates the reliability of the constructed AB-VCPRE scheme validation in the standard model, and proves that the scheme satisfies CPA security in the selective security model based on the learning with errors (LWE) assumption.

Inner product encryption from Middle-Product Learning With Errors

Inner product encryption (IPE) is an important research area of functional cryptosystems. It can improve user access control and fine-grained query, and has a wide range of applications in emerging fields such as cloud computing. Lattice-based inner product encryption has the advantages of resistance to quantum algorithm attacks and relatively simple encryption algorithms, and thus has good application prospects. Currently, the provable security of lattice-based public key encryption schemes is mostly based on the learning with errors (LWE) and polynomial learning with errors (PLWE) problems. However, most of the encryption schemes based on LWE problems suffer from the problem of oversized public keys and ciphers. Although encryption schemes based on the PLWE problem further reduce the size, their hardness is limited by polynomials and the security guarantees are weakened. Compared with the LWE and PLWE problems, the Middle-Product Learning With Errors (MP-LWE) problem relaxes the polynomial restriction and makes full use of the polynomial features to achieve a better balance between security and efficiency. Inspired by this, we have proposed the inner product encryption scheme of Sel-IND-CPA-secure in SocialSec 2022. In this paper, to extend the existing work and improve the functionality of IPE, we construct single-input and multi-input inner product encryption schemes of Ad-IND-CPA-secure, and also evaluate the efficiency of the schemes.

A reduction from an LWE problem to maximum independent set problems

The learning with errors (LWE) problem is a problem derived from machine learning that is believed to be intractable for quantum computers. This paper proposes a method that can reduce an LWE problem to a set of maximum independent set (MIS) problems, which are graph problems that are suitable for a quantum annealing machine to solve. The reduction algorithm can reduce an n-dimensional LWE problem to several small MIS problems with at most 2^{O(sqrt{n})} nodes when the lattice-reduction algorithm used in the LWE-reduction method successfully finds short vectors. The algorithm is useful for solving LWE problems in a quantum-classical hybrid manner by using an existing quantum algorithm to solve the MIS problems. For example, the smallest LWE challenge problem is reduced to MIS problems with about 40,000 vertices. This result means that the smallest LWE challenge problem will be within the scope of a real quantum computer in the near future.

Multi-key Fully Homomorphic Encryption without CRS from RLWE

Fully Homomorphic Encryption (FHE) is a powerful encryption system in cloud computing that allows homomorphic computations on encrypted data without decrypting them. Multi-key fully homomorphic encryption (MFHE), as an extension to FHE, allows homomorphic computations on ciphertexts encrypted under different keys. However, most MFHE schemes require a Common Random/Reference String (CRS), while the few that do not are based on the Learning With Errors (LWE) problem, which means that they can only deal with single bit plaintext. Consequently, MFHE schemes based on the Ring Learning With Errors (RLWE) problem are more desirable, as they can handle polynomial plaintext. Requiring the CRS seems to weaken the semantic definition of MFHE, where all users generate their own keys independently. In this paper, we study the RLWE-based MFHE in the CRS model and propose the first RLWE-based MFHE without a CRS. To this end, we remove the CRS by designing a relinearization algorithm without a CRS. Like previous MFHE schemes, our RLWE-based MFHE without CRS has a simple 1-round threshold decryption, which implies a 3-round secure MPC protocol in the plain model from the RLWE assumption.

A Provably Secure Strong PUF Based on LWE: Construction and Implementation

We construct a strong physical unclonable function (PUF) with provable security against machine learning (ML) attacks on both classical and quantum computers. The security is guaranteed by the cryptographic hardness of learning decryption functions of public-key cryptosystems, and the hardness of the learning-with-errors (LWE) problem defined on integer lattices. We call our construction the lattice PUF. We construct lattice PUF with a physically obfuscated key and an LWE decryption function block. To allow deployments in different scenarios, we demonstrate designs with different latency-area trade-offs. A compact design uses a highly serialized linear-feedback shift register (LFSR) and LWE decryption function, while a latency-optimized design uses an unrolled LFSR and a parallel datapath. We prototype lattice PUF designs with <inline-formula><tex-math notation="LaTeX">$2^{136}$</tex-math></inline-formula> challenge-response pairs (CRPs) on a spartan 6 field-programmable gate array (FPGA). In addition to theoretical security guarantee, we evaluate empirical resistance to the various leading ML techniques: the prediction error remains above <inline-formula><tex-math notation="LaTeX">$49.76\%$</tex-math></inline-formula> after 1 million training CRPs. The resource-efficient design requires only 45 slices for PUF logic proper, and 27 slices for reverse fuzzy extractor. The latency-optimized design achieves a <inline-formula><tex-math notation="LaTeX">$148X$</tex-math></inline-formula> reduction in latency, at a <inline-formula><tex-math notation="LaTeX">$10X$</tex-math></inline-formula> increase in PUF hardware utilization. The mean uniformity of PUF responses is <inline-formula><tex-math notation="LaTeX">$49.98\%$</tex-math></inline-formula> , the mean uniqueness is <inline-formula><tex-math notation="LaTeX">$50.00\%$</tex-math></inline-formula> , and the mean reliability is <inline-formula><tex-math notation="LaTeX">$1.26\%$</tex-math></inline-formula> .

LWR-based Quantum-Safe Pseudo-Random Number Generator

Learning with Rounding (LWR) is a lattice-based cryptographically hard problem which quantum computers find difficult to solve. LWR problem is a derandomized variant of Learning with Errors (LWE) where deterministic rounding is used to generate errors efficiently. LWR can construct a secure seed for Quantum-Safe Pseudo-Random Number Generator (QSPRNG). This study is an endeavor to construct a QSPRNG to generate a stream of pseudo-random bits through a Linear Feedback Shift Register (LFSR). The proposed QSPRNG uses secure seed as an input and a Homomorphic Function for preserving the security of the internal states of LFSRs. NIST statistical tests, ENT, and DIEHARD tests are performed on constructed PRNG for randomness analysis. Also, security and speed analysis for the proposed QSPRNG has been done to illustrate its possible future utilization in cryptography.

Computational fuzzy extractor from LWE

Fuzzy extractors are able to derive uniform and stable strings from noisy sources. Traditional fuzzy extractors are defined as information-theoretical primitive. Unfortunately, the components of information-theoretical fuzzy extractors consume the entropy of the sources, which results in extracted strings being too short to be applied in practice. Fuller et al. introduced the notion of Computational Fuzzy Extractor (CFE) and proposed a CFE scheme, which extracts nearly all entropy from the sources, based on the Learning with Errors (LWE) assumption. However, their construction applies to a limited type of sources and only supports sub-linear error correctness rate. In this paper, we propose a generic construction of CFE from Computationally Private Secure Sketch (CPSS) and Lossy Computational Extractor (LCExt). By instantiating CPSS and LCExt based on the LWE assumption, we obtain specific CFE schemes from LWE. Compared with the CFE scheme by Fuller et al., our CFE scheme not only extracts almost all entropy from the source, but also supports linear error correctness rate, as long as the source has enough entropy.

Attribute-Based Authentication Scheme from Partial Encryption for Lattice with Short Key

Wireless network is the basis of the Internet of things and the intelligent vehicle Internet. Due to the complexity of the Internet of things and intelligent vehicle Internet environment, the nodes of the Internet of things and the intelligent vehicle Internet are more vulnerable to malicious destruction and attacks. Most of the proposed authentication and key agreement protocols for wireless networks are based on traditional cryptosystems such as large integer decomposition and elliptic curves. With the rapid development of quantum computing, these authentication protocols based on traditional cryptography will be more and more threatened, so it is necessary to design some authentication and key agreement protocols that can resist quantum attacks. In this paper, an anti-quantum authentication scheme for wireless networks based on lattice cryptosystem is constructed. In the attribute-based authentication scheme, the length of the authenticated public-private key pair depends on the maximum order and complexity of the formula in the algorithm. In the attribute-based authentication scheme, there is a certain correlation between the authenticated data and the attribute value of the user in the scheme. We show that the attribute-based authentication scheme gives an attribute-based with smaller public-private key pairs. The security of the attribute-based authentication scheme is based on the sub-exponential hard problem of the LWE (Learning With Errors). The Q-poly made by the adversary in the scheme, and our attribute-based authentication scheme guarantees that private data about user attributes and ciphertext cannot be obtained by malicious attackers.