Lattice-based Encryption Research Articles

Defeating Low-Cost Countermeasures against Side-Channel Attacks in Lattice-based Encryption

In an effort to circumvent the high cost of standard countermeasures against side-channel attacks in post-quantum cryptography, some works have developed low-cost detection-based countermeasures. These countermeasures try to detect maliciously generated input ciphertexts and react to them by discarding the ciphertext or secret key. In this work, we take a look at two previously proposed low-cost countermeasures: the ciphertext sanity check and the decapsulation failure check, and demonstrate successful attacks on these schemes. We show that the first countermeasure can be broken with little to no overhead, while the second countermeasure requires a more elaborate attack strategy that relies on valid chosen ciphertexts. Thus, in this work, we propose the first chosen-ciphertext based side-channel attack that only relies on valid ciphertexts for key recovery. As part of this attack, a third contribution of our paper is an improved solver that retrieves the secret key from linear inequalities constructed using side-channel leakage from the decryption procedure. Our solver is an improvement over the state-of-the-art Belief Propagation solvers by Pessl and Prokop, and later Delvaux. Our method is simpler, easier to understand and has lower computational complexity, while needing less than half the inequalities compared to previous methods.

On Accuracy of Testing Decryption Failure Rate for Encryption Schemes under the LWE Assumption

Lattice-based encryption schemes are significant cryptographic primitives to defend information security against quantum menace, and the decryption failure rate is related to both theoretical and realistic security. We quantitatively analyze how the floating-point arithmetic and neglecting small probabilities impact the precision, and propose a new effective and efficient test of the failure probability. Therein explicit criteria are given to select the floating-point datatype and to decide which small probabilities should be abandoned. Furthermore, the outcome is theoretically ensured to meet a given precision. Moreover, by combining the heuristic estimate and the precise simulation, this test is more efficient than previously neglecting small probabilities in a practical way.

High-order Polynomial Comparison and Masking Lattice-based Encryption

The main protection against side-channel attacks consists in computing every function with multiple shares via the masking countermeasure. For IND-CCA secure lattice-based encryption schemes, the masking of the decryption algorithm requires the high-order computation of a polynomial comparison. In this paper, we describe and evaluate a number of different techniques for such high-order comparison, always with a security proof in the ISW probing model. As an application, we describe the full high-order masking of the NIST standard Kyber, with a concrete implementation on ARM Cortex M architecture, and a t-test evaluation.

A trust based adaptive privacy preserving authentication scheme for VANETs

In vehicular ad hoc networks (VANETs), the exchanged messages among vehicles can effectively improve traffic safety and efficiency. Since the nature of open communication in VANETs, it is necessary to verify the legitimacy of vehicles to prevent illegal vehicles from participating in VANETs. In order to reveal the real identities of malicious vehicles, many conditional privacy preserving authentication schemes have been proposed. While, unconditional privacy preserving is also need for honest vehicles. However, the single conditional or unconditional privacy preserving cannot meet the privacy needs of various vehicles. In this paper, we propose a trust based adaptive privacy preserving authentication scheme. Under the assumption that the external system provides the trust values of vehicles and drivers, the scheme can provide unconditional privacy preserving with different trust levels for high trusted vehicles, while conditional privacy preserving is adopted for low trusted vehicles. In addition, considering the public identities of vehicles and the many-to-many relationship between vehicles and drivers, we introduce a ternary based identity representation method to generate the identities of vehicles, drivers and roadside units. And then, we propose a three entity authentication algorithm to verify the legitimacy of entities. Finally, the formal verification and security analysis are carried out, and the scheme has the characteristics of supervisability and adaptive privacy preserving. Moreover, in order to resist quantum attack, the latest lattice-based encryption and signature algorithms are adopted, and then the computation and communication costs are analyzed in detail.

High-order Table-based Conversion Algorithms and Masking Lattice-based Encryption

Masking is the main countermeasure against side-channel attacks on embedded devices. For cryptographic algorithms that combine Boolean and arithmetic masking, one must therefore convert between the two types of masking, without leaking additional information to the attacker. In this paper we describe a new high-order conversion algorithm between Boolean and arithmetic masking, based on table recomputation, and provably secure in the ISW probing model. We show that our technique is particularly efficient for masking structured LWE encryption schemes such as Kyber and Saber. In particular, for Kyber IND-CPA decryption, we obtain an order of magnitude improvement compared to existing techniques.

A Searchable Encryption Scheme Based on Lattice for Log Systems in燘lockchain

With the increasing popularity of cloud storage, data security on the cloud has become increasingly visible. Searchable encryption has the ability to realize the privacy protection and security of data in the cloud. However, with the continuous development of quantum computing, the standard Public-key Encryption with Keyword Search (PEKS) scheme cannot resist quantum-based keyword guessing attacks. Further, the credibility of the server also poses a significant threat to the security of the retrieval process. This paper proposes a searchable encryption scheme based on lattice cryptography using blockchain to address the above problems. Firstly, we design a lattice-based encryption primitive to resist quantum keyword guessing attacks. Moreover, blockchain is to decentralize the cloud storage platform’s jurisdiction of data. It also ensures that the traceability of keyword retrieval process and maintains the credibility of search result, which malicious platforms are prevented as much as possible from deliberately sending wrong search results. Last but not least, through security analysis, our proposed scheme satisfies the credibility and unforgeability of the keyword ciphertext. The comprehensive performance evaluates that our scheme has certain advantages in terms of efficiency compared with others.

Homomorphic Encryption within Lattice-Based Encryption System

In 2009 a system of fully homomorphic encryption was constructed, in the future, many works were done based on it. In this work, will be performed an analysis of the possibility to use the ideal lattices for constructing homomorphic operations over ciphertexts.This paper represents the analysis of an encryption system based on the primitive of a union in ideal lattices space. The advantage of this approach consists in the possibility of segregated analysis of encryption security and homomorphic properties of the system.The work will be based on the method of analyzing generalized operations over ciphertext using the concept of the base reducing element. It will be shown that some encryption systems can be supplemented by homomorphism between opentext and ciphertext. Thus such systems can be decomposed by encryption and homomorphic parts which would affect each other but although can be analyzed separately. Different systems (probably within one class) can be represented via an identical transform of sets. Separated from the cryptographic scheme the underlying math can be used to analyze only the homomorphic part, particularly under some simplifications. The building of ideal-based ciphertext laying on the assumption that ideals can be extracted further, it will be shown in the paper what the ”remainder theorem” can be one of the principal ways to do this.

A lattice-based searchable encryption scheme with the validity period control of files

In recent years, with the dramatic increase in the use of multimedia data, rapid retrieval and sharing of the multimedia data have become major trends. The validity period control function widely used in daily softwares, which enables multimedia data to be shared from a specific time and revokes the authorization of shared data at another specific time, thereby effectively enhancing the personalized experience of multimedia data users. At the same time, to protect privacy, databases usually store data in an encrypted form and use searchable encryption technology to retrieve keywords on the ciphertext to quickly extract the required multimedia data. However, the existing searchable encryption scheme cannot control the reading of multimedia data by using validity period. To solve this problem, we propose a lattice-based searchable encryption scheme with the validity period control of files. In order that the data owners have flexible and fine-grained control over the files, we convert the time information into a lattice vector for setting a different valid time for each file. Meanwhile, we embed the time information into the ciphertext, so that the data owner only needs to set the validity period once to automatically maintain the life cycle of the files over encrypted data, instead of manually withdrawing each expired file. Furthermore, we combine searchable encryption and time-distance so that our scheme returns valid files only if the keywords match correctly and the search time matches the file’s validity period. This scheme is a candidate for time-controlled searchable encryption technology in the post-quantum era because our scheme constructed on learning with error (LWE) problem which has been proven to resist quantum attacks.

Space-Efficient Key-Policy Attribute-Based Encryption from Lattices and Two-Dimensional Attributes

Linear secret-sharing scheme (LSSS) is a useful tool for supporting flexible access policy in building attribute-based encryption (ABE) schemes. But in lattice-based ABE constructions, there is a subtle security problem in the sense that careless usage of LSSS-based secret sharing over vectors would lead to the leakage of the master secret key. In this paper, we propose a new method that employs LSSS to build lattice-based key-policy attribute-based encryption (KP-ABE) that resolves this security issue. More specifically, no adversary can reconstruct the master secret key since we introduce a new trapdoor generation algorithm to generate a strong trapdoor (instead of a lattice basis), that is, the master secret key, and remove the dependency of the master secret key on the total number of system attributes. Meanwhile, with the purpose of reducing the storage cost and support dynamic updating on attributes, we extended the traditional 1-dimensional attribute structure to 2-dimensional one. This makes our construction remarkably efficient in space cost, with acceptable time cost. Finally, our scheme is proved to be secure in the standard model.

Lattice-Based Cryptoprocessor for CCA-Secure Identity-Based Encryption

In this paper, we propose a lattice-based encryption scheme for Identity-Based Encryption (IBE) which is secure against Chosen-Ciphertext Attacks (CCA), and it is deduced from a previous Chosen-Plaintext Attack (CPA) secure IBE scheme by applying Fujisaki-Okamoto transform. Also, we present the design of a lattice-based cryptoprocessor that performs the encryption or decryption of the proposed CCA IBE scheme for the security parameters $n=512$ and $n=1024$ . In this case, the cryptoprocessor is mainly composed of one Random Number Generator (RNG), two hash function cores based on the Secure Hash Algorithm-3 (SHA-3) standard, and one Number Theoretical Transform (NTT) core for performing the polynomial ring operations. NTT core is designed using a systolic array and radix-2 multiple-path delay commutator architecture. The cryptoprocessor was synthesized on FPGA EP4SGX230KF40C2 using Quartus Prime 17.1, and verified in hardware using DE4 board and SignalTap tool. According to the obtained synthesis results, for the security parameter $n =1024$ , the IBE cryptoprocessor performs the encryption in $21.10~\mu $ s, and the decryption in $24.87~\mu $ s.

A coupled map lattice-based image encryption approach using DNA and bi-objective genetic algorithm

The paper presents a coupled map lattice (CML) and deoxyribonucleic acid (DNA)-based image encryption algorithm that uses genetic algorithm (GA) to get the optimised results. The algorithm uses the chaotic method CML and DNA to create an initial population of DNA masks in its first stage. The GA is applied in the second stage to obtain the best mask for encrypting the given plain image. The paper also discusses the use of two more chaotic functions, i.e., logistic map (LM) and transformed logistic map (TLM) with DNA-GA-based hybrid combination. The paper evaluates and compares the performance of the proposed CML-DNA-GA algorithm with LM-DNA-GA, TLM-DNA-GA hybrid approaches. The results show that the proposed approach performs better than the other two. It also discusses the impact of using a bi-objective GA optimisation for image encryption and applies the same to the all three discussed techniques. The results show that bi-objective optimisation of the proposed algorithm gives balanced results with respect to the selected fitness functions.

On the Security of LWE Cryptosystem against Subversion Attacks

Abstract Subversion of cryptography has received wide attentions especially after the Snowden Revelations in 2013. Most of the currently proposed subversion attacks essentially rely on the freedom of randomness choosing in the cryptographic protocol to hide backdoors embedded in the cryptosystems. Despite the fact that significant progresses in this line of research have been made, most of them mainly considered the classical setting, while the research gap regarding subversion attacks against post-quantum cryptography remains tremendous. Inspired by this observation, we investigate a subversion attack against existing protocol that is proved post-quantum secure. Particularly, we show an efficient way to undetectably subvert the well-known lattice-based encryption scheme proposed by Regev (STOC 2005). Our subversion enables the subverted algorithm to stealthily leak arbitrary messages to the outsider who knows the backdoor. Through theoretical analysis and experimental observations, we demonstrate that the subversion attack against the LWE encryption scheme is feasible and practical.

Modern file transfer protocol using lossless compression, lattice-based encryption, and a data integrity hashing function

With the recent advances in technology, the creation and access to voluminous amounts of data has become more and more common. From consumer computers and smartphones to big data, the transfer of data entailed a longer download and upload time as the size gets bigger, thus taking a significant amount of time for data to reach its destination. Moreover, data can be corrupted as it is being transferred over the network and most file transfer protocols do not have a file integrity check. Lastly, most file transfer protocols employ the RSA cryptosystem which can be broken through the use of a quantum algorithm known as Shor’s algorithm. The proponents have implemented a file transfer protocol that integrates file hashing, compression, and a quantum-resilient cryptosystem. The results show that the proposed file transfer protocol is faster than plain FTP and even faster against FTP over TLS.

Portable Implementation of Postquantum Encryption Schemes and Key Exchange Protocols on JavaScript-Enabled Platforms

Quantum computers have the potential to solve some difficult mathematical problems efficiently and thus will inevitably exert a more significant impact on the traditional asymmetric cryptography. The National Institute of Standards and Technology (NIST) has opened a formal call for the submission of proposals of quantum-resistant public-key cryptographic algorithms to set the next-generation cryptography standards. Compared to powerful machines with ample amount of hardware resources such as racks of servers and IoT devices, including the massive number of microcontrollers, smart terminals, and sensor nodes with limited computing capacity, should also have some postquantum cryptography features for security and privacy. To ensure the correct execution of encryption algorithms on any platforms, the portability of implementation becomes more important. As distinguished from C/C++, JavaScript is a popular cross-platform language that can be used for the web applications and some hardware platforms directly, and it could be one of the solutions of portability. Therefore, we investigate and implement several recent lattice-based encryption schemes and public-key exchange protocols including Lizard, ring-Lizard, Kyber, Frodo, and NewHope in JavaScript, which are the active candidates of postquantum cryptography due to their applicabilities and efficiencies. We show and compare the performance of our JavaScript implementation on web browsers, embedded device Tessel2, Android phone, and several JavaScript-enabled platforms on PC and Mac. Our work shows that implementing lattice-based cryptography on JavaScript-enabled platforms is achievable and results in desirable portability.

Design and Implementation of a Lattice-Based Public-Key Encryption Scheme

Due to its advantage of quantum resistance and the provable security under some worst-case hardness assumptions, lattice-based cryptography is being increasingly researched. This paper tries to explore and present a novel lattice-based public key cryptography and its implementation of circuits. In this paper, the LWE (learning with error) cryptography is designed for circuit realization in a practical way. A strategy is proposed to dramatically reduce the stored public key size from [Formula: see text] to [Formula: see text], with only several additional linear feedback shift registers. The circuit design is implemented on Xilinx Spartan-3A FPGA and performs very well with limited resources. Only 125 slices and 8 BRAMs are occupied, and there are no complex operation devices such as multipliers or dividers, all the involved arithmetic operations are additions. This design is smaller than most hardware implementations of LWE or Ring-LWE cryptography in current state, while having an acceptable frequency at 111 MHz. Therefore, LWE cryptography can be practically realized, and its advantages of quantum resistance and simple implementation make the public key cryptography promising for some applications in devices such as smart cards.

Lattice-based searchable public-key encryption scheme for secure cloud storage

With the improvement of awareness of data privacy, the user's sensitive data are usually encrypted before uploading them to cloud. Searchable encryption is a critical technique on promoting secure and efficient cloud storage. In particular, publickey encryption with keyword search (PEKS) provides an elegant approach to achieve data retrieval in encrypted storage. All existing searchable publickey encryption schemes only provide the security based on classical cryptography hardness assumption. With the development of quantum computers, these schemes will be insecure. Based on the lattice hardness assumptions, we propose a new searchable publickey encryption scheme with a designated tester (dPEKS). Our scheme has advantages: First, our scheme is the first searchable publickey encryption scheme that is considered to be secure even if quantum computers are ever developed. Second, our scheme achieves the trapdoor indistinguishability. The trapdoor indistinguishability implies the security against outside offline keyword guessing attacks (KGAs). Last, our scheme can achieve the trapdoor anonymity for server.

Full secure identity-based encryption scheme over lattices for wireless sensor networks in the standard model

This paper proposes a lattice-based identity-based encryption scheme which can be used in wireless sensor networks to achieve secure communication. More precisely, a known lattice-based chosen plain-text secure encryption scheme and the bonsai trees primitive are used to design an identity-based encryption (IBE) scheme in this paper. To reduce the public key size of the proposed IBE scheme, a public matrices chosen rule is used in this paper which reduces the public key size of proposed scheme to be close to half of that of a known lattice-based scheme. Under the hardness of the decision variant of the learning with errors (LWE) problem, we prove that the proposed IBE scheme is indistinguishable against the adaptive chosen identities and chosen-plaintext attack in the standard model. Moreover, the message-to-ciphtertext expanse factor of this scheme is also controlled efficiently which is nearly closed to that of Gentry's scheme. Due to the quantum intractability of the LWE problem on which the scheme is based, the proposed IBE scheme is secure even in quantum-era.

Lattice-based Dynamical and Anonymous Broadcast Encryption Scheme for Wireless Ad Hoc Networks

A lattice-based broadcast encryption scheme is proposed for ad hoc networks in this paper. The proposed scheme is dynamical and anonymous simultaneously. The achievements of the dynamic and anonymity properties are efficient. In fact, the broadcaster can send the message to any receivers set without any added operations. The anonymity properties of the proposed scheme can protect the identity of an authorized receiver. Both dynamic and anonymity properties are important for broadcast encryption to used in many cases like wireless ad hoc network. The semantic security of the proposed scheme is proven in the standard model under the hardness of the learning with errors problem (LWE). Compared with known lattice-based broadcast encryption schemes, the proposed scheme shares some advantages with respect to the ciphtertext length and the message-ciphtertext expanse factor.

Lattice-based certificateless encryption scheme

Certificateless public key cryptography (CL-PKC) can solve the problems of certificate management in a public key infrastructure (PKI) and of key escrows in identity-based public key cryptography (ID-PKC). In CL-PKC, the key generation center (KGC) does not know the private keys of all users, and their public keys need not be certificated by certification authority (CA). At present, however, most certificateless encryption schemes are based on large integer factorization and discrete logarithms that are not secure in a quantum environment and the computation complexity is high. To solve these problems, we propose a new certificate-less encryption scheme based on lattices, more precisely, using the hardness of the learning with errors (LWE) problem. Compared with schemes based on large integer factorization and discrete logarithms, the most operations are matrixvector multiplication and inner products in our scheme, our approach has lower computation complexity. Our scheme can be proven to be indistinguishability chosen ciphertext attacks (IND-CPA) secure in the random oracle model.

Efficient Chosen-Ciphtertext Secure Public Key Encryption Scheme From Lattice Assumption

Using the Bonsai trees primitive and Gentry's CPA-secure (chosen-p laintext attack) public-key encryption (PKE) scheme, we propose an efficient chosen-ciphtertext secure PKE scheme ove r lattice. If the decision variant of the learning with errors (LWE) problem is hard and the one-time signature used in this scheme is strong unforgeable, the proposed PKE scheme is indistinguishable against the adaptive chosen-ciphtertext attack (IND-CCA2). One of the characters for this scheme is that, before any encryption operation, the encryption algorithm uses a new choice rule to fix the public pa rameter matrixes used in the encryption operation. With the help of this new choice rule, we can achieve the chosen-ciphtertext security with much shorter the public key size in contrast to the lattice-based encryption scheme proposed in STOC'09 by Peikert. M oreover, as a CCA-secure PKE scheme, the message-to- ciphtertext expanse factor of this scheme which is controlled efficiently is n early closed to the message-to-ciphtertext expanse factor of Gentry's scheme which is CPA secure. Due to the quantum intractability of the LWE problem on which the scheme is based, the proposed PKE scheme is secure even in quantum-era.