Biblio

With the ever-increasing use of large-scale IoT networks in different sectors of the industry, it has become critical to realise seamless and secure communication between devices in the network. Realising secure group communication in the IoT requires solving the problem of group-key establishment. In this work, we solve the problem by designing a new lattice-based Key Encapsulation Mechanism (KEM) for resource-constrained devices that enable the distribution of a symmetric key or any other data between all the devices in a given network. This is achieved by coupling multiple private keys to a unique public key. Moreover, we present a proof-of-concept implementation based on the GGH algorithm. The results show it is feasible to use lattice-based cryptography to allow for seamless and secure group communications within a decentralised IoT network. It has been bench-marked against other common post-quantum constructs and proven to be more practical with respect to memory consumption and security, although considerably slower due to lack of optimisation in the implementation.

Blockchain as a tamper-proof, non-modifiable and traceable distributed ledger technology has received extensive attention. Although blockchain's immutability provides security guarantee, it prevents the development of new blockchain technology. As we think, there are several arguments to prefer a controlled modifiable blockchain, from the possibility to cancel the transaction and necessity to remove the illicit or harmful documents, to the ability to support the scalability of blockchain. Meanwhile, the rapid development of quantum technology has made the establishment of post-quantum cryptosystems an urgent need. In this paper, we put forward the first lattice-based redactable consortium blockchain scheme that makes it possible to rewrite or repeal the content of any blocks. Our approach uses a consensus-based election and lattice-based chameleon hash function (Cash and Hofheinz etc. EUROCRYPT 2010). With knowledge of secret trapdoor, the participant could find the hash collisions efficiently. And each member of the consortium blockchain has the right to edit the history.

Lattice-based Attribute-based encryption is a well-known cryptographic mechanism that can resist quantum attacks and has the ability of fine-grained access control, and it has a wide range of application scenarios in current Internet of Thing (IoT) era. However, lack of efficiency and existing the problem of large ciphertext expansion rate are the main disadvantages impede the applications of this mechanism. Thus, we propose an efficient and practical ciphertext policy attribute-based encryption (CP-ABE) scheme from lattices in the paper. In this scheme, to make the secret key reusable, we adjust access tree and propose a basic access tree structure, which can be converted from disjunctive normal form, and combine it with a light post-quantum scheme of Kyber. In addition, the compression method and plaintext expansion method are introduced to optimize the scheme. Our CP-ABE scheme is secure against chosen plaintext attack under the hardness of module learning with errors problem. We implement our scheme and compare it with three recent related schemes in terms of security, function and communication cost. Experiments and comparisons show that our CP-ABE scheme has advantages in high encryption efficiency, small matrix dimension, small key sizes, and low ciphertext expansion rate, which has some merit in practice.

The security of lattice-based cryptosystems that are secure for the post-quantum period is based on the difficulty of the shortest vector problem (SVP) and the closest vector problem (CVP). In the literature, many sieving algorithms are proposed to solve these hard problems. In this paper, efficient implementation of HashSieve sieving algorithm is discussed. A modular software library to have an efficient implementation of HashSieve algorithm is developed. Modular software library is used as an infrastructure in order for the HashSieve efficient implementation to be better than the sample in the literature (Laarhoven's standard HashSieve implementation). According to the experimental results, it is observed that HashSieve efficient implementation has a better running time than the example in the literature. It is concluded that both implementations are close to each other in terms of the memory space used.

Public key encryption with equality test (PKEET) enables the testing whether two ciphertexts encrypt the same message. Identity-based encryption with equality test (IBEET) simplify the certificate management of PKEET, which leads to many potential applications such as in smart city applications or Wireless Body Area Networks. Lee et al. (ePrint 2016) proposed a generic construction of IBEET scheme in the standard model utilising a 3-level hierachy IBE together with a one-time signature scheme, which can be instantiated in lattice setting. Duong et al. (ProvSec 2019) proposed the first direct construction of IBEET in standard model from lattices. However, their scheme achieve CPA security only. In this paper, we improve the Duong et al.'s construction by proposing an IBEET in standard model which achieves CCA2 security and with smaller ciphertext and public key size.

An ideal lattice is defined over a ring learning with errors (Ring-LWE) problem. Polynomial multiplication over the ring is the most computational and time-consuming block in lattice-based cryptography. This paper presents the first hardware design of the polynomial multiplication for LAC, one of the Round-2 candidates of the NIST PQC Standardization Process, which has byte-level modulus p=251. The proposed architecture supports polynomial multiplications for different degree n (n=512/1024/2048). For designing the scheme, we used the Vivado HLS compiler, a high-level synthesis based hardware design methodology, which is able to optimize software algorithms into actual hardware products. The design of the scheme takes 274/280/291 FFs and 204/217/208 LUTs on the Xilinx Artix-7 family FPGA, requested by NIST PQC competition for hardware implementation. Multiplication core uses only 1/1/2 pieces of 18Kb BRAMs, 1/1/1 DSPs, and 90/94/95 slices on the board. Our timing result achieved in an alternative degree n with 5.052/4.3985/5.133ns.

In this work, we will present a new hybrid cryptography method based on two hard problems: 1- The problem of the discrete logarithm on an elliptic curve defined on a finite local ring. 2- The closest vector problem in lattice and the conjugate problem on square matrices. At first, we will make the exchange of keys to the Diffie-Hellman. The encryption of a message is done with a bad basis of a lattice.

Access authentication is a key technology to identify the legitimacy of mobile users when accessing the space-ground integrated networks (SGIN). A hierarchical identity-based signature over lattice (L-HIBS) based mobile access authentication mechanism is proposed to settle the insufficiencies of existing access authentication methods in SGIN such as high computational complexity, large authentication delay and no-resistance to quantum attack. Firstly, the idea of hierarchical identity-based cryptography is introduced according to hierarchical distribution of nodes in SGIN, and a hierarchical access authentication architecture is built. Secondly, a new L-HIBS scheme is constructed based on the Small Integer Solution (SIS) problem to support the hierarchical identity-based cryptography. Thirdly, a mobile access authentication protocol that supports bidirectional authentication and shared session key exchange is designed with the aforementioned L-HIBS scheme. Results of theoretical analysis and simulation experiments suggest that the L-HIBS scheme possesses strong unforgeability of selecting identity and adaptive selection messages under the standard security model, and the authentication protocol has smaller computational overhead and shorter private keys and shorter signature compared to given baseline protocols.

The impending realization of scalable quantum computers will have a significant impact on today's security infrastructure. With the advent of powerful quantum computers public key cryptographic schemes will become vulnerable to Shor's quantum algorithm, undermining the security current communications systems. Post-quantum (or quantum-resistant) cryptography is an active research area, endeavoring to develop novel and quantum resistant public key cryptography. Amongst the various classes of quantum-resistant cryptography schemes, lattice-based cryptography is emerging as one of the most viable options. Its efficient implementation on software and on commodity hardware has already been shown to compete and even excel the performance of current classical security public-key schemes. This work discusses the next step in terms of their practical deployment, i.e., addressing the physical security of lattice-based cryptographic implementations. We survey the state-of-the-art in terms of side channel attacks (SCA), both invasive and passive attacks, and proposed countermeasures. Although the weaknesses exposed have led to countermeasures for these schemes, the cost, practicality and effectiveness of these on multiple implementation platforms, however, remains under-studied.

Symbolic methods have been used extensively for proving security of cryptographic protocols in the Dolev-Yao model, and more recently for proving security of cryptographic primitives and constructions in the computational model. However, existing methods for proving security of cryptographic constructions in the computational model often require significant expertise and interaction, or are fairly limited in scope and expressivity. This paper introduces a symbolic approach for proving security of cryptographic constructions based on the Learning With Errors assumption (Regev, STOC 2005). Such constructions are instances of lattice-based cryptography and are extremely important due to their potential role in post-quantum cryptography. Following (Barthe, Grégoire and Schmidt, CCS 2015), our approach combines a computational logic and deducibility problems—a standard tool for representing the adversary's knowledge, the Dolev-Yao model. The computational logic is used to capture (indistinguishability-based) security notions and drive the security proofs whereas deducibility problems are used as side-conditions to control that rules of the logic are applied correctly. We then use AutoLWE, an implementation of the logic, to deliver very short or even automatic proofs of several emblematic constructions, including CPA-PKE (Gentry et al., STOC 2008), (Hierarchical) Identity-Based Encryption (Agrawal et al. Eurocrypt 2010), Inner Product Encryption (Agrawal et al. Asiacrypt 2011), CCA-PKE (Micciancio et al., Eurocrypt 2012). The main technical novelty beyond AutoLWE is a set of (semi-)decision procedures for deducibility problems, using extensions of Gröbner basis computations for subalgebras in the (non-)commutative setting (instead of ideals in the commutative setting). Our procedures cover the theory of matrices, which is required for lattice-based assumption, as well as the theory of non-commutative rings, fields, and Diffie-Hellman exponentiation, in its standard, bilinear and multilinear forms. Additionally, AutoLWE supports oracle-relative assumptions, which are used specifically to apply (advanced forms of) the Leftover Hash Lemma, an information-theoretical tool widely used in lattice-based proofs.

We report on our implementation of a new Gaussian sampling algorithm for lattice trapdoors. Lattice trapdoors are used in a wide array of lattice-based cryptographic schemes including digital signatures, attributed-based encryption, program obfuscation and others. Our implementation provides Gaussian sampling for trapdoor lattices with prime moduli, and supports both single- and multi-threaded execution. We experimentally evaluate our implementation through its use in the GPV hash-and-sign digital signature scheme as a benchmark. We compare our design and implementation with prior work reported in the literature. The evaluation shows that our implementation 1) has smaller space requirements and faster runtime, 2) does not require multi-precision floating-point arithmetic, and 3) can be used for a broader range of cryptographic primitives than previous implementations.

Internet of Thing (IoT) provide services by linking the different platform devices. They have the limitation in providing intelligent service. The IoT devices are heterogeneous which includes wireless sensors to less resource constrained devices. These devices are prone to hardware/software and network attacks. If not properly secured, it may lead to security issues like privacy and confidentiality. To resolve the above problem, an Intelligent Security Framework for IoT Devices is proposed in this paper. The proposed method is made up of (1) the light weight Asymmetric cryptography for securing the End-To-End devices which protects the IoT service gateway and the low power sensor nodes and (2) implements Lattice-based cryptography for securing the Broker devices/Gateway and the cloud services. The proposed architecture implements Asymmetric Key Encryption to share session key between the nodes and then uses this session key for message transfer This protects the system from Distributed Denial of Service Attacks, eavesdropping and Quantum algorithm attacks. The proposed protocol uses the unique Device ID of the sensors to generate key pair to establish mutual authentication between Devices and Services. Finally, the Mutual authentication mechanism is implemented in the gateway.

This work describes the design, implementation, and evaluation of Λολ, a general-purpose software framework for lattice-based cryptography. The Λολ framework has several novel properties that distinguish it from prior implementations of lattice cryptosystems, including the following. Generality, modularity, concision: Λολ defines a collection of general, highly composable interfaces for mathematical operations used across lattice cryptography, allowing for a wide variety of schemes to be expressed very naturally and at a high level of abstraction. For example, we implement an advanced fully homomorphic encryption (FHE) scheme in as few as 2–5 lines of code per feature, via code that very closely matches the scheme's mathematical definition. Theory affinity: Λολ is designed from the ground-up around the specialized ring representations, fast algorithms, and worst-case hardness proofs that have been developed for the Ring-LWE problem and its cryptographic applications. In particular, it implements fast algorithms for sampling from theory-recommended error distributions over arbitrary cyclotomic rings, and provides tools for maintaining tight control of error growth in cryptographic schemes. Safety: Λολ has several facilities for reducing code complexity and programming errors, thereby aiding the correct implementation of lattice cryptosystems. In particular, it uses strong typing to statically enforce—i.e., at compile time—a wide variety of constraints among the various parameters. Advanced features: Λολ exposes the rich hierarchy of cyclotomic rings to cryptographic applications. We use this to give the first-ever implementation of a collection of FHE operations known as "ring switching," and also define and analyze a more efficient variant that we call "ring tunneling." Lastly, this work defines and analyzes a variety of mathematical objects and algorithms for the recommended usage of Ring-LWE in cyclotomic rings, which we believe will serve as a useful knowledge base for future implementations.

Many lattice-based cryptosystems are based on the security of the Ring learning with errors (Ring-LWE) problem. The most critical and computationally intensive operation of these Ring-LWE based cryptosystems is polynomial multiplication. In this paper, we exploit the number theoretic transform to build a high-speed polynomial multiplier for the Ring-LWE based public key cryptosystems. We present a versatile pipelined polynomial multiplication architecture to calculate the product of two \$n\$-degree polynomials in about ((nlg n)/4 + n/2) clock cycles. In addition, we introduce several optimization techniques to reduce the required ROM storage. The experimental results on a Spartan-6 FPGA show that the proposed hardware architecture can achieve a speedup of on average 2.25 than the state of the art of high-speed design. Meanwhile, our design is able to save up to 47.06% memory blocks.