In recent years, the definition of security in a locked design has been reformulated, and mechanisms that use cryptosystems and dense obfuscation techniques have been proposed. However, they increase the hardware complexity of a locked design significantly, restricting their application. In this paper, we present a novel logic locking technique using diffusion enabled by a matrix-vector multiplications (MVM) block, which can realize the multiplication of a variable vector first by a variable key matrix and second by a constant matrix in the integral domain and finite/Galois field. It takes advantage of the weakness of the well-known SAT-based attack and its variants, and the removal and structural analysis attacks by inserting an MVM block with a long chain of and and xor gates with key inputs into the original design and removing the traces of such an insertion through logic synthesis. It also uses optimization algorithms to reduce the number of adders/subtractors (xor) gates in the multiplication of a constant matrix by a variable vector in the integral domain (Galois field) and a key obfuscation technique to increase the security level. Experimental results show that the hardware complexity of locked circuits generated by the logic locking techniques using ciphers AES and Trivium is up to 17 × and 88 × larger than that of secure locked circuits generated by the proposed technique, respectively. It is also shown that these locked designs are resilient against the SAT-based attack and its variants, and they render existing removal and structural analysis attacks inefficient.

Ascon is the National Institute of Standards and Technology (NIST) standard for lightweight cryptography, providing Authenticated Encryption with Associated Data (AEAD), hash, eXtendable-Output Function (XOF), and Customizable XOF (CXOF). Prior studies mainly target AEAD implementations of earlier Ascon versions with a little focus on hash and unified designs, and generally explore the area and latency tradeoff by varying permutation rounds per one clock cycle. In this work, we present a comprehensive design space exploration of the complete Ascon family of the NIST standard for the first time through two design architectures: (i) the conventional round-based variants that perform 1, 2, and 4 rounds per one clock cycle, i.e., v1r1c, v2r1c, and v4r1c, respectively, and (ii) the operation-based variants that execute one 64-bit and 32-bit operation per one clock cycle using a cycle-optimized schedule that completes one permutation round with a total of 28 and 56 cycles, i.e., v1op1c_64b_28 and v1op1c_32b_56, respectively. Our design space exploration includes the Ascon-AEAD128 encryption, decryption, unified encryption/decryption, unified Ascon-Hash256, Ascon-XOF128, Ascon-CXOF128, and a complete Ascon unified family. Experimental results show that the round-based variants achieve low latency and energy consumption, while the operation-based variants lead to designs with low area. Our implementations also have smaller hardware complexity than the state-of-the-art designs. For example, on the Ascon-AEAD128 designs performing encryption, our round-based v1r1c variant achieves an area reduction of \(39.99\%\) when compared to a round-based state-of-the-art design, while our v1op1c_64b_28 variant reduces latency and energy consumption by \(48.11\%\) and \(32.29\%\), respectively when compared to the state-of-the-art design using one 64-bit operation per one clock cycle, completing one permutation round in 59 clock cycles.

Facing the potential threat raised by quantum computing, a great deal of research from many groups and industrial giants has gone into building public‐key post‐quantum cryptographic primitives that are resistant to the quantum attackers. Among them, there is a large number of post‐quantum key encapsulation mechanisms (KEMs), whose purpose is to provide a secure key exchange, which is a very crucial component in public‐key cryptography. This paper presents a formal security analysis of three lattice‐based KEMs including Kyber, Saber, and SK‐MLWR. We use Maude, a specification language supporting equational and rewriting logic and a high‐performance tool equipped with many advanced features, such as a reachability analyzer that can be used as a model checker for invariant properties, to model the three KEMs as state machines. Because they all belong to the class of lattice‐based KEMs, they share many common parts in their designs, such as polynomials, vectors, and message exchange patterns. We first model these common parts and combine them into a specification, called base specification. After that, for each of the three KEMs, by extending the base specification, we just need to model some additional parts and the mechanism execution. Once completing the three specifications, we conduct invariant model checkings with the Maude search command, pointing out a similar man‐in‐the‐middle attack. The occurrence of this attack is due to the fact that authentication is not part of the KEMs, and therefore an active attacker can modify all communication between two honest parties.

The security of most public-key cryptosystems currently in use today is threatened by advances in quantum computing.That is the reason why recently many researchers and industrial companies have spent lots of effort on constructing post-quantum cryptosystems, which are resistant to quantum attackers.A large number of post-quantum key encapsulation mechanisms (KEMs) have been proposed to provide secure key establishment -one of the most important building blocks in asymmetric cryptography.This paper presents a formal security analysis of Saber lattice-based KEM.We first formally specify the mechanism in Maude, a rewriting logic-based specification/programming language equipped with many functionalities, such as a reachability analyzer (or the search command) that can be used as an invariant model checker, and then conduct invariant model checking with the Maude search command, finding an attack.

Internet of Things (IoT) is a paradigm shifting technology that enables many innovative applications in the near future. Proactive measures are required to protect such architecture from cyber attacks. One of the most important security issues in this architecture is the authentication of edge nodes, which can be resolved through the deployment of digital signatures. However, existing standardized digital signatures are vulnerable to attacks from quantum computers, which can be unsafe in the near future. In this article, we propose a new signature scheme based on multivariate polynomials with efficient key and signature sizes, which is resistant to quantum computer attacks. The proposed scheme is also very friendly to parallel implementation, enabling efficient deployment of edge nodes authentication at high throughput. When implemented on a GPU device, the proposed scheme can generate 113 signatures/s and verify 120 signatures/s, which is 12.56× and 10.00× faster than a serial implementation in CPU.

In this study, the authors generalise Hadamard matrix over and propose a new form of Hadamard matrix, which they call generalised Hadamard (GHadamard) matrix. Then, they focus on generating lightweight (involutory) maximum distance separable (MDS) matrices. They also extend this idea to any matrix form, where k is not necessarily a power of 2. The new matrix form, GHadamard matrix, is used to generate new involutory MDS matrices over and , and involutory/non‐involutory MDS matrices over by considering the minimum exclusive OR (XOR) count, which is a metric defined to estimate the hardware implementation cost. In this context, they improve the best‐known results of XOR counts for involutory/non‐involutory MDS matrices over .

In this study, the authors propose new methods using a divide‐and‐conquer strategy to generate n × n binary matrices (for composite n ) with a high/maximum branch number and the same Hamming weight in each row and column. They introduce new types of binary matrices: namely, ( BHwC ) t , m and ( BCwC ) q , m types, which are a combination of Hadamard and circulant matrices, and the recursive use of circulant matrices, respectively. With the help of these hybrid structures, the search space to generate a binary matrix with a high/maximum branch number is drastically reduced. By using the proposed methods, they focus on generating 12 × 12, 16 × 16 and 32 × 32 binary matrices with a maximum or maximum achievable branch number and the lowest implementation costs (to the best of their knowledge) to be used in block ciphers. Then, they discuss the implementation properties of binary matrices generated and present experimental results for binary matrices in these sizes. Finally, they apply the proposed methods to larger sizes, i.e. 48 × 48, 64 × 64 and 80 × 80 binary matrices having some applications in secure multi‐party computation and fully homomorphic encryption.

In this paper, we propose a new method to generate n × n binary matrices (for n = k·2t where k and t are positive integers) with a maximum/high of branch numbers and a minimum number of fixed points by using 2t×2t Hadamard (almost) maximum distance separable matrices and k × k cyclic binary matrix groups. By using the proposed method, we generate n × n (for n = 6, 8, 12, 16, and 32) binary matrices with a maximum of branch numbers, which are efficient in software implementations. The proposed method is also applicable with m × m circulant matrices to generate n × n(for n = k·m) binary matrices with a maximum/high of branch numbers. For this case, some examples for 16 × 16, 48 × 48, and 64 × 64 binary matrices with branch numbers of 8, 15, and 18, respectively, are presented. Copyright © 2016 John Wiley & Sons, Ltd.

Abstract In this paper, we propose novel deterministic and probabilistic public key cryptographic schemes based on an effective and compact subgroup trace representation cryptosystem to handle with the problem of secure and efficient communication between the server and resource‐constrained device. The proposed schemes use the hardness of the Trace‐discrete logarithmic like problem. We also show that the deterministic version of the proposed scheme is a one‐way trapdoor, and the probabilistic version of the proposed scheme is semantically secure. Moreover, we discuss the efficiency of the proposed schemes by comparing with effective and compact subgroup schemes. Copyright © 2015 John Wiley & Sons, Ltd.

In this study, the authors give a generalisation of special moduli for faster interleaved Montgomery modular multiplication algorithm with simplified pre‐computational phase for GF ( p n ), where p ≥ 2 is a prime number and n is a positive integer. The authors propose different sets of moduli that can be used in elliptic curve crytographic applications and pairing‐based cryptography. Moreover, this method also leads to efficient implementations for the elliptic curve parameters given in standards. It is shown that one can obtain efficient Montgomery modular multiplication architecture in view of the number of AND gates and XOR gates by choosing proposed sets of moduli. The authors eliminate final substraction step with proposed sets of moduli. These methods are easy to implement for hardware.

We give an efficient multiplication method for polynomials in Chebyshev form. This multiplication method is different from the previous ones. Theoretically, we show that the number of multiplications is at least as good as Karatsuba-based algorithm. Moreover, using the proposed method, we improve the number of additions slightly. We remark that our method works efficiently for any N and it is easy to implement. To the best of our knowledge, the proposed method has the best multiplication and addition complexity for the N-term polynomial multiplication in Chebyshev form with 3 ≤ N ≤ 13.

We give a modified redundant representation for designing arithmetic circuits with small complexity. Using our modified redundant representation, we improve many of the complexity values significantly. Our method works for any finite field. We also give some applications in cryptography.