This paper continues the ElectroNic ExeRcises for CiphEricaL Learning (ENERCELL) project by introducing Lithium, a simplified version of the Dilithium digital signature scheme which is currently being standardized by the National Institute of Standards and Technology. This scheme is “post-quantum” in the sense that while it does not require a quantum computer to run, it is expected to be secure against practical quantum computers, which could be developed in the near future. No previous knowledge of quantum or postquantum cryptography is necessary for this paper or to teach Lithium in your classes. Versions of the system will be presented which are suitable for linear algebra, abstract algebra, and/or cryptography classes, along with some analysis of the results in a cryptography class.

Quantum Key Distribution (QKD) is revolutionizing cryptography by promising information-theoretic security through the laws of quantum mechanics. Yet, the challenge of transforming these idealized security models into practical systems remains a pressing issue, especially as quantum computing evolves. In this review, we critically examine the latest advancements in QKD protocols and their security vulnerabilities, with an emphasis on rigorous security proofs. We actively categorize contemporary QKD schemes into three key classes: uncertainty principle-based protocols (e.g., BB84), hybrid architectures that enable secure direct communication (e.g., three-stage protocol), and continuous-variable frameworks. We further include two modern classes of QKD protocols, Twin-field and Device-Independent QKD, both of which were developed to have practical implementations over the last decade. Moreover, we highlight experimental breakthroughs and innovative mitigation strategies, including the deployment of advanced Quantum Error Correction Codes, that significantly enhance channel fidelity and system robustness. By mapping the current landscape, from sophisticated quantum attacks to state-of-the-art error-correction methods, this review fills an important gap in the literature. To bring everything together, the relevance of this review concerning quantum augmented networks (QuANets) is also presented. This allows the readers to gain a comprehensive understanding of the security promises of quantum key distribution from theoretical-proofs to experimental-validations.

A Python module is presented for software simulation of the historic KL-7 cipher machine. The cryptographic principles, assembly, and operation of the KL-7 are first reviewed. The structure and execution of the Python module are then detailed. Module performance is evaluated against a previous KL-7 simulator developed by Rijmenants. Differences in encryption and decryption are traced to probable rotor assembly errors within the Rijmenants simulator. The objectives of this article are to maximize the authenticity of KL-7 simulation and to provide a foundation for future study.

Secret sharing scheme distribute the secret key among multiple participants to ensure the reliability of the key. A new version of secret sharing called counting-based secret sharing (CBSS) has emerged to divide the secret key into multiple shares (copies of the secret key with some modifications) and distribute these key shares among several individuals in such a way that only the authorized subset of participants needs to agree together to reconstruct the original secret key. Existing CBSS schemes suffer from heavy computational and storage requirements for generating the key shares and reconstructing the secret key, and are also vulnerable to share leakage. This research overcomes the challenges that appear in the existing CBSS methods by dividing the secret key into adjacent blocks and by generating ambiguous secret shares based on block-based masking. In this approach, the secret shares are generated by XOR-ing each separate block of the secret key with a specific sequence of 1s where the total number of 1 is determined based on the block size. Our proposed approach can also reconstruct the secret key efficiently by assembling a subset of shares following a threshold (minimum number of secret shares that are able to reconstruct the secret key). Through experimentation, we found that our proposed CBSS strategy offers a remarkably secure contribution in making a tradeoff between security and cost of computation. Our experiment results also suggest that the average similarity between the secret key and secret shares decreases and the security level increases, when the block size of the secret key in our proposed strategy increases.

The lightweight cipher, SPECK 32/64, is designed to be a secure cipher that can be used in a resource-constrained environment. SPECK 32/64 involves a pair of rotation constant parameters ( α , β ) . Different investigators, including the original designers, suggested different choices of ( α , β ) primarily keeping the implementation issues in mind. The objective of this study is to check whether these choices compromise the security of SPECK-like ciphers, namely SPECK 32/64 and SPECK 64/128. For this, using both neural differential distinguisher (NDD) and pure differential distinguisher (PDD), we establish the following: (i) The pair of rotation constants suggested by the designers are by no means optimal while tested on both NDD and PDD. (ii) Based on our limited experiments, the rotation constant pair (6, 4) is found to be a better choice for differential cryptanalysis. (iii) With the increase in the number of rounds, different choices become equally effective. (iv) Choices of α and β that are close to multiples of 8 can provide computational efficiency, however, they are not necessarily good for differential attacks (v) The NDD and PDD behave very consistently on round-reduced SPECK 32/64, and generally, NDD is found to perform better than PDD.

The Second World War saw a major influx of mathematical talent into the areas of cryptanalysis and cryptography. This was particularly true at the UK’s Government Code and Cypher School (GCCS) at Bletchley Park. The success of introducing mathematical thinking into activities previously dominated by linguists is well studied, but the reciprocal question of how cryptography affected the field of mathematics has not been investigated as thoroughly. Although their cryptologic achievements are not as celebrated as those of Alan Turing, Bill Tutte, and Gordon Welchman, some eminent mathematicians supplemented Bletchley Park’s efforts and provided leadership and direction for mathematical research in the United Kingdom. Among their number were Ian Cassels, Sandy Green, Philip Hall, Max Newman, and Henry Whitehead. This paper considers how the experience of these and other mathematicians at Bletchley Park informed and influenced the mathematics produced in their postwar careers.

Abraham Adrian Albert “A cubed” (1905–1972) was an algebraist best known academically for his study of associative and non-associative algebras. By the 1940s he had also developed an interest in cryptology and its relationship to mathematics. Throughout the following two decades, Albert would participate in several mathematics programs to study and advise on cryptanalysis. In particular, Albert’s work with the National Security Agency (NSA) set a framework for the development of cryptology as a mathematical discipline. This research aims to present a timeline for and the breadth of Albert’s promotion of cryptology in the post-WWII American mathematical community and to examine, for the first time, reports Albert authored under contract with the NSA. In doing so, we hope to better understand the relationship between the NSA and academic mathematicians at the time of writing. The reports, released in 2020 by the NSA in response to a 2010 Freedom of Information Act request, have been arranged by the author into eleven collections based on content. Each collection will be introduced with their ideas and results given in a roughly chronological order. These collections span ideas in group theory, field theory, matrix algebra, and geometry, most often with application to cryptological systems.

NBC is a class of Type-II generalized Feistel structure algorithms with excellent software and hardware implementation performance. In this paper, we evaluate the security of NBC from the view point of multiple impossible differential. More precisely, using the idea of combining the matrix method and “meet-in-the-middle,” we first obtain 4 types of 11-round impossible differentials for NBC-128 and 32 types of 14-round impossible differentials for NBC-256, respectively. Then, according to the characteristics of Feistel structure and the distinguisher, we perform 17-round, 19-round, and 22-round multiple impossible differential cryptanalysis on NBC-128-128, NBC-128-256, and NBC-256-256, respectively. Results indicate that NBC has sufficient security to resist an impossible differential attack, and the data and time complexity of our attack has been significantly reduced compared to previous ones.