In World War I, Germany employed a multitude of codes and codebooks for the communications of diplomats and attaches - naval and military - in remote embassies across European neutral countries, the Balkans, South and North America, and Asia. The Germans also introduced increasingly sophisticated superencipherment methods to enhance the security of their communication. However, these proved to be no match for the codebreakers of the Allied Powers, who could read nearly all enciphered traffic to and from those embassies throughout the war. The impact of such decryptions, like the Zimmermann Telegram in 1917, has been extensively studied. Still, until now, technical information on the codebooks used in embassies and their superencipherments has been sketchy and fragmentary. The recent discovery of files on Dutch codebreaking in WWI, coupled with an extensive survey and in-depth analysis of archival sources in the UK, Germany, France, and the US, enables us to paint a comprehensive and detailed picture of the various families of German codebooks used by embassies. This allows us to evaluate the achievements of the French, British, and US codebreaking services against those codes and underscore the previously unknown successes of the codebreakers of the Netherlands.
We focus on improving the Gaudry-Schost algorithm, which solves the multi-dimensional discrete logarithm problem. We have proposed a modification that reduces the cost of each iteration by a factor of D-1/Delta +1/l C-s(_) D/C-f /D-1/Delta+1 where D is the dimension of the problem, l a specially designed quantity, C-g the cost of computing any function g, s(D)(-), f are functions and (1/l + C-sD/C-f) < 1. The cost of our algorithm for subgroups mod-Cf ulo a prime p, which arises in electronic voting and cash schemes diminishes by a factor of ||p||/Delta(gs)/l log (||p||)/Delta(tt) where the Delta's are the ott iterations to reach a certain type of points. Our implementation confirms theoretical analysis. The reduction of cost per iteration is advantageous when a complete number of iterations have to be done to find logarithms. Also, both theory and experiments confirm that the new algorithm reduces the dominant multiplication cost along with other additional costs, and the gain would be more as we increase the size of the group. We obtained a 12 times speed-up for groups of size 2076-bits. The abstraction of our algorithm will lead to a reduction in security of schemes based on multi-dimensional pseudo-random walks like electronic-voting, cash-schemes, point-counting, speeding-up elliptic-curve arithmetic, group-actions, CSIDH, etc. However, the present application is restricted to subgroups of Z(p)*.
In recent years, cryptographic research has seen a surge of interest in post-quantum cryptography driven by the potential threat that quantum computers pose to traditional public-key cryptosystems. Isogeny-based cryptography is a promising method in post-quantum cryptography, relying on the computational challenge of calculating isogenies, which are specific mappings between elliptic curves. The efficiency of isogeny computations is vital for real-world cryptographic applications. However, these computations, particularly with large parameters, can be highly resource intensive. In this work, we derive odd degree isogeny formulae for Extended Jacobi Quartic Curves based on u- coordinate, a novel approach to facilitate isogeny computations. These formulae are derived by analyzing the algebraic structure of the Extended Jacobi Quartic Curves, leveraging properties of the u- coordinate to express an isogeny map in terms of simpler, computationally efficient operations. We also explore the algebraic complexity of these computations and compute their runtimes for isogeny computations across different prime numbers and compare them with different models of an elliptic curve to check the performance.
Quantum Key Distribution (QKD) is revolutionizing cryptography by promising information-theoretic security through the immutable laws of quantum mechanics. Yet, the challenge of transforming these idealized security models into practical, resilient systems remains a pressing issue, especially as quantum computing evolves. In this review, we critically dissect and synthesize the latest advancements in QKD protocols and their security vulnerabilities, with a strong 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 (eg, three-stage protocol), and continuous-variable frameworks. We further include two modern classes of QKD protocols, namely Twin-field QKD and Device-Independent QKD, both of which were developed to have practical implementations over the last decade. Moreover, we highlight important experimental breakthroughs and innovative mitigation strategies, including the deployment of advanced Quantum Error Correction Codes (QECCs), 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.
We introduce a new probabilistic public-key cryptosystem which combines the main ingredients of the well-known RSA and Rabin cryptosystems. We investigate the security and performance of our new scheme in comparison to the other two.
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.
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.
In the shadow of World War II, the cryptographic landscape was shaped by mechanical cipher machines such as the Enigma and the Lorenz cipher. These devices were systematically deciphered by the cryptanalysts at Bletchley Park, whose work propelled forward the fields of mathematical cryptography and computational science. This paper explores the feasibility of designing cryptographic schemes using only the mechanical and early digital computation technologies available at the time but informed by contemporary cryptographic knowledge. We propose a security scheme with a stream cipher, key-distribution, authentication, implemented with contemporary mechanical technology. We then evaluate the computational power available during the period and assess the required key sizes and algorithm complexities that would have been necessary to thwart decryption efforts.
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.
