Unbreakable Codes: RSA Public Key Cryptosystem

The purpose of this paper is to comprehend the evolution of codes and ciphers; along with understanding how to encode and decode a message using RSA coding. In this paper Unbreakable Codes we will highlight the historical advances of communicating secure messages by illustrating the process of RSA coding with an example

A Comparison of Cryptography Courses

The author taught two courses on cryptography, one at Duke University aimed at non-mathematics majors and one at Rose-Hulman Institute of Technology aimed at mathematics and computer science majors. Both tried to incorporate technical and societal aspects of cryptography, with varying emphases. This paper will discuss the strengths and weaknesses of both courses and compare the differences in the author's approach.Comment: 14 pages; to appear in Cryptologi

On weak rotors, Latin squares, linear algebraic representations, invariant differentials and cryptanalysis of Enigma

Since the 1920s until today it was assumed that rotors in Enigma cipher machines do not have a particular weakness or structure. A curious situation compared to hundreds of papers about S-boxes and weak setup in block ciphers. In this paper we reflect on what is normal and what is not normal for a cipher machine rotor, with a reference point being a truly random permutation. Our research shows that most original wartime Enigma rotors ever made are not at all random permutations and conceal strong differential properties invariant by rotor rotation. We also exhibit linear/algebraic properties pertaining to the ring of integers modulo 26. Some rotors are imitating a certain construction of a perfect quasigroup which however only works when N is odd. Most other rotors are simply trying to approximate the ideal situation. To the best of our knowledge these facts are new and were not studied before 2020

Solving Elgar's Enigma

On June 19, 1899, Elgar's opus 36, Variations on a Theme, was introduced to the public for the first time. It was accompanied by an unusual program note: "It is true that I have sketched for their amusement and mine, the idiosyncrasies of fourteen of my friends, not necessarily musicians; but this is a personal matter, and need not have been mentioned publicly. The Variations should stand simply as a "piece" of music. The Enigma I will not explain-its "dark saying" must be left unguessed, and I warn you that the connexion between the Variations and the Theme is often of the slightest texture; further, through and over the whole set [of variations 1 another and larger theme "goes" but is not played ... So the principal Theme never appears, even as in some late dramas-e.g., Maeterlinck's "L'Intruse" and "Les sept Princesses" -the chief character is never on the stage. (Burley and Carruthers 1972:119)" After this premier Elgar give hints about the piece's "Enigma;' but he never gave the solution outright and took the secret to his grave. Since that time scholars, music lovers, and cryptologists have been trying to solve the Enigma. Because the solution has not been discovered in spite of over 108 years of searching, many people have assumed that it would never be found. In fact, some have speculated that there is no solution, and that the promise of an Enigma was Elgar's rather shrewd way of garnering publicity for the piece. Others have even argued that the larger Enigma was a joke or a hoax; that Elgar never had any Enigma but instead tricked people to search in vain (Rushton 1999:64). Elgar refused to validate any solution offered during his lifetime, and therefore no solution can ever be proven beyond the shadow of a doubt. However, the composer offered a series of hints that provide a rubric for evaluating the plausibility of various solutions

Multi-algorithmic Cryptography using Deterministic Chaos with Applications to Mobile Communications

In this extended paper, we present an overview of the principal issues associated with cryptography, providing historically significant examples for illustrative purposes as part of a short tutorial for readers that are not familiar with the subject matter. This is used to introduce the role that nonlinear dynamics and chaos play in the design of encryption engines which utilize different types of Iteration Function Systems (IFS). The design of such encryption engines requires that they conform to the principles associated with diffusion and confusion for generating ciphers that are of a maximum entropy type. For this reason, the role of confusion and diffusion in cryptography is discussed giving a design guide to the construction of ciphers that are based on the use of IFS. We then present the background and operating framework associated with a new product - CrypsticTM - which is based on the application of multi-algorithmic IFS to design encryption engines mounted on a USB memory stick using both disinformation and obfuscation to ‘hide’ a forensically inert application. The protocols and procedures associated with the use of this product are also briefly discussed

Review on DNA Cryptography

Cryptography is the science that secures data and communication over the network by applying mathematics and logic to design strong encryption methods. In the modern era of e-business and e-commerce the protection of confidentiality, integrity and availability (CIA triad) of stored information as well as of transmitted data is very crucial. DNA molecules, having the capacity to store, process and transmit information, inspires the idea of DNA cryptography. This combination of the chemical characteristics of biological DNA sequences and classical cryptography ensures the non-vulnerable transmission of data. In this paper we have reviewed the present state of art of DNA cryptography.Comment: 31 pages, 12 figures, 6 table

All the King’s Men: British Codebreaking Operations: 1938-43

The Enigma code was one of the most dangerous and effective weapons the Germans wielded at the outbreak of the Second World War. The Enigma machine was capable of encrypting radio messages that seemed virtually unbreakable. In fact, there were 158,900, 000,000,000 possible combinations in any given message transmitted. On the eve of the war’s outbreak, the British had recently learned that the Poles had made significant progress against this intimidating cipher in the early 1930s. Incensed and with little help, the British Government Code & Cipher School began the war searching for a solution. Drawing from their experiences from the First World War, and under the visionary guidance of Alan Turing, Gordon Welchman, and countless others, the British created a new, mechanical approach to breaking the seemingly impossible German code. By breaking the code, they could very well save Britain