Cryptography in Java

Drawer UPC-A in Java Cryptography

When war broke out in 1939, Turing went to work for the Government Code and Cypher School at Bletchley Park Turing played a seminal role in breaking German secret codes, and it has been said that his work saved more lives during the war than that of any other person One of his great achievements during this time was the construction of the Bombe machine, a device for cracking all the encoded messages generated by the dreaded German Enigma machine In fact Turing used ideas from abstract logic, together with some earlier contributions of Polish mathematicians, to design the Bombe Turing s important contributions to the war effort were recognized with the award of an OBE (Order of the British Empire) in 1945 After the war Turing was invited by the National Physical Laboratory in London speci cally to design a computer He wrote a detailed proposal for the Automatic Computing Machine in 1946, and that document is in fact a discursive prospectus for a stored-program computer The project that Turing proposed turned out to be too grandiose for practical implementation, and it was shelved Turing s interests turned to topics outside of mathematics, including neurology and physiology But he maintained his passion for computers In 1948 he accepted a position at the University of Manchester There he became involved in a project, along with F C Williams and T Kilburn, to construct a computing machine In 1951 Alan Turing was elected a Fellow of the Royal Society the highest honor that can be bestowed upon a British scientist This accolade was largely in recognition of his work on Turing machines Turing had a turbulent personal life In 1952 he was arrested for violation of the British homosexuality statutes He was convicted, and sentenced to take the drug oestrogen for one year Turing subsequently rededicated himself to his scienti c work, concentrating particularly on spinors and relatively theory Unfortunately, because of his legal dif culties, Turing lost his security clearance and was labeled something of a security risk He had continued working with the cypher school at Bletchley, but his loss of clearance forced that collaboration to end These events had a profound and saddening effect on Alan Turing Turing died in 1954 of potassium cyanide poisoning while conducting electrolysis experiments The cyanide was found on a half-eaten apple The police concluded that the death was a suicide, though people close to Turing argue that it was an accident

We use Alan Turing s contributions as a touchstone for our study of cryptography Cryptography is currently a very hot eld, due in part to the availability of high speed digital computers to carry out decryption algorithms, in part to new and

exciting connections between cryptography and number theory and logic, and in part to the need for practical coding methods both in industry and in government The discussion of cryptography that appears below is inspired by the lovely book [KOB] We refer the reader to that source for additional ideas and further reading As we always do in mathematics, let us begin by introducing some terminology Cryptography is the study of methods for sending text messages in disguised form in such a manner that only the intended recipient can remove the disguise and read the message The original message that we wish to send is called the plaintext and the disguised message is called the ciphertext We shall always assume that both our plaintext and our ciphertext are written in the standard roman alphabet (that is, the letters A through Z ) together perhaps with some additional symbols like blank space (denoted ), question mark ( ), and so forth The process of translating a plaintext message into a ciphertext message is called encoding or enciphering or encrypting The process of translating an encoded message back to a plaintext message is called deciphering or sometimes de-encryting For convenience, we usually break up both the plaintext message and the ciphertext message into blocks or units of characters We call these pieces the message units, but we may think of them as words (but they are not necessarily English words) Sometimes we will declare in advance that all units are just single letters, or perhaps pairs of letters (these are called digraphs) or sometimes triples of letters (called trigraphs) Other times we will let the units be of varying sizes just as the words in any body of text have varying sizes An enciphering transformation is a function that assigns to each plaintext unit a ciphertext unit The deciphering transformation is the inverse mapping that recovers the plaintext unit from the ciphertext unit Any setup as we have just described is called a cryptosystem In general it is awkward to mathematically manipulate the letters of the alphabet We have no notions of addition or multiplication on these letters So it is convenient to associate to each letter a number Then we can manipulate the numbers For instance, it will be convenient to make the assignment A 0 B 1 C 2 X 23 Y 24 Z 25