The Mathematics of Modern Computerized Cryptography
Cryptography has been used for thousands of years to provide security for messages. It is only during the twentieth century that encryption came to be viewed as essentially a mathematical process.
Much of this change can be traced back to Professor Lester S. Hill's work which was published in the American Math Math Monthly. In 1929 he published the article "Cryptography in an Algebraic Alphabet".
In 1931 Hill published an expanded article entitled "Concerning Certain Linear Transformation Apparatus of Cryptography". Hill's work used integers to represent the letters. Hill's cryptosystem stored these integer in matrices and vectors. Hill's cryptosystem defined matrix by vector multiplication as the encryption and decryption operations.
What Hill did not realize is that additional cryptographic strength could be obtained by having a prime number of symbols in the alphabet. This allowed processing to occur in a Galois Field. Professor Rodney Cooper published this idea in Cryptologia under the title "Linear Transformations in Galois Fields and their Application to Cryptography".
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Most recent update on 28-SEP-96.