The author introduces the concept of connecting cryptography with mathematics and explains that this idea has not been explored extensively in the literature. They argue that cryptography is more than just a subject for mathematical formulation, but rather is identical to abstract mathematics itself. The author then discusses the theory of non-singular mappings in cryptography and defines cryptography as the study of all non-singular mappings from a set of messages to a set of cryptograms. They also introduce the concept of cipher systems and codes in cryptography. One example of a cipher system discussed is transposition ciphers, which involve rearranging the order of symbols in a message.
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