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On a cryptosystem using simple continued fractions. (English) Zbl 1015.94544

Summary: We introduce a new type of cryptosystem. We show that if to each letter or character of a plaintext message written in some alphabet we label a positive integer \(a_i>1\), \(i=1,\dots\) and consider the finite simple continued fraction \(\langle 0,a_1, \dots,a_n \rangle\) that is generated by these positive integers, then the plaintext message can be enciphered as a rational number in \((0,1)\). Conversely, any plaintext message can be recovered from its ciphertext, which is expressed as a rational in \((0, 1)\), using simple continued fractions and corresponding to each partial quotient its assigned letter or character. Of course, there are many different ways of labeling the letters or characters of an alphabet using positive integers greater than 1 in some range in order to encipher or decipher a message using simple continued fractions. In fact, this labeling is the secret key that any two parties have to know in order to communicate safely.

MSC:

94A60 Cryptography
11T71 Algebraic coding theory; cryptography (number-theoretic aspects)
14G50 Applications to coding theory and cryptography of arithmetic geometry
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