Prime Numbers and Cryptography

  • Hans Riesel
Part of the Progress in Mathematics book series (PM, volume 57)


There is a remarkable disparity between the degree of difficulty of the task of multiplication and that of factorization. Multiplying integers together is a reasonable exercise for a young child if the integers are small, and it remains a very straightforward task even when the integers are very large. The reverse operation, however, that of resolving a given integer into factors, is cumbersome except for the very smallest integers and becomes nearto impossible for large numbers. This assymmetry is exploited in a new kind of cryptosystem, called RSA after its discoverers, Rivest, Shamir and Adleman. In the RSA system secrecy is provided by placing a would-be codebreaker in a situation where in principle he commands all information necessary for reading the protected message but is confronted with an arithmetic task which in practice is prohibitively time-consuming.


Prime Number Encryption Algorithm Punctuation Mark Small Prime Factor Multiple Precision Arithmetic 


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Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • Hans Riesel
    • 1
  1. 1.VällingbySweden

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