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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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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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