Abstract
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 near to 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.
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Riesel, H. (2011). Prime Numbers and Cryptography. In: Prime Numbers and Computer Methods for Factorization. Modern Birkhäuser Classics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8298-9_7
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DOI: https://doi.org/10.1007/978-0-8176-8298-9_7
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