Part of the Lecture Notes in Computer Science book series (LNCS, volume 218)
An M3 Public-Key Encryption Scheme
It is well known that the RSA public-key cryptosystem can be broken if the composite modulus can be factored. It is nor known, however, whether the problem of breaking any RSA system is equivalent in difficulty to factoring the modulus. In 1979 Rabin  introduced a public-key cryptosystem which is as difficult to break as it is to factor a modulus R=p1p2, where p1p2 are two distinct large primes. Esaentially Rabin suggested that the designer of such a scheme first determine p1 and p2, keep them secret and make R public. Anyone wishing to send a secure message H (0 < M < R ) to the designer would encrypt M as K , where
and 0 < K < R, then transmit K to the designer.
$$ K \equiv M^2 (\bmod R)$$
KeywordsChinese Remainder Theorem Secure Message Linear Congruence Jacobi Symbol Primitive Cube Root
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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- D.H. Lehmer, Computer technology applied to the theory of numbers, Studies in Number Theory, Math. Assoc. of America, 1969, Theorem 5, p. 133.Google Scholar
- M.O. Rabin, Digitized signatures and public-key functions as intractable as factorization, M.I.T. Lab. for Computer Science, Tech. Rep. LCS/TR212, 1979.Google Scholar
© Springer-Verlag Berlin Heidelberg 1986