Probabilistic encryption & how to play mental poker keeping secret all partial information

This paper proposes an Encryption Scheme that possess the following property : An adversary, who knows the encryption algorithm and is given the cyphertext, cannot obtain any information about the clear-text. Any implementation of a Public Key Cryptosystem, as proposed by Diffie and Hellman in [8], should possess this property. Our Encryption Scheme follows the ideas in the number theoretic implementations of a Public Key Cryptosystem due to Rivest, Shamir and Adleman [13], and Rabin [12].

[1]  Gary L. Miller,et al.  Riemann's Hypothesis and tests for primality , 1975, STOC.

[2]  D. Bernstein DISTINGUISHING PRIME NUMBERS FROM COMPOSITE NUMBERS , 2022 .

[3]  Adi Shamir,et al.  A method for obtaining digital signatures and public-key cryptosystems , 1978, CACM.

[4]  Gilles Brassard,et al.  Relativized cryptography , 1979, 20th Annual Symposium on Foundations of Computer Science (sfcs 1979).

[5]  M. Rabin DIGITALIZED SIGNATURES AND PUBLIC-KEY FUNCTIONS AS INTRACTABLE AS FACTORIZATION , 1979 .

[6]  Gary L. Miller,et al.  On taking roots in finite fields , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).

[7]  Whitfield Diffie,et al.  New Directions in Cryptography , 1976, IEEE Trans. Inf. Theory.

[8]  N. S. Barnett,et al.  Private communication , 1969 .

[9]  D. Shanks Solved and Unsolved Problems in Number Theory , 1964 .