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Since its inception in the mid 1970’s, public-key cryptography has flourished as a research activity, and significant theoretical advances have been made. In more recent years, many public-key concepts have gained acceptance in the commercial world. Without question, the best-known public-key cryptosystem is the RSA system of Rivest, Shamir and Adleman [28]. Although not as well-known, another public-key cryptosystem of practical interest is that due to ElGamal [11]. The latter system and its variations use a basic extension of Diffie-Hellman key exchange [9] for encryption, together with an accompanying signature scheme. Elliptic curve cryptosystems, introduced by Miller [24] and Koblitz [12], have also recently received much attention as cryptographic alternatives.

A Comparison of Practical Public-Key Cryptosystems based on Integer Factorization and Discrete Logarithms