An Application Example: The RSA Cryptosystem

Abstract

As we approach the endof our story we would like to investigate the possibility of testing what we have labored over chapter by chapter against a realistic and current example, one that clearly demonstrates the connection between the theme of cryptographic application and the deployment of our programmed functions. We shall make a brief excursion into the principle of asymmetric cryptosystems and then turn our attention to the RSA algorithm as the classic example of such a system, which was published in 1978 by its inventors/discoverers, Ronald Rivest, Adi Shamir, and Leonard Adleman (see [Rive], [Elli]), and which by now has been implemented worldwide.¹ The RSA algorithm is patented in the United States of America, but the patent expired on 20 September 2000. Against the free use of the RSA algorithm stood the claims of RSA Security, who possessed rights to the trade name “RSA,” which triggered vehement discussion in connection with work on the standard P1363 [IEEE], with in some cases rather grotesque results, for example, the suggestion of rechristening the RSA procedure “biprime cryptography.” There have also appeared less serious suggestions, such as FRA (former RSA algorithm), RAL (Ron, Adi, Leonard), and QRZ (RSA — 1). Upon expiry of their patent RSA Security weighed in with its opinion:

Clearly, the terms “RSA algorithm,” “RSA public-key algorithm,” “RSA cryptosystem,” and “RSA public-key cryptosystem” are well established in standards and open academic literature. RSA Security does not intend to prohibit the use of these terms by individuals or organizations that are implementing the RSA algorithm (“RSA-Security—Behind the Patent,” September 2000).²

The next question was the obvious one, “Can this be done with ordinary encipherment? Can we produce a secure encrypted message, readable by the authorised recipient without any prior secret exchange of the key etc?” ... I published the existence theorem in 1970.

—J H Ellis, “The Story of Non-Secret Encryption”