ABSTRACT
The cryptographic system, called the R. Rivest, A. Shamir, and L. Adleman (RSA) system, depends instead on Euler’s Function and Euler’s Theorem. Though introduced in the late 1970’s, this system remains in wide use today for digital communications of all sorts, including in particular financial transactions such as on-line payments with a credit card. An important new idea in the RSA system is that it involves public keys. This conceptual breakthrough showed that it is possible to avoid the dependence on private keys which themselves require secure exchange. As designed in RSA, the public keys are made possible by the fact that factorization of integers is hard, especially when the primes involved in the factorization are large.
