Abstract
When Z/PZ (P is an odd prime) is decomposed into suitable two sets, Chebyshev polynomials have properties that each set is invariant under their operations and that for their degrees, they show different periods corresponding to each set. We construct a public key cryptography of RSA type based on Chebyshev polynomial by using the properties. Compared with RSA cryptography, our cryptography has possibility of realizing higher security and its deciphering time increases merely about 10%. However compared with fast RSA cryptography, it is about 4.5 times.
