An asymmetric cryptographic integrated circuit 20 and a data processing device 10 in which the integrated circuit 20 is used are disclosed. A security boundary 44 is confined to the interior of integrated circuit 20. A random number generator 50 with a hardware entropy source 54 and an arithmetic unit 62 programmed through microcode 38″ to perform a variety of cryptographically useful functions are included within security boundary 44. One of these functions is a primality tester 72. A controller 36 for integrated circuit 20 may cause cryptographically sensitive data, such as large random prime numbers and a clear private key to be generated within the confines of security boundary 44. A symmetric key encryption engine 56 is included within security boundary 44 and used to encrypt the clear private key so that a resulting encrypted private key may be stored outside security boundary 44 in a non-volatile memory 12.