A method and apparatus are disclosed for improving public key encryption and decryption schemes that employ a composite number formed from three or more distinct primes. The encryption or decryption tasks may be broken down into sub-tasks to obtain encrypted or decrypted sub-parts that are then combined using a form of the Chinese Remainder Theorem to obtain the encrypted or decrypted value. A parallel encryption/decryption architecture is disclosed to take advantage of the inventive method.REEXAMINATION RESULTS.Iadd.The questions raised in reexamination request No. 90/005,733, filed May 18, 2000 and reexamination request No. 90/005,776, filed on Jul. 28, 2000, have been considered and the results thereof are reflected in this reissue patent which constitutes the reexamination certificate required by 35 U.S.C. 307 as provided in 37 CFR 1.570(e). .Iaddend.