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Abstract

A public-key data encryption system employing RSA public-key data encryption including a message encrypter capable of encrypting messages using a non-secret encryption key, a transmitter-receiver coupled to the message encrypter which transmits or receives an encrypted message to or from a remote location, the transmitter-receiver also being coupled to a decrypter capable of decrypting a received encrypted message using a decryption key which is a secret input to the decrypter, and an encryption-decryption key generator, including a microprocessor or other large-scale integrated circuit or circuits formed to generate a sequence of prime numbers beginning with a selected known prime number having a length relatively short with respect to the desired length of the last in the sequence of prime numbers, and which is constructed to form the sequence of prime numbers in the form hP+1 where P is the preceding prime number in the sequence, and to test hP+1 for primality by first determining if hP+1 has a GCD of 1 with x, wherein x is a composite number consisting of the product of all known prime numbers less than or equal to a pre-selected known prime number and if the GCD is not equal to 1, incrementing h to form a new hP+1 to be tested for a GCD equal to 1, and when a GCD is found to be 1, performing the primality tests to determine whether 2.sup.hP .ident.1 [mod (hP+1)] and 2.sup.h .notident.1 [mod (hP+1)], and if either 2.sup.hP .notident.1 [mod (hP+1)] or 2.sup.h .ident.1 [mod (hP+1)] further incrementing h and so on until a prime is found in this manner and then determining if the length of the prime number is of or greater than the desired length. If the hP+1 which has been determined to be prime is not of the desired length, hP+1 is placed in the sequence of prime numbers and a new h selected to be used to find the next prime number in the sequence in accordance with the above described procedure by forming a new hP+1 in which P is the previously determined prime number in the sequence of prime numbers. When a prime number in the sequence of prime numbers is found which is of the desired length it is input into the encryption-decryption key generator for generating the RSA public-key encryption and decryption keys.

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First Claim