Abstract: Methods are disclosed for improving public key cryptography schemes, such as RSA and its variants, to allow for decryption of messages using less than all of the prime factors of the modulus that is used for encryption of said messages.

Abstract: A public key cryptosystem and methods for using same including at least one encrypted message wherein the encryption occurs using RSA methods; and at least one key for decrypting the encrypted message(s) wherein the key further comprising a predetermined number of prime factors, including the prime number P, used for the generation of a public modulus N and an exponent e, wherein a proper subset of the prime factors of the modulus N, along with the exponent e, are required to decrypt messages encrypted using the public exponent e and the public modulus N, where e and N are generated using RSA methods, wherein the exponent d for decryption is generated to be as small as possible without compromising security, such that e*d=1 mod (P?1) and gcd(e,d)=1 and the public exponent e contains approximately the same number of bits as the prime number P.

Abstract: A system and method for public key cryptosystem for secure communication of messages including at least one message encrypted by standard RSA methods; and a predetermined number of prime factors used for the generation key(s) for decryption including a modulus N and an exponent e, wherein a proper subset of the prime factors of the modulus N, along with the exponent e, are required to decrypt messages encrypted using the public exponent e and the public modulus N, N is generated using RSA methods, and encryption occurs using RSA methods, wherein the exponents d and e are generated such that e*d=1 mod (N?1) and gcd(e,d)=1, and further including additional method steps for preprocessing plaintext messages to prevent potential security attacks within the context of superset RSA; and wherein the system is operable to decrypt encrypted messages using the key(s).

Abstract: Methods are disclosed for improving public key cryptography schemes, such as RSA and its variants, to allow for decryption of messages using less than all of the prime factors of the modulus that is used for encryption of said messages.

Abstract: Systems and methods are disclosed for establishing secure communications to a group rather than to an individual recipient. The systems and methods presented include mechanisms for encryption to a group, decryption by one or more group members, digital signature generation and verification, and the addition/removal of group members.