Patent ID: 7760872

Claim:
A method for establishing cryptographic communications comprising the steps of: providing a group G of user members distributed over a network of devices configured and connected for electronic communication with each other; providing and associating at least one private key with each member of group G, wherein the key(s) are operable for decryption of encrypted messages sent over the network; transmitting an encrypted message to at least one member; and at least one member of group G using its private key to decrypt the encrypted message, thereby providing a secure system for cryptographic communications across the group G, wherein group G consists of K members, G 1 , G 2 , . . . G K ; further including the step of associating each member of group G, G M , with a public key P GM ; wherein each public key P GM includes a public modulus N GM and a plaintext maximum MAX GM ; wherein the group public key P G includes public exponent e G , public modulus N G , plaintext minimum MIN G , and plaintext maximum MAX G ; wherein N G is generated as the product of the public moduli N G1 , N G2 , . . . N GK ; wherein MIN G equals zero; wherein MAX G is generated as the minimum of the plaintext maximums MAX G1 , MAX G2 , . . . MAX Gk ; N G =N G1 *N G2 * . . . N GK MAX G =MIN(MAX G1 , MAX G2 , . . . MAX GK ) wherein e G is preferably generated as a prime number.