Abstract: This invention describes and specifies a cryptographic method/system employing one-way invertible transforms. In one embodiment, many different encryption keys can correspond to one single decryption key that decrypts different versions of ciphertext created by the many different encryption keys uniquely to the original plaintext; and in another embodiment one single encryption key can correspond to many different decryption keys that give different decrypted results. The encryption key is so constructed that it allows a high level of parallel computation.

Abstract: A cryptographic information and communication system of the knapsack type characterized by secret logical segregation of the key sets into sections by different construction methods, where different transformations are applied to different sections, and characterized by non-constant number of subset sum solutions to ciphertext, where resolution protocols are employed when necessary to resolve non-unique subset sum solutions at the decryptor.