Secure and linear cryptosystems using error - correcting codes

(received ; accepted) PACS. .89.90n – Computer science and technology. Abstract. – A public-key cryptosystem, digital signature and authentication procedures based on a Gallager-type parity-check error-correcting code are presented. The complexity of the encryption and the decryption processes scale linearly with the size of the plaintext Alice sends to Bob. The public-key is pre-corrupted by Bob, whereas a private-noise added by Alice to a given fraction of the ciphertext of each encrypted plaintext serves to increase the secure channel and is the cornerstone for digital signatures and authentication. Various scenarios are discussed including the possible actions of the opponent Oscar as an eavesdropper or as a disruptor. The goal of cryptography is to enable two people, usually referred to as Alice and Bob, to communicate over an insecure channel in such a way that the opponent Oscar cannot understand and decrypt the transmitted message.[1] A block message is called a plaintext, and a long message is a sequence of plaintexts. In a general scenario, the plaintext is encrypted by Alice through the key E k and the result, ciphertext, is sent over the channel. A third party, eavesdropping on the channel, cannot determine what the plaintext was. However, Bob, who knows the encryption key, can decrypt the ciphertext using the key D k and recover the plaintext. In a private-key system, the keys E k and D k are known only to Alice and Bob, and it obviously increases the security of the channel. However, a private-key system requires communication between Alice and Bob prior to the transmission of any plaintext. This prerequisite makes the private-key communication impractical in modern communication, especially in such areas as electronic commerce and Internet-based communication. The goal of public-key systems is to devise a cryptosystem where it is computationally infeasible to determine D k given E k , and hence the encryption rule E k can be made public. The secure channel and the efficiency of a public-key cryptosystem depends on many parameters, among them: (a) the complexity to determine D k given E k ; (b) the complexity of the encryption/decryption processes; (c) the length of the ciphertext and the public-key in comparison to the length of the plaintext. The commonly used RSA cryptosystem[2] is based on the difficulty of factorizing large integers. Its main drawback is that the complexity of the encryption/decryption processes is of O(N 2)/O(N 3), where N is the …