A connection between the theory of neural networks and cryptography is presented. A new phenomenon, namely synchronization of neural networks is leading to a new method of exchange of secret messages. Numerical simulations show that two artificial networks being trained by Hebbian learning rule on their mutual outputs develop an antiparallel state of their synaptic weights. The synchronized weights are used to construct an ephemeral key exchange protocol for a secure transmission of secret data. It is shown that an opponent who knows the protocol and all details of any transmission of the data has no chance to decrypt the secret message, since tracking the weights is a hard problem compared to synchronization. The complexity of the generation of the secure channel is linear with the size of the network.PACS numbers: 87.18.Sn,89.70.+cThe ability to build a secure channel is one of the most challenging fields of research in modern communication. Since the secure channel has many applications, in particular for mobile phone, satellite and internet-based communications, there is a need for fast, effective and secure transmission protocols [1]. Here we present a novel principle of a cryptosystem based on a new phenomenon which we observe for artificial neural networks.The goal of cryptography is to enable two partners to communicate over an insecure channel in such a way that an opponent cannot understand and 1

(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 length of the plaintext (see figure 1). For small N these complexities are also small, but then the complexity to determine D k given E k may also be accessible to Oscar. It was recently found that even N = 512 may be too small to ensure a secure channel. Hence the complexity of the encryption/decryption becomes the bottleneck Typeset using EURO-T E X