Neural synchronization based secret key exchange over public channels: A survey <s> VII. QUERIES, SYNAPTIC DEPTH AND ERRONEOUS INFORMATION <s> Neural cryptography is based on a competition between attractive and repulsive stochastic forces. A feedback mechanism is added to neural cryptography which increases the repulsive forces. Using numerical simulations and an analytic approach, the probability of a successful attack is calculated for different model parameters. Scaling laws are derived which show that feedback improves the security of the system. In addition, a network with feedback generates a pseudorandom bit sequence which can be used to encrypt and decrypt a secret message. <s> BIB001 </s> Neural synchronization based secret key exchange over public channels: A survey <s> VII. QUERIES, SYNAPTIC DEPTH AND ERRONEOUS INFORMATION <s> Neural cryptography is based on synchronization of tree parity machines by mutual learning. We extend previous key-exchange protocols by replacing random inputs with queries depending on the current state of the neural networks. The probability of a successful attack is calculated for different model parameters using numerical simulations. The results show that queries restore the security against cooperating attackers. The success probability can be reduced without increasing the average synchronization time. <s> BIB002 </s> Neural synchronization based secret key exchange over public channels: A survey <s> VII. QUERIES, SYNAPTIC DEPTH AND ERRONEOUS INFORMATION <s> Different scaling properties for the complexity of bidirectional synchronization and unidirectional learning are essential for the security of neural cryptography. Incrementing the synaptic depth of the networks increases the synchronization time only polynomially, but the success of the geometric attack is reduced exponentially and it clearly fails in the limit of infinite synaptic depth. This method is improved by adding a genetic algorithm, which selects the fittest neural networks. The probability of a successful genetic attack is calculated for different model parameters using numerical simulations. The results show that scaling laws observed in the case of other attacks hold for the improved algorithm, too. The number of networks needed for an effective attack grows exponentially with increasing synaptic depth. In addition, finite-size effects caused by Hebbian and anti-Hebbian learning are analyzed. These learning rules converge to the random walk rule if the synaptic depth is small compared to the square root of the system size. <s> BIB003 </s> Neural synchronization based secret key exchange over public channels: A survey <s> VII. QUERIES, SYNAPTIC DEPTH AND ERRONEOUS INFORMATION <s> This work is a new proposal of neural synchronization, which is a communication of two Tree Parity Machines (TPMs) for agreement on a common secret key over a public channel. This can be achieved by two TPMs, which are trained on their mutual output, which can synchronize to a time dependent state of identical synaptic weight vectors. In the proposed TPMs random inputs are replaced with queries, which are considered. The queries depend on the current state of A and B TPMs. Then, TPM's hidden layers of each output vectors are compared. That is, the output vectors of hidden unit using Hebbian learning rule and dynamic unit using Random walk learning rule are compared. Among the compared values, the output layer receives one of the best values. In this paper, the increased synchronization time of the co-operating attacker against the flipping attack is also analyzed. <s> BIB004 </s> Neural synchronization based secret key exchange over public channels: A survey <s> VII. QUERIES, SYNAPTIC DEPTH AND ERRONEOUS INFORMATION <s> Neural cryptography deals with the problem of “key exchange” between two neural networks using the mutual learning concept. The two networks exchange their outputs (in bits) and the key between the two communicating parties is eventually represented in the final learned weights, when the two networks are said to be synchronized. Security of neural synchronization is put at risk if an attacker is capable of synchronizing with any of the two parties during the training process. Therefore, diminishing the probability of such a threat improves the reliability of exchanging the output bits through a public channel. The synchronization with feedback algorithm is one of the existing algorithms that enhances the security of neural cryptography. This paper proposes three new algorithms to enhance the mutual learning process. They mainly depend on disrupting the attacker confidence in the exchanged outputs and input patterns during training. The first algorithm is called “Do not Trust My Partner” (DTMP), which relies on one party sending erroneous output bits, with the other party being capable of predicting and correcting this error. The second algorithm is called “Synchronization with Common Secret Feedback” (SCSFB), where inputs are kept partially secret and the attacker has to train its network on input patterns that are different from the training sets used by the communicating parties. The third algorithm is a hybrid technique combining the features of the DTMP and SCSFB. The proposed approaches are shown to outperform the synchronization with feedback algorithm in the time needed for the parties to synchronize. <s> BIB005
In 2005, Ruttor et al. extended previous key-exchange protocols in a novel way. They introduced the concept of querie BIB002 . More information, in the form of queries, was used to train the neural networks at the two end points of the channel. Random inputs to these networks were replaced with queries, which were a function of the current state of the neural networks. The authors demonstrated that these queries improved the security against cooperating or majority attacks. This was hailed as a major result in the field. As previously Shacham et al. showed that cooperative attackers can break the security provided by neural synchronization based cryptography. Furthermore, these authors had also demonstrated that the success probability of the attacker, even if it is a cooperative attacker, can be reduced without increasing the average synchronization time of the neural networks. The concept of queries was further extended and explored later. It was demonstrated that if the connections (end points of the channels) are generating inputs which are correlated with their state, and the end points are asking their partner for the corresponding output bit, then the overlap between input and weight vector is so low that the additional information does not reveal much about the internal states [18] . In this way the queries introduced a mutual influence between end points which was not available to the attacking network. When queries are incorporated along with the Hebbian training rule, then it was found that the probability of successful attack decreases significantly, even for cooperative attacks BIB004 . Again in 2006, Ruttor et al. demonstrated and also proved that incrementing the synaptic depth of the neural networks increased the synchronization time of the networks, but only polynomially BIB003 . But this ensured that the probability of successful geometric attacks on the neural synchronization based key exchange system is reduced exponentially. They utilized the genetic algorithm method to select the fittest neural networks for such a process. Furthermore, it was shown in their work that the number of networks needed for a majority/cooperative attack to be successful grows exponentially with increasing synaptic depth. As discussed previously, security of neural synchronization based key exchange is put at risk if an attacker is capable of synchronizing with any of the two parties during the training or learning process. Therefore, diminishing the probability of such a threat improves the reliability of exchanging the output bits through a public channel. The synchronization with feedback algorithm is one of the existing algorithms that enhance the security of neural cryptography BIB001 . In the beginning of this decade (2010), algorithms were proposed to enhance the mutual learning process. They mainly depended on disrupting the attacker confidence in the exchanged outputs and input patterns during training. One such algorithm relies on one party sending erroneous output bits, with the other party being capable of predicting and correcting this error BIB005 . Another such proposed algorithm functions in a way where inputs are kept partially secret and the attacker has to train its network on input patterns that are different from the training sets used by the communicating parties. It was also shown that a hybrid of these two approaches is also satisfactory.