Successful attack on permutation-parity-machine-based neural cryptography

Abstract

An algorithm is presented which implements a probabilistic attack on the key-exchange protocol based on permutation parity machines. Instead of imitating the synchronization of the communicating partners, the strategy consists of a Monte Carlo method to sample the space of possible weights during inner rounds and an analytic approach to convey the extracted information from one outer round to the next one. The results show that the protocol under attack fails to synchronize faster than an eavesdropper using this algorithm. Interacting feed-forward neural networks can synchronize by mutual learning [1,2]. If two networks A and B are trained with examples consisting of random inputs and the corresponding output of the other one, their weight vectors converge. In the case of tree parity machines (TPMs) this mutual synchronization of A and B requires fewer examples than training a third network E successfully [3][4][5][6][7]. Based on this effect a TPM-based neural key-exchange protocol has been developed [8][9][10][11] and shown to be useful in embedded devices [12,13] as well as being sufficiently secure against several attacks [7].

Security analysis and improvement to permutation parity machine

“…Hence these attacks are most suited for TPM. Recently proposed probabilistic attack on neural cryptography does not mimic the synchronization process, instead tries to guess the state vector of one of the participant by taking sample of weights in a space using Monte Carlo approach and transfer the information acquired in the preceding outer round to the next one using analytical approach [3].…”

“…PPM E has parameters (G, K, N) equal to . Additionally, the eavesdropper has probabilistic vector which is initialized to ⁄ at the beginning of the attack since there is no prior knowledge obtained about the synchronization [3], [4]. position in the probability vector based on π.…”

“…The most successful attack on the PPM based key exchange protocol is the probabilistic attack [3]. The eavesdropper E uses similar PPM architecture with parameter G, K and N and it is assumed that eavesdropper also knows the synchronization algorithm, such that eavesdropper applies a feedback to PPM E network using output of hidden neuron and parity of weights of each perceptron.…”

“…Cryptography is the practice of ensuring confidentiality, integrity and availability [1][2][3][4][5]. It is a crucial viewpoint for secure correspondence.…”

Neural synchronization based secret key exchange over public channels: A survey

“…(Fig.2. ) Another widely used model of such end point networks is a binary variation of the TPM-the Permutation Parity Machine [15]. Another upcoming model of such networks, which is also a variation of the Tree Parity Machine, is the c, which has almost similar topology to the TPM [16].…”