Synchronization of Tree Parity Machines Using Nonbinary Input Vectors

Abstract

Neural cryptography is the application of artificial neural networks (ANNs) in the subject of cryptography. The functionality of this solution is based on a tree parity machine (TPM). It uses ANNs to perform secure key exchange between network entities. This brief proposes improvements to the synchronization of two TPMs. The improvement is based on learning ANN using input vectors that have a wider range of values than binary ones. As a result, the duration of the synchronization process is reduced. Therefore, TPMs achieve common weights in a shorter time due to the reduction of necessary bit exchanges. This approach improves the security of neural cryptography.

Security of Neural Network-Based Key Agreement Protocol for Smart Grids

“…During simulations, the number of total iterations, number of weight update steps, synchronization scores of benign TPMs and synchronization scores of the best-synchronized adversarial TPMs are gathered. The formula for synchronization score is defined in (7) [19]. Additionally, the index of synchronization when S score of one evil TPMs is equal to 1 is also collected.…”

“…TPM has been the subject of much research [2,3,[10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. Metzler et al [2], Kinzel et al [3] and Ruttor et al [11] have shown that interacting neural networks can synchronize efficiently by using the mutual learning algorithm.…”

“…In [13][14][15][16][17][18][19], various improvements to TPMs were proposed. Researchers proposed an improved variant of the learning algorithm in scenarios where both parties are able to share a secret beforehand [13].…”

“…Vector-Valued Tree Parity Machine (VVTPM) is the generalization of this idea and uses binary vectors as inputs [18]. The last improvement from this group is NBTPM, wherein the authors proposed the usage of integers instead of binary numbers [19]. NBTPM speeds up the synchronization of TPMs and introduces a new parameter M, which controls the variability of input vectors and adds an additional dimension for determining the most suitable TPM structure for users.…”

“…NBTPM speeds up the synchronization of TPMs and introduces a new parameter M, which controls the variability of input vectors and adds an additional dimension for determining the most suitable TPM structure for users. Moreover, in [19], the authors discuss the effect of extrema of values and the reason for synchronization time reduction caused by the introduction of parameter M.…”