Generative Trapdoors for Public Key Cryptography Based on Automatic Entropy Optimization

摘要

Trapdoor is a key component of public key cryptography design which is the essential security foundation of modern cryptography.Normally,the traditional way in designing a trapdoor is to identify a computationally hard problem,such as the NPC problems.So the trapdoor in a public key encryption mechanism turns out to be a type of limited resource.In this paper,we generalize the methodology of adversarial learning model in artificial intelligence and introduce a novel way to conveniently obtain sub-optimal and computationally hard trapdoors based on the automatic information theoretic search technique.The basic routine is constructing a generative architecture to search and discover a probabilistic reversible generator which can correctly encoding and decoding any input messages.The architecture includes a trapdoor generator built on a variational autoencoder(VAE)responsible for searching the appropriate trapdoors satisfying a maximum of entropy,a random message generator yielding random noise,and a dynamic classifier taking the results of the two generator.The evaluation of our construction shows the architecture satisfying basic indistinguishability of outputs under chosen-plaintext attack model(CPA)and high efficiency in generating cheap trapdoors.