Generative trapdoors for public key cryptography based on automatic entropy optimization

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.