This paper proposes a security architecture for optical code division multiple access networks based on lattice cryptography. Unlike existing approaches, which have mainly focused on optical components such as phase masks and delay lines, our cryptosystem encompasses a secure code construction process. In fact, given a set of optical orthogonal codewords, we associate a pair of bases (a public basis and a private basis) to every user and we show that the projection of a codeword on the public basis of the receiver and the addition of a random error enhances the confidentiality performance of the code. The proposed public key cryptosystem is based on lattice cryptography. The security of this scheme relies mainly on the complexity of the closest vector-problem in an integer lattice. We found that our technique performs better than the existing approaches in terms of robustness to cryptanalysis. We also study the security of our lattice cryptosystem with regard to the properties of the bases pairs and the error vectors.
Abstract In 2005, O.Regev proposed the first LWE public key cryptosystem at Tel Aviv University in Israel based on LWE distribution
As,χ . Because of this paper, Regev won the highest award for theoretical computer science in 2018—the Godel Award. The size of public key is
O~(n2) bits, and the size of private key s and ciphertext is
O~(n) bits. The plaintext encrypted each time is 1 bit. In fact, the LWE public key cryptosystem is a probabilistic cryptosystem, which depends on a high probability algorithm. Since the security of LWE problem has been clearly proved (see Chap. 3 ), the LWE cryptosystem has received extensive attention as soon as it was proposed, and it becomes the most cutting-edge research topic in the lattice-based cryptosystem study.