| The appearance of quantum computer will impose a serious threat on thesecurity of the traditional public key cryptosystems based on the number-theoreticintractable problems. The design and analysis of quantum-resistant public keycryptosystems have been a hot research topic in recent years in the cryptographicliterature. Lattice-based public key cryptosystems is a typical post-quantum publickey cipher, and the linear algebraic structure of lattices makes lattice-based publickey cryptosystems obtain relatively high encryption and decryption speed. However,lattice-based public key cryptosystems always have some shortcomings; forexample, the secret/public key sizes are too large. Lattice cryptography is a hotresearch area in recent years.The dissertation mainly studies the implementation related issues of latticealgorithms, and also two lattice cryptosystems. Firstly, we analyze and implementsome special lattice algorithms used in lattice encryption schemes. Then we verifythe implementations via a strong designated verifier signature scheme. Finally, weimplement an learning with errors (LWE)-based lattice public key cryptosystems,and carry out a serious software examination on the implementation. Thecontributions of the dissertation are summarized as follows.1. We analyze the features of the lattice algorithms, study the implementationmethods of the lattice algorithms, and define the basic methods for thesoftware implementation and examination on the lattice algorithms.2. We implement the generation of Gaussian distribution on lattices, smalllattice basis delegation technique based on the number theory library (NTL).We also implement a strong designated verifier signature scheme, and studythe implementation scheme with respect to the computational efficiency andparameter specification.3. We implement a LWE-based key dependent message (KDM) secureencryption scheme, and test the scheme in terms of correctness,computational time, and marginal conditions. |
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