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This open access book covers the most cutting-edge and hot research topics and fields of post-quantum cryptography. The main purpose of this book is to focus on the computational complexity theory of lattice ciphers, especially the reduction principle of Ajtai, in order to fill the gap that post-quantum ciphers focus on the implementation of encryption and decryption algorithms, but the theoretical proof is insufficient. In Chapter 3, Chapter 4 and Chapter 6, author introduces the theory and technology of LWE distribution, LWE cipher and homomorphic encryption in detail. When using random...

Lignin is the main natural resource of aromatic structures on Earth. With the depletion of fossil oil and increased environmental concerns, renewable resources for energy and chemical production have attracted tremendous attention from scientists and engineers. As a renewable aromatic polymer, lignin has been, for a long time, studied in terms of its biosynthesis, structures, reactivities and applications although few portions of lignins available from the industry, mainly pulping mills, have been utilized for various applications. The key for complete and efficient utilization of lignins is...

This open access book covers the most cutting-edge and hot research topics and fields of post-quantum cryptography. The main purpose of this book is to focus on the computational complexity theory of lattice ciphers, especially the reduction principle of Ajtai, in order to fill the gap that post-quantum ciphers focus on the implementation of encryption and decryption algorithms, but the theoretical proof is insufficient. In Chapter 3, Chapter 4 and Chapter 6, author introduces the theory and technology of LWE distribution, LWE cipher and homomorphic encryption in detail. When using random...