by Weisheng Qiu (Peking University, China)

This book introduces the recent progress on the multiplier conjecture, prime power conjecture, Lander conjecture; including the author's and his graduate student T Feng's work on the multiplier conjecture. It provides a sufficiently broad introduction to algebraic approach for studying difference sets, including group ring, representation theory of finite groups, cyclotomic fields, etc. It also introduces the intricate relationships between difference sets and cryptography, for example, quasi-perfect sequences and cyclic (4n-1, 2n-1, n-1)- difference sets, bent functions and Hadamard difference sets, perfect nonlinear maps and semiregular relative difference sets.

• Stream Cipher and Difference Sets
• Symmetric Designs and Difference Sets
• Algebraic Approach for Studying Difference Sets
• Multipliers and Multiplier Conjecture
• Difference Sets with Singer Parameters
• Paley-Hadamard Difference Sets
• Skew Difference Sets
• Planar Difference Sets
• Prime Power Conjecture
• Lander Conjecture
• Bent Functions and Hadamard Difference Sets
• The other Difference Sets with gcd(v,n)>1. Schmidt's Exponent Bound
• Perfect Nonlinear Maps for Preventing Differential Cryptanalysis
• Relative Difference Sets