Binary Additive Counter Stream Ciphers&Cunsheng Ding,Wenpei Si 1
1 Introduction 1
2 Possible attacks and design criteria 3
3 Example 1:the Legendre cipher 9
4 Example 2:the two-prime cipher 14
5 Conclusions and concluding remarks 19
References 21
Partial Difference Sets from Quadratic Forms and p-ary Weakly Regular Bent Functions&Tao Feng,Bin Wen,Qing Xiang,Jianxing Yin 25
1 Introduction 25
2 Partial difference sets from quadratic forms and uniform cyclotomy 30
3 Partial difference sets from weakly regular p-ary bent functions 34
References 39
Governing Fields of the 4-rank of K20(？)as p Varies Xuejun Guo,Hourong Qin 41
1 Introduction 41
2 The governing field of the 4-rank of K2？F 43
3 The governing field of the 8-rank of K2？F 47
References 49
Word-oriented Linear Feedback Shift Registers:σ-LFSRs Wenbao&Han,Xianghui Liu,Guang Zeng,Gangmin Tan 51
1 Introduction 51
2 Model of σ-LFSR 53
3 Cryptographic properties 55
4 σ-LFSRs suitable for software implementation 62
5 Application of σ-LFSRs 65
6 Conclusion 69
Statistics of Zeros of Families of L-functions over Function Fields:A Survey&Wen-Ching Winnie Li,Maosheng Xiong 73
1 Introduction 73
2 Hyperelliptic curves 75
3 Cyclic l-fold covers of the projective line 78
4 Elliptic curves over a rational function field and generalizations 80
5 Concluding remarks 82
References 82
Lectures on p-adic Zeta Functions and(ψ,Γ)-modules&Yi Ouyang 85
1 Introduction 85
2 Continuous functions,measures and distributions over Zp 86
3 The p-adic zeta function of Kubota-Leopoldt 111
4 (ψ,Γ)-modules and Galois cohomology 118
5 (ψ,Γ)-modules and 1wasawa theory 135
References 146
Conjectures and Results on x2 mod p2 with 4p=x2+dy2&Zhi-Wei Sun 149
1 Introduction 149
2 Using Apéry polynomials and products of three binomial coefficients 160
3 Using the polynomials Sn(x)=∑？ 167
4 Using the function Fn(x)=？ 176
5 Using the function Gn(x)=？ 181
6 Using an(x)=？ 183
7 Miscellaneous things 188
References 195
Harmonic Weak Maass Forms,Automorphic Green Functions,and Period Integrals&Tonghai Yang 199
1 Introduction 199
2 Shimura varieties of orthogonal type and their Kudla cycles 203
3 Harmonic weak Maass forms,regularized theta lifting,and automorphic Green functions 205
4 Eisenstein series associated to coherent and incoherentquadratic spaces 210
5 Period integrals of the automorphic Green functionφ(z,h;f) 213
6 Big CM values of automorphic Green functions 218
References 222
Some Recent Progress in Higher Koszulity&Yu Ye,Pu Zhang 225
1 Preliminaries 226
2 Higher Koszulity 227
3 Higher Koszul complexes 228
4 Hilbert and Poincaré series 230
5 Dual algebras and Ext-algebras 232
6 Generalized d-Koszul modules 233
7 Lattice distributivity and Koszulity 234
8 More related topics 236
References 238