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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