Number-Theoretic Methods in Cryptology

Front Matter ....Pages I-XX
Front Matter ....Pages 1-1
 A Crossbred Algorithm for Solving Boolean Polynomial Systems  (Antoine Joux, Vanessa Vitse)....Pages 3-21
Front Matter ....Pages 23-23
 Generation and Implementation of Cryptographically Strong Elliptic Curves  (Przemysław Dąbrowski, Rafał Gliwa, Janusz Szmidt, Robert Wicik)....Pages 25-36
 On the Possibility of Transformation of Multidimensional ECDLP into 1-Dimensional ECDLP  (Michał Wroński, Tomasz Kijko)....Pages 37-47
 Explicit Bound for the Prime Ideal Theorem in Residue Classes  (Maciej Grześkowiak)....Pages 48-68
Front Matter ....Pages 69-69
 Short Solutions to Nonlinear Systems of Equations  (Alan Szepieniec, Bart Preneel)....Pages 71-90
 A Novel RSA-Like Cryptosystem Based on a Generalization of the Rédei Rational Functions  (Nadir Murru, Francesco M. Saettone)....Pages 91-103
 Commutativity, Associativity, and Public Key Cryptography  (Jacques Patarin, Valérie Nachef)....Pages 104-117
Front Matter ....Pages 119-119
 Computational Differential Privacy from Lattice-Based Cryptography  (Filipp Valovich, Francesco Aldà)....Pages 121-141
 Explicit Formula for Gram-Schmidt Vectors in LLL with Deep Insertions and Its Applications  (Junpei Yamaguchi, Masaya Yasuda)....Pages 142-160
Front Matter ....Pages 161-161
 Factoring n and the Number of Points of Kummer Hypersurfaces mod n  (Robert Dryło, Jacek Pomykała)....Pages 163-177
 Detection of Primes in the Set of Residues of Divisors of a Given Number  (Rafał Bystrzycki)....Pages 178-194
Front Matter ....Pages 195-195
 The Measures of Pseudorandomness and the NIST Tests  (László Mérai, Joël Rivat, András Sárközy)....Pages 197-216
 On the Cross-Combined Measure of Families of Binary Lattices and Sequences  (Katalin Gyarmati)....Pages 217-238
Front Matter ....Pages 239-239
 The Cube Attack on Courtois Toy Cipher  (Janusz Szmidt)....Pages 241-253
 Near Butson-Hadamard Matrices and Nonlinear Boolean Functions  (Sibel Kurt, Oğuz Yayla)....Pages 254-266
 Multi-secret Sharing Scheme for Level-Ordered Access Structures  (Appala Naidu Tentu, Abdul Basit, K. Bhavani, V. Ch. Venkaiah)....Pages 267-278
Back Matter ....Pages 279-279