- CONSTRUCTING ISOGENIES BETWEEN ELLIPTIC CURVES OVER FINITE FIELDS
- EFFICIENT ARITHMETIC ON HYPERELLIPTIC CURVES WITH
- Preliminary Remarks on Algebraic This is a draft chapter from version 1.0 of the book "Mathematics of Public Key Cryptography" by
- Factoring and Discrete Logarithms in Subexponential Time
- EASY DECISION-DIFFIE-HELLMAN GROUPS STEVEN D. GALBRAITH AND VICTOR ROTGER
- Implementing the Tate Steven Galbraith
- Author Index Abdalla, M., 436, 439
- Invisibility and Anonymity of Undeniable and Con rmer Steven D. Galbraith ?1 and Wenbo Mao 2??
- Factoring and Discrete Logarithms using Pseudorandom Walks
- Curves and Divisor Class Groups This is a draft chapter from version 1.0 of the book "Mathematics of Public Key Cryptography" by
- Easy decisions: Applications of pairings in cryptography
- Elliptic Curves This is a draft chapter from version 1.0 of the book "Mathematics of Public Key Cryptography"
- Rational Maps on Curves and This is a draft chapter from version 1.0 of the book "Mathematics of Public Key Cryptography"
- The Diffie-Hellman Problem and Cryptographic Applications
- Hyperelliptic Curves This is a draft chapter from version 1.0 of the book "Mathematics of Public Key Cryptography" by
- Applications of Frobenius Expansions
- Limitations of Constructive Weil Descent Steven D. Galbraith \Lambda
- An analysis of the vector decomposition problem Steven D. Galbraith1
- This is a draft chapter from version 1.0 of the book "Mathematics of Public Key Cryptography" by Steven Galbraith, available from http://www.isg.rhul.ac.uk/~sdg/crypto-book/ The copyright for
- Equations For Modular Curves Steven D. Galbraith
- An Improvement to the Gaudry-Schost Algorithm for Multidimensional Discrete Logarithm Problems
- DISTORTION MAPS FOR GENUS TWO CURVES STEVEN D. GALBRAITH AND JORDI PUJOL`AS
- Efficient Hyperelliptic Arithmetic using Balanced Representation for Divisors
- WEIL DESCENT OF JACOBIANS STEVEN D. GALBRAITH
- VERBOSE VERSION RATIONAL POINTS ON X+
- THE PROBABILITY THAT THE NUMBER OF POINTS ON AN ELLIPTIC CURVE OVER A FINITE FIELD IS PRIME
- The Weil pairing on elliptic curves over C Steven D. Galbraith
- 1 Introduction 25 1.1 Public Key Cryptography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
- Acknowledgements The book grew out of my lecture notes from the Masters course "Public key cryptography" at Royal
- Introduction This is a draft chapter from version 1.0 of the book "Mathematics of Public Key Cryptography" by
- Basic Algorithmic Number Theory This is a draft chapter from version 1.0 of the book "Mathematics of Public Key Cryptography" by
- Hash Functions and MACs Hash functions are important tools in cryptography. In public key cryptography, they are used in
- Tori, LUC and XTR This is a draft chapter from version 1.0 of the book "Mathematics of Public Key Cryptography" by
- Basic Discrete Logarithm This is a draft chapter from version 1.0 of the book "Mathematics of Public Key Cryptography" by
- This is a draft chapter from version 1.0 of the book "Mathematics of Public Key Cryptography" by Steven Galbraith. The copyright for this chapter is held by Steven Galbraith.
- Lattice Basis Reduction This is a draft chapter from version 1.0 of the book "Mathematics of Public Key Cryptography" by
- Algorithms for the Closest and Shortest Vector Problems
- Coppersmith's Method and Related Applications
- Cryptosystems Based on Lattices This is a draft chapter from version 1.0 of the book "Mathematics of Public Key Cryptography" by
- Digital Signatures Based on Discrete Logarithms
- Public Key Encryption Based on Discrete Logarithms
- Isogenies of Elliptic Curves This is a draft chapter from version 1.0 of the book "Mathematics of Public Key Cryptography" by
- On the Decisional Diffie-Hellman Problem Jordi Pujol`as Boix
- Improvements to the Gaudry-Schost Algorithm for Multidimensional discrete
- Bibliography [1] M. Abdalla, M. Bellare, and P. Rogaway, DHIES: An encryption scheme based on the Diffie-
- RSA-based Undeniable Signatures For General Steven D. Galbraith 1 , Wenbo Mao 2 and Kenneth G. Paterson 3
- Elliptic Curve Paillier Schemes Steven D. Galbraith ?
- Primality Testing and Integer Factorisation using Algebraic
- SUPERSINGULAR CURVES IN CRYPTOGRAPHY STEVEN D. GALBRAITH
- Tunable balancing of RSA S. D. Galbraith, C. Heneghan and J. F. McKee
- Supersingular curves in cryptography Steven Galbraith
- The RSA and Rabin Cryptosystems
- Hyperelliptic pairings Steven D. Galbraith1
- The Diffie-Hellman Problem This is a draft chapter from version 1.0 of the book "Mathematics of Public Key Cryptography" by
- 2D Gaudry-Schost Algorithm On Equivalence December 1, 2010
- Equations For Modular Curves Steven D. Galbraith
- Hints and Solutions to Chapter 1: Introduction