Utilizing graphics processing units in cryptographic applications.

Fleissner Sebastian.Thesis (M.Phil.)--Chinese University of Hong Kong, 2006.Includes bibliographical references (leaves 91-95).Abstracts in English and Chinese.Abstract --- p.iAcknowledgement --- p.iiiChapter 1 --- Introduction --- p.1Chapter 1.1 --- The Legend of Hercules --- p.1Chapter 1.2 --- Background --- p.2Chapter 1.3 --- Research Purpose --- p.2Chapter 1.4 --- Research Overview --- p.3Chapter 1.5 --- Thesis Organization --- p.4Chapter 2 --- Background and Definitions --- p.6Chapter 2.1 --- General Purpose GPU Computing --- p.6Chapter 2.1.1 --- Four Generations of GPU Hardware --- p.6Chapter 2.1.2 --- GPU Architecture & Terms --- p.7Chapter 2.1.3 --- General Purpose GPU Programming --- p.9Chapter 2.1.4 --- Shader Programming Languages --- p.12Chapter 2.2 --- Cryptography Overview --- p.13Chapter 2.2.1 --- "Alice, Bob, and Friends" --- p.14Chapter 2.2.2 --- Cryptographic Hash Functions --- p.14Chapter 2.2.3 --- Secret Key Ciphers --- p.15Chapter 2.2.4 --- Public Key Encryption --- p.16Chapter 2.2.5 --- Digital Signatures --- p.17Chapter 2.3 --- The Montgomery Method --- p.18Chapter 2.3.1 --- Pre-computation Step --- p.19Chapter 2.3.2 --- Obtaining the Montgomery Representation --- p.19Chapter 2.3.3 --- Calculating the Montgomery Product(s) --- p.19Chapter 2.3.4 --- Calculating final result --- p.20Chapter 2.3.5 --- The Montgomery Exponentiation Algorithm . . --- p.20Chapter 2.4 --- Elliptic Curve Cryptography --- p.21Chapter 2.4.1 --- Introduction --- p.21Chapter 2.4.2 --- Recommended Elliptic Curves --- p.22Chapter 2.4.3 --- Coordinate Systems --- p.23Chapter 2.4.4 --- Point Doubling --- p.23Chapter 2.4.5 --- Point Addition --- p.24Chapter 2.4.6 --- Double and Add --- p.25Chapter 2.4.7 --- Elliptic Curve Encryption --- p.26Chapter 2.5 --- Related Research --- p.28Chapter 2.5.1 --- Secret Key Cryptography on GPUs --- p.28Chapter 2.5.2 --- Remotely Keyed Cryptographics --- p.29Chapter 3 --- Proposed Algorithms --- p.30Chapter 3.1 --- Introduction --- p.30Chapter 3.2 --- Chapter Organization --- p.31Chapter 3.3 --- Algorithm Design Issues --- p.31Chapter 3.3.1 --- Arithmetic Density and GPU Memory Access . --- p.31Chapter 3.3.2 --- Encoding Large Integers with Floating Point Numbers --- p.33Chapter 3.4 --- GPU Montgomery Algorithms --- p.34Chapter 3.4.1 --- Introduction --- p.34Chapter 3.4.2 --- GPU-FlexM-Prod Specification --- p.37Chapter 3.4.3 --- GPU-FlexM-Mul Specification --- p.43Chapter 3.4.4 --- GPU-FlexM-Exp Specification --- p.45Chapter 3.4.5 --- GPU-FixM-Prod Specification --- p.46Chapter 3.4.6 --- GPU-FixM-Mul Specification --- p.50Chapter 3.4.7 --- GPU-FixM-Exp Specification --- p.52Chapter 3.5 --- GPU Elliptic Curve Algorithms --- p.54Chapter 3.5.1 --- GPU-EC-Double Specification --- p.55Chapter 3.5.2 --- GPU-EC-Add Specification --- p.59Chapter 3.5.3 --- GPU-EC-DoubleAdd Specification --- p.64Chapter 4 --- Analysis of Proposed Algorithms --- p.67Chapter 4.1 --- Performance Analysis --- p.67Chapter 4.1.1 --- GPU-FlexM Algorithms --- p.69Chapter 4.1.2 --- GPU-FixM Algorithms --- p.72Chapter 4.1.3 --- GPU-EC Algorithms --- p.77Chapter 4.1.4 --- Summary --- p.82Chapter 4.2 --- Usability of Proposed Algorithms --- p.83Chapter 4.2.1 --- Signcryption --- p.84Chapter 4.2.2 --- Pure Asymmetric Encryption and Decryption --- p.85Chapter 4.2.3 --- Simultaneous Signing of Multiple Messages --- p.86Chapter 4.2.4 --- Relieving the Main Processor --- p.87Chapter 5 --- Conclusions --- p.88Chapter 5.1 --- Research Results --- p.88Chapter 5.2 --- Future Research --- p.89Bibliography --- p.9