| Description |
1 online resource |
| Series |
Schriftenreihe der Institute Für Systemdynamik (ISD) und Optische Systeme (IOS) |
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Schriftenreihe der Institute Für Systemdynamik (ISD) und Optische Systeme (IOS)
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| Contents |
Intro -- Acknowledgements -- Abstract -- Contents -- Acronyms -- List of Figures -- List of Tables -- 1 Introduction -- 1.1 Problem Statement and Motivation -- 1.2 Structure of the Thesis -- 2 Elliptic Curve Cryptography -- 2.1 Cryptography for Flash Memory Controllers -- 2.2 Applications of Elliptic Curve Cryptographic (ECC) Systems -- 2.2.1 Elliptic Curves -- 2.2.2 Key Exchange -- 2.2.3 Digital Signatures -- 2.3 Elliptic Curve Point Multiplication -- 2.4 Elliptic Curve Geometry and Group Laws -- 2.4.1 Elliptic Curve Geometry -- 2.4.2 Group Laws for Prime Curves |
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4.1 Montgomery Arithmetic -- 4.2 Reduction over Gaussian Integers using the Absolute Value -- 4.3 Reduction over Gaussian integers using the Manhattan Weight -- 4.3.1 Montgomery reduction algorithm using the Manhattan weight -- 4.3.2 Reduction after addition (or subtraction) -- 4.4 Simplifying the Reduction based on the Manhattan Weight -- 4.5 Discussion -- 5 Architecture of the ECC Coprocessor for Gaussian Integers -- 5.1 Coprocessor Architecture for Gaussian Integers -- 5.1.1 Basic Concepts of the Proposed Design -- 5.1.2 Hardware Architecture -- 5.1.3 Instruction Set Architecture |
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5.1.4 Data Memory -- 5.1.5 Arithmetic Unit for Gaussian Integer Fields -- 5.2 ECC Coprocessor Architecture for Prime Fields -- 5.2.1 Preliminary Considerations and Modulo Reduction -- 5.2.2 Architecture -- 5.2.3 Instruction Set -- 5.2.4 Arithmetic Unit -- 5.3 Implementation Results -- 5.4 Discussion -- 6 Compact Architecture of the ECC Coprocessor for Binary Extension Fields -- 6.1 Group Laws and Projective Coordinates for Binary Extension Fields -- 6.1.1 Group Law for Binary Extension Curves -- 6.1.2 Projective Coordinates for Elliptic Curves over Binary Extension Fields |
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6.2 ECC Coprocessor Architecture -- 6.2.1 Instruction Set Architecture -- 6.2.2 Data Memory -- 6.2.3 Arithmetic Unit -- 6.3 Results and Discussion -- 7 The Parallel Dictionary LZW Algorithm for Flash Memory Controllers -- 7.1 Data Compression for Flash Memory Devices -- 7.1.1 Reducing the Write Amplification -- 7.1.2 Combining Data Compression and Error-correcting Codes -- 7.1.3 Suitable Data Compression Scheme -- 7.2 Parallel Dictionary LZW (PDLZW) Algorithm -- 7.3 Address Space Partitioning for the PDLZW -- 7.3.1 Data Model -- 7.3.2 Partitioning the PDLZW Address Space |
| Summary |
In this work, algorithms and architectures for cryptography and source coding are developed, which are suitable for many resource-constrained embedded systems such as non-volatile flash memories. A new concept for elliptic curve cryptography is presented, which uses an arithmetic over Gaussian integers. Gaussian integers are a subset of the complex numbers with integers as real and imaginary parts. Ordinary modular arithmetic over Gaussian integers is computational expensive. To reduce the complexity, a new arithmetic based on the Montgomery reduction is presented. For the elliptic curve point multiplication, this arithmetic over Gaussian integers improves the computational efficiency, the resistance against side channel attacks, and reduces the memory requirements. Furthermore, an efficient variant of the Lempel-Ziv-Welch (LZW) algorithm for universal lossless data compression is investigated. Instead of one LZW dictionary, this algorithm applies several dictionaries to speed up the encoding process. Two dictionary partitioning techniques are introduced that improve the compression rate and reduce the memory size of this parallel dictionary LZW algorithm. About the Author Malek Safieh is a research scientist in the field of cryptography and data compression |
| Bibliography |
Includes bibliographical references |
| Notes |
Online resource; title from PDF title page (SpringerLink, viewed August 25, 2021) |
| Subject |
Cryptography.
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Data encryption (Computer science)
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Revision control (Computer science) -- Mathematics
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Nonvolatile random-access memory.
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Cryptography
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Data encryption (Computer science)
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Nonvolatile random-access memory
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| Form |
Electronic book
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| ISBN |
9783658344597 |
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3658344598 |
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