| Description |
1 online resource |
| Series |
London Mathematical Society lecture note series
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| Bibliography |
Includes bibliographical references and index. |
| Contents |
Cover -- Half title -- Title -- Copyright -- Contents -- List of Contributors -- Preface -- 1 Introduction -- 1.1 Outline -- 1.2 Biographical Sketch -- 1.3 Overview -- 1.4 Simultaneous Inversion -- 2 Montgomery Arithmetic from a Software Perspective -- 2.1 Introduction -- 2.2 Montgomery Multiplication -- 2.2.1 Interleaved Montgomery Multiplication -- 2.2.2 Using Montgomery Arithmetic in Practice -- 2.2.3 Computing the Montgomery Constants [(mu)] and R[sup(2)] -- 2.2.4 On the Final Conditional Subtraction |
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2.2.5 Montgomery Multiplication in F[sub(2sup(k))]2.3 Using Primes of a Special Form -- 2.3.1 Faster Modular Reduction with Primes of a Special Form -- 2.3.2 Faster Montgomery Reduction with Primes of a Special Form -- 2.4 Concurrent Computing of Montgomery Multiplication -- 2.4.1 Related Work on Concurrent Computing of Montgomery Multiplication -- 2.4.2 Montgomery Multiplication Using SIMD Extensions -- 2.4.3 A Column-Wise SIMD Approach -- 2.4.4 Montgomery Multiplication Using the Residue Number System Representation |
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3 Hardware Aspects of Montgomery Modular Multiplication3.1 Introduction and Summary -- 3.2 Historical Remarks -- 3.3 Montgomery's Novel Modular Multiplication Algorithm -- 3.4 Standard Acceleration Techniques -- 3.5 Shifting the Modulus N -- 3.5.1 The Classical Algorithm -- 3.5.2 Montgomery -- 3.6 Interleaving Multiplication Steps with Modular Reduction -- 3.7 Accepting Inaccuracy in Quotient Digits -- 3.7.1 Traditional -- 3.7.2 Bounding the Partial Product -- 3.7.3 Montgomery -- 3.7.4 Summary -- 3.8 Using Redundant Representations -- 3.8.1 Traditional |
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3.8.2 Montgomery3.9 Changing the Size of the Hardware Multiplier -- 3.10 Shifting an Operand -- 3.10.1 Traditional -- 3.10.2 Montgomery -- 3.11 Precomputing Multiples of B and N -- 3.12 Propagating Carries and Carry-Save Inputs -- 3.13 Scaling the Modulus -- 3.14 Systolic Arrays -- 3.14.1 A Systolic Array for A [(times)] B -- 3.14.2 Scalability -- 3.14.3 A Linear Systolic Array -- 3.14.4 A Systolic Array for Modular Multiplication -- 3.15 Side-Channel Concerns and Solutions -- 3.16 Logic Gate Technology -- 3.17 Conclusion |
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4 Montgomery Curves and the Montgomery Ladder4.1 Introduction -- 4.2 Fast Scalar Multiplication on the Clock -- 4.2.1 The Lucas Ladder -- 4.2.2 Differential Addition Chains -- 4.3 Montgomery Curves -- 4.3.1 Montgomery Curves as Weierstrass Curves -- 4.3.2 The Group Law for Weierstrass Curves -- 4.3.3 Other Views of the Group Law -- 4.3.4 Edwards Curves and Their Group Law -- 4.3.5 Montgomery Curves as Edwards Curves -- 4.3.6 Elliptic-Curve Cryptography (ECC) -- 4.3.7 Examples of Noteworthy Montgomery Curves -- 4.4 Doubling Formulas without y |
| Summary |
This book highlights the many ideas and algorithms that Peter L. Montgomery has contributed to computational number theory and cryptography. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Montgomery, Peter L., 1947-
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Montgomery, Peter L., 1947- https://id.oclc.org/worldcat/entity/E39PBJdmkcjM7DdQHRH6Fc3hHC |
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Number theory.
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Cryptography -- Mathematics.
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MATHEMATICS -- Algebra -- Intermediate. |
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Algoritmos computacionales |
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Criptografía |
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Cryptography -- Mathematics |
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Number theory |
| Added Author |
Bos, Joppe W., editor.
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Lenstra, A. K. (Arjen K.), 1956- editor. https://id.oclc.org/worldcat/entity/E39PBJx8KbQxkqH7GcDV48VQv3
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| Other Form: |
Print version: Topics in computational number theory inspired by Peter L. Montgomery. Cambridge : Cambridge University Press, 2017 9781107109353 (DLC) 2017023049 (OCoLC)991727148 |
| ISBN |
9781108585958 (electronic bk.) |
|
1108585957 (electronic bk.) |
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9781316271575 |
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1316271579 |
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9781107109353 |
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1107109353 |
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