Generalized Powering Functions and Their Application to Digital Signatures 1st edition by Hisayoshi Sato, Tsuyoshi Takagi, Satoru Tezuka, Kazuo Takaragi ISBN 3540205920 9783540205920
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Authors:Hisayoshi Sato, Tsuyoshi Takagi, Satoru Tezuka; Kazuo Takaragi , Tags:Advances in Cryptology – ASIACRYPT 2003 , Author sort:Hisayoshi Sato, Tsuyoshi Takagi, Satoru Tezuka & Takaragi, Kazuo , Languages:Languages:eng , Published:Published:Oct 2003
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ISBN 10: 3540205920
ISBN 13: 978-3540205920
Author: Hisayoshi Sato, Tsuyoshi Takagi, Satoru Tezuka, Kazuo Takaragi
This paper investigates some modular powering functions suitable for cryptography. It is well known that the Rabin encryption function is a 4-to-1 mapping and breaking its one-wayness is secure under the factoring assumption. The previously reported encryption schemes using a powering function are variants of either the 4-to-1 mapping or higher n-to-1 mapping, where n>4. In this paper, we propose an optimized powering function that is a 3-to-1 mapping using a p 2 q-type modulus. The one-wayness of the proposed powering function is as hard as the infeasibility of the factoring problem. We present an efficient algorithm for computing the decryption for a p 2 q-type modulus, which requires neither modular inversion nor division. Moreover, we construct new provably secure digital signatures as an application of the optimized functions. In order to achieve provable security in the random oracle model, we usually randomize a message using random hashing or padding. However, we have to compute the randomization again if the randomized message is a non-cubic residue element — it is inefficient for long messages. We propose an algorithm that can deterministically find the unique cubic residue element for a randomly chosen element.
Generalized Powering Functions and Their Application to Digital Signatures 1st Table of contents:
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Introduction
- 1.1 Overview of Digital Signatures
- 1.2 Importance of Powering Functions in Cryptography
- 1.3 Motivation for Generalized Powering Functions
- 1.4 Contribution of the Paper
- 1.5 Organization of the Paper
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Preliminaries
- 2.1 Cryptographic Basics: Digital Signatures
- 2.2 Powering Functions: Definitions and Properties
- 2.3 Generalized Powering Functions
- 2.4 Existing Approaches to Digital Signatures
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Generalized Powering Functions
- 3.1 Mathematical Definition of Generalized Powering Functions
- 3.2 Algebraic Properties of Generalized Powering Functions
- 3.2.1 Closure Properties
- 3.2.2 Inverse Functions
- 3.3 Computational Complexity and Efficiency
- 3.4 Generalizations of Standard Power Functions
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Application to Digital Signatures
- 4.1 Review of Conventional Digital Signature Schemes
- 4.1.1 RSA and ElGamal
- 4.1.2 Schnorr and DSA
- 4.2 The Role of Powering Functions in Digital Signatures
- 4.2.1 Enhancement of Signature Security
- 4.2.2 Computational Efficiency
- 4.3 Generalized Powering Functions in Signature Generation and Verification
- 4.4 Security Analysis of Digital Signature Schemes Using Generalized Powering Functions
- 4.1 Review of Conventional Digital Signature Schemes
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Efficient Implementations
- 5.1 Implementation of Generalized Powering Functions in Digital Signatures
- 5.2 Optimizations for Performance in Cryptographic Systems
- 5.3 Trade-offs Between Security and Efficiency in Real-World Applications
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Theoretical and Practical Security Considerations
- 6.1 Provable Security of Digital Signatures Based on Generalized Powering Functions
- 6.2 Resistance to Common Cryptographic Attacks
- 6.2.1 Brute-Force Attacks
- 6.2.2 Adaptive Chosen-Message Attacks
- 6.2.3 Replay and Forgery Attacks
- 6.3 Future Challenges and Security Implications
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Extensions and Generalizations
- 7.1 Application to Other Cryptographic Protocols (e.g., Public-Key Encryption, Authentication)
- 7.2 Generalized Powering Functions in Identity-Based Cryptography
- 7.3 Cross-Application of Generalized Power Functions to Multi-Signature Schemes
- 7.4 Higher-Dimensional Generalizations and Their Implications
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Case Studies and Practical Applications
- 8.1 Use of Generalized Powering Functions in Existing Cryptographic Systems
- 8.2 Performance Comparisons with Traditional Signature Schemes
- 8.3 Real-World Deployments and Their Effectiveness
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Conclusion
- 9.1 Summary of Key Findings
- 9.2 Contributions to Digital Signature Security and Efficiency
- 9.3 Future Directions for Research on Generalized Powering Functions
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