The use of elliptic curves in cryptography
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Summary
An analogue of the Diffie-Hellmann key exchange protocol is proposed which appears to be immune from attacks of the style of Western, Miller, and Adleman.
- Type
- dissertation
- Published
- 2007-06-01
- Cited by
- 2,335
- References
- 57
- Access
- Open access
- OpenAlex
- https://openalex.org/W111706629
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:115970463
Keywords
Elliptic curve cryptography, Elliptic curve, Cryptography, Computer science, Mathematics
References
- Efficient Algorithms for Pairing-Based Cryptosystems
- p-adic Numbers, p-adic Analysis, and Zeta-Functions
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- Review: Joseph H. Silverman, The arithmetic of elliptic curves
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- The State of Elliptic Curve Cryptography
- A general framework for subexponential discrete logarithm algorithms
- Evaluation of discrete logarithms in a group of p-torsion points of an elliptic curve in characteristic p
- Generalising the GHS Attack on the Elliptic Curve Discrete Logarithm Problem
- On random walks for Pollard's rho method
- An improved Monte Carlo factorization algorithm
- Reducing elliptic curve logarithms to logarithms in a finite field
- Elliptic curve cryptosystems
- Counting points on elliptic curves over finite fields
- Improving the parallelized Pollard lambda search on anomalous binary curves
- The Discrete Logarithm Problem on Elliptic Curves of Trace One
- A Subexponential Algorithm for Discrete Logarithms over Hyperelliptic Curves of Large Genus over GF(q)
- Computing discrete logarithms in high-genus hyperelliptic Jacobians in provably subexponential time
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- Cryptanalysis of Pseudorandom Number Generators in Wireless Sensor Networks
- Mapping an Arbritrary Message to an Elliptic Curve When Defined over GF(2^n)
- Faster Group Operations on Elliptic Curves
- PCPA: A Practical Certificateless Conditional Privacy Preserving Authentication Scheme for Vehicular Ad Hoc Networks
- Fast 160-Bits GF (P) Elliptic Curve Crypto Hardware of High-Radix Scalable Multipliers
- Physical Unclonable Functions, FPGAs and Public-Key Crypto for IP Protection.
- Analysis of ECIES and Other Cryptosystems Based on Elliptic Curves
- Génération automatique de circuits pour le calcul de couplages cryptographiques en matériel
- Solutions opérationnelles d'une transaction électronique sécurisée et respectueuse de la vie privée. (Operational solutions for secure electronic transactions ensuring the privacy.)
- Authentification d'objets à distance
- Pairing computation on hyperelliptic curves of genus 2
- Applications of elliptic curve pairings in cryptography
- Authenticated Encryption Schemes: Current Status and Key Issues
- Stream ciphers for secure display
- Pairings in Cryptology: efficiency, security and applications
- Security in Smart Object Networks
- Scalable VLSI design for fast GF (p) montgomery inverse computation
- Joint Sparse Form of Window Three for Koblitz Curve
- Étude théorique et implantation matérielle d'unités de calcul en représentation modulaire des nombres pour la cryptographie sur courbes elliptiques. (Theoretical study and hardware implementation of arithmetical units in Residue Number System (RNS) for Elliptic Curve Cryptography (ECC))
- Novel approach design of elliptic curve cryptography implementation in VLSI