Endomorphisms for Faster Elliptic Curve Cryptography on a Large Class of Curves

DOI10.1007/978-3-642-01001-9_30zbMath1239.94048OpenAlexW1761314766WikidataQ61914046 ScholiaQ61914046MaRDI QIDQ3627455

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Publication date: 12 May 2009

Published in: Advances in Cryptology - EUROCRYPT 2009 (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-642-01001-9_30

zbMATH Keywords

elliptic curvesisogeniesGLV methodpoint multiplication

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Cryptography (94A60)

Related Items (21)

Faster Hashing to ${\mathbb G}_2$ ⋮ Extending the signed non-zero bit and sign-aligned columns methods to general bases for use in cryptography ⋮ Families of SNARK-friendly 2-chains of elliptic curves ⋮ Efficient 3-dimensional GLV method for faster point multiplication on some GLS elliptic curves ⋮ A variant of the Galbraith-Ruprai algorithm for discrete logarithms with improved complexity ⋮ Some techniques for faster scalar multiplication on GLS curves ⋮ Efficiently computable endomorphism for genus 3 hyperelliptic curve cryptosystems ⋮ Fast subgroup membership testings for \(\mathbb{G}_1, \mathbb{G}_2\) and \(\mathbb{G}_T\) on pairing-friendly curves ⋮ Implementing the 4-dimensional GLV method on GLS elliptic curves with \(j\)-invariant 0 ⋮ Fast hashing to \(\mathbb{G}_2\) on pairing-friendly curves with the lack of twists ⋮ Constructing pairing-friendly hyperelliptic curves using Weil restriction ⋮ Speeding up regular elliptic curve scalar multiplication without precomputation ⋮ Endomorphisms for faster elliptic curve cryptography on a large class of curves ⋮ Constructing Isogenies on Extended Jacobi Quartic Curves ⋮ Refinement of the four-dimensional GLV method on elliptic curves ⋮ Four-dimensional Gallant-Lambert-Vanstone scalar multiplication ⋮ Jacobi Quartic Curves Revisited ⋮ On Modular Decomposition of Integers ⋮ On the Security of Pairing-Friendly Abelian Varieties over Non-prime Fields ⋮ Fast Hashing to G 2 on Pairing-Friendly Curves ⋮ Koblitz curves over quadratic fields

Uses Software

• EFD
• MIRACL
• eBASH
• mpFq
• eBACS
• eBATS
• Curve25519

Cites Work

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• Index calculus for abelian varieties of small dimension and the elliptic curve discrete logarithm problem
• Faster Multi-exponentiation through Caching: Accelerating (EC)DSA Signature Verification
• Exponentiation in Pairing-Friendly Groups Using Homomorphisms
• Affine Precomputation with Sole Inversion in Elliptic Curve Cryptography
• Speeding the Pollard and Elliptic Curve Methods of Factorization
• Improving the parallelized Pollard lambda search on anomalous binary curves
• Analyzing the Galbraith-Lin-Scott Point Multiplication Method for Elliptic Curves over Binary Fields
• Cryptographic Hardware and Embedded Systems - CHES 2004
• Handbook of Elliptic and Hyperelliptic Curve Cryptography
• Inverted Edwards Coordinates
• Faster Addition and Doubling on Elliptic Curves
• Accelerated Verification of ECDSA Signatures
• New Composite Operations and Precomputation Scheme for Elliptic Curve Cryptosystems over Prime Fields
• Fractional Windows Revisited:Improved Signed-Digit Representations for Efficient Exponentiation
• Public Key Cryptography - PKC 2006

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