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Elliptic-curve cryptography - Wikipedia
https://en.wikipedia.org:443/wiki/Elliptic-curve_cryptography
WEBElliptic-curve cryptography ( ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC allows smaller keys compared to non-EC cryptography (based on plain Galois fields) [vague] to provide equivalent security.
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Elliptic Curve Discrete Logarithm Problem | SpringerLink
https://link.springer.com:443/referenceworkentry/10.1007/978-1-4419-5906-5_246
WEBThe ECDLP is a special case of the discrete logarithm problem in which the cyclic group G is represented by the group \ (\langle P\rangle\) of points on an elliptic curve. It is of cryptographic interest because its apparent intractability is the basis for the security of elliptic curve cryptography.
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Development of Solving the ECDLP | IEEE Conference Publication
https://ieeexplore.ieee.org:443/document/9476133/
WEBFeb 25, 2021 · Abstract: The study and analysis of the Elliptic curve Discrete Logarithm Problem (ECDLP) is very important, because one of the strongest cryptosystems is based on this problem, which is elliptic curve cryptosystem. This aspect has led to make a clear change in cryptography and open new research field for treatment with special group that is ...
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The Elliptic Curve Discrete Logarithm Problem (ECDLP) - Public …
https://www.oreilly.com:443/library/view/public-key-cryptography-theory/9788131708323/9788131708323_ch04lev1sec5.html
WEBThe Elliptic Curve Discrete Logarithm Problem (ECDLP) Unlike the finite field DLP, there are no general-purpose subexponential algorithms to solve the ECDLP. Though good algorithms are known for certain … - Selection from Public-key Cryptography: Theory and Practice [Book]
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Elliptic Curve Discrete Logarithm Problem (ECDLP): Hardness
https://www.youtube.com:443/watch?v=iKAotDNz5o8
WEBMay 25, 2023 · 3.1M views 3 days ago. New. Join us as we delve into the world of Elliptic Curve Discrete Logarithm Problem (ECDLP), a fundamental concept in modern cryptography. Discover how ECDLP...
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Recent Advances in the Index Calculus Method for Solving the ECDLP …
https://link.springer.com:443/chapter/10.1007/978-981-99-4626-6_23
WEBOct 11, 2023 · Kim and Jiao proposed an index calculus technique for ECDLP over finite fields with modest features. The complexity of the suggested method is L(1/4 + o(1)), which is more than L(1/3 + o(1)). Using index calculus and Weil descent, the approach reduces the ECDLP to a low-degree extension field issue.
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Recent progress on the elliptic curve discrete logarithm …
https://eprint.iacr.org:443/2015/1022.pdf
WEBNov 10, 2009 · discuss pairing-based cryptography. Instead, we focus entirely on the ECDLP and related computational problems. An active area of research is index calculus algorithms based on summation poly-nomials. Recently several papers have suggested potential subexponential algorithms for the ECDLP.
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Discrete logs and the ECDLP - Ryan Tully-Doyle
https://rtullydo.github.io:443/cryptography-notes/section-ecdlp.html
WEBRyan Tully-Doyle. Prev Up Next. 🔗. 4.4 Discrete logs and the ECDLP. 🔗. What will be the hard problem at the center of elliptic curve cryptographic methods? We'll take the discrete log problem in F ∗ p F p ∗ and modify it to take account of the additive structure of E(Fp). E ( F p). We begin with a computational algorithm. 🔗. Recall that.
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Recent progress on the elliptic curve discrete logarithm problem …
https://link.springer.com:443/article/10.1007/s10623-015-0146-7
WEBNov 23, 2015 · The elliptic curve discrete logarithm problem (ECDLP) is the following computational problem: given points \(P, Q \in E( {\mathbb {F}}_q )\) to find an integer a, if it exists, such that \(Q = aP\). This problem is the fundamental building block for elliptic curve cryptography and pairing-based cryptography, and has been a major area of ...
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Elliptic Curve Cryptography (ECC) | Practical Cryptography for
https://cryptobook.nakov.com:443/asymmetric-key-ciphers/elliptic-curve-cryptography-ecc
WEBThe Elliptic Curve Cryptography (ECC) is modern family of public-key cryptosystems, which is based on the algebraic structures of the elliptic curves over finite fields and on the difficulty of the Elliptic Curve Discrete Logarithm Problem (ECDLP).
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