Elliptic curve cryptography | Finite fields | Public-key cryptography

Elliptic-curve cryptography

Elliptic-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) to provide equivalent security. Elliptic curves are applicable for key agreement, digital signatures, pseudo-random generators and other tasks. Indirectly, they can be used for encryption by combining the key agreement with a symmetric encryption scheme. Elliptic curves are also used in several integer factorization algorithms based on elliptic curves that have applications in cryptography, such as Lenstra elliptic-curve factorization. (Wikipedia).

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Elliptic Curve Cryptography Tutorial - Understanding ECC through the Diffie-Hellman Key Exchange

Learn more advanced front-end and full-stack development at: https://www.fullstackacademy.com Elliptic Curve Cryptography (ECC) is a type of public key cryptography that relies on the math of both elliptic curves as well as number theory. This technique can be used to create smaller, fast

From playlist Elliptic Curves - Number Theory and Applications

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Application of Elliptic Curves to Cryptography

Cryptography and Network Security by Prof. D. Mukhopadhyay, Department of Computer Science and Engineering, IIT Kharagpur. For more details on NPTEL visit http://nptel.iitm.ac.in

From playlist Computer - Cryptography and Network Security

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What is... an elliptic curve?

In this talk, we will define elliptic curves and, more importantly, we will try to motivate why they are central to modern number theory. Elliptic curves are ubiquitous not only in number theory, but also in algebraic geometry, complex analysis, cryptography, physics, and beyond. They were

From playlist An Introduction to the Arithmetic of Elliptic Curves

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An Introduction to Elliptic Curve Cryptography

Cryptography and Network Security by Prof. D. Mukhopadhyay, Department of Computer Science and Engineering, IIT Kharagpur. For more details on NPTEL visit http://nptel.iitm.ac.in

From playlist Computer - Cryptography and Network Security

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Elliptic Curve Cryptography and Applications

At the SIAM Annual Meeting held in Minneapolis in July, Dr. Kristin Lauter of Microsoft Research discussed Elliptic Curve Cryptography as a mainstream primitive for cryptographic protocols and applications. The talk surveyed elliptic curve cryptography and its applications, including appli

From playlist What is math used for?

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Elliptic Curve ElGamal Cryptosystem

In this video I primarily do through the Elliptic Curve ElGamal crytposystem (Bob's variables/computations, Alice's variables/computations, what is sent, and how it is decrypted by Bob). In addition, I go over the basics of elliptic curves such as their advantages and how they are written.

From playlist Cryptography and Coding Theory

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Lenstras Algorithm

For more cryptography, subscribe @JeffSuzukiPolymath

From playlist Elliptic Curves - Number Theory and Applications

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Implementation of Elliptic Curve Cryptography

Cryptography and Network Security by Prof. D. Mukhopadhyay, Department of Computer Science and Engineering, IIT Kharagpur. For more details on NPTEL visit http://nptel.iitm.ac.in

From playlist Computer - Cryptography and Network Security

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The Elliptic Curve Digital Signature Algorithm and raw transactions on Bitcoin

https://en.wikipedia.org/wiki/Elliptic_Curve_Digital_Signature_Algorithm https://hackernoon.com/what-is-the-math-behind-elliptic-curve-cryptography-f61b25253da3 https://en.wikipedia.org/wiki/Elliptic_curve https://en.bitcoin.it/wiki/Secp256k1 http://www.ijsrp.org/research-paper-1117/ij

From playlist Programming

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Mathematics in Post-Quantum Cryptography - Kristin Lauter

2018 Program for Women and Mathematics Topic: Mathematics in Post-Quantum Cryptography Speaker: Kristin Lauter Affiliation: Microsoft Research Date: May 21, 2018 For more videos, please visit http://video.ias.edu

From playlist My Collaborators

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Elliptic Curve Arithmetic and Bitcoin | Nathan Dalaklis

Bitcoin is a cryptocurrency that uses elliptic curves in the ECDSA. Since cryptosystems often require some form of arithmetic to encode and decode information we have a couple questions to ask; What are elliptic curves? And how can we do arithmetic on an elliptic curve? ________ Standards

From playlist The New CHALKboard

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Craig Costello - Post-quantum key exchange from supersingular isogenies- IPAM at UCLA

Recorded 26 July 2022. Craig Costello of Microsoft Research presents "Post-quantum key exchange from supersingular isogenies" at IPAM's Graduate Summer School Post-quantum and Quantum Cryptography. Abstract: This talk will give an overview of Supersingular isogeny Diffie-Hellman (SIDH): t

From playlist 2022 Graduate Summer School on Post-quantum and Quantum Cryptography

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Elliptic Curves: Good books to get started

A few books for getting started in the subject of Elliptic Curves, each with a different perspective. I give detailed overviews and my personal take on each book. 0:00 Intro 0:41 McKean and Moll, Elliptic Curves: Function Theory, Geometry, Arithmetic 10:14 Silverman, The Arithmetic of El

From playlist Math

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Kritin Lauter, Supersingular isogeny graphs in cryptography

VaNTAGe Seminar, September 20, 2022 License: CC-BY-NC-SA Some of the papers mentioned in this talk: Charles, Goren, Lauter 2007: https://doi.org/10.1007/s00145-007-9002-x Mackenzie 2008: https://doi.org/10.1126/science.319.5869.1481 Pizer 1990: https://doi.org/10.1090/S0273-0979-1990-15

From playlist New developments in isogeny-based cryptography

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Elliptic Curves - Lecture 6a - Ramification (continued)

This video is part of a graduate course on elliptic curves that I taught at UConn in Spring 2021. The course is an introduction to the theory of elliptic curves. More information about the course can be found at the course website: https://alozano.clas.uconn.edu/math5020-elliptic-curves/

From playlist An Introduction to the Arithmetic of Elliptic Curves

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Mathematics in Cryptography II - Toni Bluher

2018 Program for Women and Mathematics Topic: Mathematics in Cryptography II Speaker: Toni Bluher Affiliation: National Security Agency Date: May 21, 2018 For more videos, please visit http://video.ias.edu

From playlist Mathematics

Related pages

Doubling-oriented Doche–Icart–Kohel curve | Order (group theory) | Integer factorization | Algebraic structure | Computational hardness assumption | Elliptic-curve Diffie–Hellman | Lenstra elliptic-curve factorization | Finite field | Schoof–Elkies–Atkin algorithm | Tate pairing | Algebraic variety | Curve25519 | Elliptic Curve Digital Signature Algorithm | Twisted Hessian curves | Identity element | FourQ | Encryption | Schnorr signature | Shor's algorithm | RSA Security | Counting points on elliptic curves | Point at infinity | Homomorphic signatures for network coding | Pairing-based cryptography | Hyperelliptic curve cryptography | Digital Signature Algorithm | IEEE P1363 | Supersingular isogeny key exchange | Toffoli gate | RSA (cryptosystem) | Tripling-oriented Doche–Icart–Kohel curve | Montgomery curve | Post-quantum cryptography | Power analysis | Proxy re-encryption | Security level | Characteristic (algebra) | Jacobian curve | Mersenne prime | Twisted Edwards curve | Lagrange's theorem (group theory) | Discrete logarithm | Public-key cryptography | Barrett reduction | Bitcoin | Cryptographically secure pseudorandom number generator | Identity-based encryption | SECG | EdDSA | Side-channel attack | Symmetric-key algorithm | Key size | Divisor (algebraic geometry) | Edwards curve | DNSCurve | ECC patents | Elliptic curve | Implicit certificate | Pollard's rho algorithm for logarithms | Signcryption | Digital signature | Differential fault analysis | Dual EC DRBG | Quantum cryptography | Weil pairing | Plane curve | Baby-step giant-step | Algorithm | Abelian group | Bitwise operation | Schoof's algorithm | Elliptic curve point multiplication | Quantum computing