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www.johndcook.com | ||
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www.jeremykun.com
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| | | | | So far in this series we've seen elliptic curves from many perspectives, including the elementary, algebraic, and programmatic ones. We implemented finite field arithmetic and connected it to our elliptic curve code. So we're in a perfect position to feast on the main course: how do we use elliptic curves to actually do cryptography? History As the reader has heard countless times in this series, an elliptic curve is a geometric object whose points have a surprising and well-defined notion of addition. | |
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andrea.corbellini.name
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| | | | | [AI summary] The text provides an in-depth explanation of elliptic curve cryptography (ECC), covering fundamental concepts such as elliptic curves over finite fields, point addition, cyclic subgroups, subgroup orders, and the discrete logarithm problem. It also discusses practical aspects like finding base points, cofactors, and the importance of choosing subgroups with high order for cryptographic security. The text emphasizes that ECC relies on the difficulty of solving the discrete logarithm problem on elliptic curves, which is considered computationally hard and forms the basis for secure cryptographic protocols like ECDH and ECDSA. | |
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www.imperialviolet.org
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| | | | | [AI summary] The article explains the mathematical foundations of elliptic curves, their group structure, and their application in cryptography, particularly the Diffie-Hellman key agreement protocol, while also discussing implementation challenges in finite fields. | |
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bluebirdofbitterness.com
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| | | Reblogged on WordPress.com | ||
