The elliptic curve only hash (ECOH) algorithm was submitted as a candidate for SHA-3 in the NIST hash function competition. However, it was rejected in the beginning of the competition since a second pre-image attack was found. The ECOH is based on the hash algorithm, that has not yet been successfully attacked. However, MuHASH is too inefficient for practical use and changes had to be made. The main difference is that where MuHASH applies a random oracle, ECOH applies a padding function. Assuming random oracles, finding a collision in MuHASH implies solving the discrete logarithm problem. MuHASH is thus a provably secure hash, i.e. we know that finding a collision is at least as hard as some hard known mathematical problem. ECOH does not use random oracles and its security is not strictly directly related to the discrete logarithm problem, yet it is still based on mathematical functions. ECOH is related to the Semaev's problem of finding low degree solutions to the summation polynomial equations over binary field, called the Summation Polynomial Problem. An efficient algorithm to solve this problem has not been given so far. Although the problem was not proven to be NP-hard, it is assumed that such an algorithm does not exist. Under certain assumptions, finding a collision in ECOH may be also viewed as an instance of the subset sum problem. Besides solving the Summation Polynomial Problem, there exists another way how to find second pre-images and thus collisions, Wagner's generalized birthday attack. ECOH is a good example of hash function that is based on mathematical functions (with the provable security approach) rather than on classical ad hoc mixing of bits to obtain the hash. (Wikipedia).
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From playlist Elliptic Curves - Number Theory and Applications
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
An informal introduction to cryptography. Part of a larger series teaching programming at http://codeschool.org
From playlist Cryptography
Cryptographic Hash Functions: Part 1
Cryptographic Hash Functions Applications of Crypto Hash Functions Birthday Problem Secure Hash Algorithm (SHA)
From playlist Network Security
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
Cryptographic Hash Functions: Part 2
Cryptographic Hash Functions Applications of Crypto Hash Functions Birthday Problem Secure Hash Algorithm (SHA)
From playlist Network Security
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
From playlist Cryptography Lectures
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
Benjamin Smith, Isogenies in genus 2 for cryptographic applications
VaNTAGe seminar, October 4, 2022 License: CC-BY-NC-SA
From playlist New developments in isogeny-based cryptography
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
Bitcoin Q&A: Important Terminology Explained
I am confused by terminology in Bitcoin. Please explain the following terms: private / public keys, hash functions, elliptic curve, addresses, and signatures. How can you create an address offline? How does the Bitcoin network "find out" about the address? Chapters 0:00 I'm confused by th
From playlist Bitcoin Q&A
Mathematics in Post-Quantum Cryptography II - Kristin Lauter
2018 Program for Women and Mathematics Topic: Mathematics in Post-Quantum Cryptography II Speaker: Kristin Lauter Affiliation: Microsoft Research Date: May 22, 2018 For more videos, please visit http://video.ias.edu
From playlist My Collaborators
WRI TwitchTalks Cryptography 101719
Presenter: Dariia Porechna Wolfram Research developers demonstrate the new features of Version 12 of the Wolfram Language that they were responsible for creating. Previously broadcast live on October 17, 2019 at twitch.tv/wolfram. For more information, visit: https://www.wolfram.com/langu
From playlist Twitch Talks
!!Con 2016 - Making Money Disappear with Hash Functions! By Brendan Cordy
Making Money Disappear with Hash Functions! By Brendan Cordy What is a Bitcoin address? Where do all those weird letters and numbers come from!? Once we figure it out, we can dig deep between the cushions of the cryptocurrency couch and find lost coins claimed by bugs. You might think thi
From playlist RailsConf 2016
John Cremona: The symplectic type of congruences between elliptic curves
In this talk I will describe a systematic investigation into congruences between the mod $p$ torsion modules of elliptic curves defined over $\mathbb{Q}$. For each such curve $E$ and prime $p$ the $p$-torsion $E[p]$ of $E$, is a 2-dimensional vector space over $\mathbb{F}_{p}$ which carrie
From playlist Number Theory
Failing to Hash Into Supersingular Isogeny Graphs
CFAIL 2022. Authors: Jeremy Booher, Ross Bowden, Javad Doliskani, Tako Boris Fouotsa, Steven D. Galbraith, Sabrina Kunzweiler, Simon-Philipp Merz, Christophe Petit, Benjamin Smith, Katherine Stange, Yan Bo Ti, Christelle Vincent, José Felipe Voloch, Charlotte Weitkämper and Lukas Zobernig
From playlist My Math Talks
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