Asymmetric-key algorithms | Computational hardness assumptions | Modular arithmetic | Logarithms

Discrete logarithm records

Discrete logarithm records are the best results achieved to date in solving the discrete logarithm problem, which is the problem of finding solutions x to the equation given elements g and h of a finite cyclic group G. The difficulty of this problem is the basis for the security of several cryptographic systems, including Diffie–Hellman key agreement, ElGamal encryption, the ElGamal signature scheme, the Digital Signature Algorithm, and the elliptic curve cryptography analogs of these. Common choices for G used in these algorithms include the multiplicative group of integers modulo p, the multiplicative group of a finite field, and the group of points on an elliptic curve over a finite field. The current record for integers modulo prime numbers, set in December 2019, is a discrete logarithm computation modulo a prime with 240 digits. For characteristic 2, the current record for finite fields, set in July 2019, is a discrete logarithm over . When restricted to prime degree, the current record, set in October 2014, is over . For characteristic 3, the current record, set in July 2016, is over . For fields of "moderate" characteristic, the current record, set in January 2013, is over . (Wikipedia).

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Simplifying Logarithms 3

In this video, we simplify a logarithm.

From playlist Logs - Worked Examples

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What are natural logarithms and their properties

👉 Learn all about the properties of logarithms. The logarithm of a number say a to the base of another number say b is a number say n which when raised as a power of b gives a. (i.e. log [base b] (a) = n means that b^n = a). The logarithm of a negative number is not defined. (i.e. it is no

From playlist Rules of Logarithms

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Ex: Determine the Value of a Number on a Logarithmic Scale (Log Form)

This video explains how to determine the value of several numbers on a logarithmic scale scaled in logarithmic form. http://mathispower4u.com

From playlist Using the Definition of a Logarithm

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What are the properties of logarithms and natural logarithms

👉 Learn all about the properties of logarithms. The logarithm of a number say a to the base of another number say b is a number say n which when raised as a power of b gives a. (i.e. log [base b] (a) = n means that b^n = a). The logarithm of a negative number is not defined. (i.e. it is no

From playlist Rules of Logarithms

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Combining Logs 2

This is an worked example of logarithms in Algebra 2.

From playlist Logs Group Quiz

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What are the properties of logarithms

👉 Learn all about the properties of logarithms. The logarithm of a number say a to the base of another number say b is a number say n which when raised as a power of b gives a. (i.e. log [base b] (a) = n means that b^n = a). The logarithm of a negative number is not defined. (i.e. it is no

From playlist Rules of Logarithms

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When is a logarithm undefined? log4 (-32)

👉 Learn all about the properties of logarithms. The logarithm of a number say a to the base of another number say b is a number say n which when raised as a power of b gives a. (i.e. log [base b] (a) = n means that b^n = a). The logarithm of a negative number is not defined. (i.e. it is no

From playlist Rules of Logarithms

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Overview of log properties - Inverse properties

👉 Learn all about the properties of logarithms. The logarithm of a number say a to the base of another number say b is a number say n which when raised as a power of b gives a. (i.e. log [base b] (a) = n means that b^n = a). The logarithm of a negative number is not defined. (i.e. it is no

From playlist Rules of Logarithms

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Cyclic Groups in Cryptography

Some detail about cyclic groups and their application to cryptography, especially Diffie Hellman Key Exchange.

From playlist PubKey

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Aurore Guillevic: Computing discrete logarithms in GF(pn): practical improvement of ...

Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b

From playlist Women at CIRM

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Solving the Logarithmic Equation log(A) = log(B) - C*log(x) for A

Solving the Logarithmic Equation log(A) = log(B) - C*log(x) for A Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys

From playlist Logarithmic Equations

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Jan Maas : Gradient flows and Ricci cuevature in discrete and quantum probability

Recording during the thematic meeting : "Geometrical and Topological Structures of Information" the August 28, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent

From playlist Geometry

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DLP Attacks and intro to El Gamal

We cover basic attacks on the discrete logarithm problem. The El Gamal Cipher is presented. We start discussion digital signatures.

From playlist PubKey

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Eugenia Malinnikova : Uncertainty principles for discrete Schrödinger evolutions

Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b

From playlist Analysis and its Applications

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Bastien Vialla - Analyse du produit matrice creuse avec un ou plusieurs vecteur

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From playlist Journées Codage et Cryptographie 2014

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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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Dominic Berry - Optimal scaling quantum linear systems solver via discrete adiabatic theorem

Recorded 25 January 2022. Dominic Berry of Macquarie University presents "Optimal scaling quantum linear systems solver via discrete adiabatic theorem" at IPAM's Quantum Numerical Linear Algebra Workshop. Abstract: Recently, several approaches to solving linear systems on a quantum compute

From playlist Quantum Numerical Linear Algebra - Jan. 24 - 27, 2022

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Lecture 6: Gauge-equivariant Mesh CNN - Pim de Haan

Video recording of the First Italian School on Geometric Deep Learning held in Pescara in July 2022. Slide: https://www.sci.unich.it/geodeep2022/slides/2022-07-27%20Mesh%20-%20First%20Italian%20GDL%20School.pdf

From playlist First Italian School on Geometric Deep Learning - Pescara 2022

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Logarithms - Basics | What are Logs? | Don't Memorise

What are Logarithms or logs? How are they related to Exponents? Watch this video to know the answers. To learn more about Logarithms, enroll in our full course now: https://infinitylearn.com/microcourses?utm_source=youtube&utm_medium=Soical&utm_campaign=DM&utm_content=4UNkQcBrLaQ&utm_ter

From playlist Logarithms

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Charlotte Hardouin: Galois theory and walks in the quarter plane

Abstract: In the recent years, the nature of the generating series of walks in the quarter plane has attracted the attention of many authors in combinatorics and probability. The main questions are: are they algebraic, holonomic (solutions of linear differential equations) or at least hype

From playlist Combinatorics

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Function field sieve | Prime number | Pollard's rho algorithm for logarithms | ElGamal signature scheme | Strong prime | Elliptic curve | Finite field | Safe prime | Pollard's kangaroo algorithm | Discrete logarithm | ElGamal encryption | Peter Montgomery (mathematician) | Cyclic group | Digital Signature Algorithm