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Fermat's primality test
 
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Check my previous video on simpler primality testing algorithms: https://www.youtube.com/watch?v=LULHTKznczA Check my previous video on how powmod can be built in polynomial time: https://www.youtube.com/watch?v=qed48E92qXc Fermat's primality test: https://en.wikipedia.org/wiki/Fermat_primality_test Carmichael numbers: https://en.wikipedia.org/wiki/Carmichael_number Soup's number theory book: http://www.shoup.net/ntb/ntb-v2.pdf This is an implementation of Fermat's primality test in Python. The algorithm is polynomial in the size of the input and it works in O(k polylog(p)) where k is the test accuracy parameter and p is the candidate being tested. Because Fermat's algorithm uses randomness, it is a probabilistic algorithm. Fermat's test is a flawed algorithm because Carmichael numbers are composite numbers that the test thinks are prime. Polynomial-time primality testing has many applications in cryptography such as key generation. If you liked this video, please thumbs up and subscribe. This is one of my first videos. Please leave feedback about what you think I can improve and what other topics you would like to see. I've just created a Patreon where you can buy me a cup of coffee. Thanks so much for supporting me! https://www.patreon.com/dionyziz
Views: 890 dionyziz
Programming Interviews: Primality Testing: Randomized Algorithm
 
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This video lecture is produced by IITian S.Saurabh. He is B.Tech from IIT and MS from USA. How will you find if a number is prime. Can you suggest a randomized algorithm to find if a number is prime. This channel is an ultimate guide to prepare for job interviews for software engineers, software test engineers, computer scientists, engineering students specially computer science and IT engineers, Master of computer application (MCA) and Bachelor of Computer Application (BCA) students. The content of this channel will help students prepare for C,C++, Java, data structures and algorithms. It also covers courses related to networking and database. This channel can be used by students of NIIT, IGNOU etc too. tags: "find repeated element", "randomized algorithms","randomized algorithms example","randomized algorithms ppt", "randomized algorithms pdf","repeated element in an array","primality testing fermat","primality testing fermat's little theoram","fermat's theoram primality testing","primality testing using fermat's little theoram"
Views: 14172 saurabhschool
Elgamal Encryption and Decryption Algorithm | Elgamal Cryptosysterm With Solved Example
 
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This video explains how the elgama cryptosystem encryption and decryption is done 😎😎 Visit Our Channel :- https://www.youtube.com/channel/UCxik... In this lecture we have taught about Diffie Hellman Key Exchange and how it operates. Also a quick overview of AES and the basics of encryption. Follow Smit Kadvani on :- Facebook :- https://www.facebook.com/smit.kadvani Instagram :- https://www.instagram.com/the_smit0507 Follow Dhruvan Tanna on :- Facebook :- https://www.facebook.com/dhruvan.tanna1 Instagram :- https://www.instagram.com/dhru1_tanna Follow Keyur Thakkar on :- Facebook :- https://www.facebook.com/keyur.thakka... Instagram :- https://www.instagram.com/keyur_1982 Snapchat :- keyur1610 Follow Ankit Soni on:- Instagram :- https://www.instagram.com/ankit_soni1511
Views: 16323 Quick Trixx
Miller-Rabin primality test
 
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The Miller-Rabin primality test: https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test A python implementation of the probabilistic Miller-Rabin primality test. This test runs in polynomial time O(k polylog(p)) and has a negligible probability of failure 4^(-k), making it suitable for cryptographic applications. This video builds up from Fermat's primality test. Watch my previous video where I explain it: https://www.youtube.com/watch?v=qDakpCEW5-0 Euclid's lemma: https://en.wikipedia.org/wiki/Euclid%27s_lemma Fermat's little theorem: https://en.wikipedia.org/wiki/Fermat%27s_little_theorem Soup's number theory book: http://www.shoup.net/ntb/ntb-v2.pdf If you enjoyed this video, please 👍 and +Subscribe. This is one of my first videos. Please leave feedback about what you think I can improve and what other topics you would like to see. I've just created a Patreon where you can buy me a cup of coffee. Thanks so much for supporting me! https://www.patreon.com/dionyziz
Views: 2827 dionyziz
Introduction to Number Theory
 
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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
Views: 42207 nptelhrd
Diffie Hellman - Applied Cryptography
 
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This video is part of an online course, Applied Cryptography. Check out the course here: https://www.udacity.com/course/cs387.
Views: 976 Udacity
Sieve of Eratosthenes
 
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The Sieve of Eratosthenes: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes Trial division: https://en.wikipedia.org/wiki/Trial_division For an introduction to complexity and big-O, big-Ω notation see: https://dionyziz.com/complexity/ Soup's number theory book: http://www.shoup.net/ntb/ntb-v2.pdf This is a classical number theory algorithm implementation in Python. The Sieve of Eratosthenes and trial division are the simplest way of determining whether a number is a prime, a primality test. This is an exponential way of checking for primality, as the complexity is Ω(sqrt(n)). Primality testing has many applications including cryptography. If you liked this video, please thumbs up and subscribe. This is one of my first videos. Please leave feedback about what you think I can improve and what other topics you would like to see. I've just created a Patreon where you can buy me a cup of coffee. Thanks so much for supporting me! https://www.patreon.com/dionyziz
Views: 1929 dionyziz
What was Fermat’s “Marvelous" Proof? | Infinite Series
 
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If Fermat had a little more room in his margin, what proof would he have written there? Support us on Patreon at https://www.patreon.com/pbsinfiniteseries Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com Resources: Contemporary Abstract Algebra by Joseph Gallian https://www.amazon.com/Contemporary-Abstract-Algebra-Joseph-Gallian/dp/1133599702 Standard Definitions in Ring Theory by Keith Conrad http://www.math.uconn.edu/~kconrad/blurbs/ringtheory/ringdefs.pdf Rings and First Examples (online course by Prof. Matthew Salomone) https://www.youtube.com/watch?v=h4UCMd8dyiM Fermat's Enigma by Simon Singh https://www.amazon.com/Fermats-Enigma-Greatest-Mathematical-Problem/dp/0385493622 Who was first to differentiate between prime and irreducible elements? (StackExchange) https://hsm.stackexchange.com/questions/3754/who-was-first-to-differentiate-between-prime-and-irreducible-elements Previous Episodes: What Does It Mean to be a Number? https://www.youtube.com/watch?v=3gBoP8jZ1Is What are Numbers Made of? https://www.youtube.com/watch?v=S4zfmcTC5bM Gabe's references from the comments: Blog post about the Peano axioms and construction of natural numbers by Robert Low: http://robjlow.blogspot.co.uk/2018/01/whats-number-1-naturally.html Recommended by a viewer for connections to formulation of numbers in computer science: https://softwarefoundations.cis.upenn.edu/ In 1637, Pierre de Fermat claimed to have the proof to his famous conjecture, but, as the story goes, it was too large to write in the margin of his book. Yet even after Andrew Wiles’s proof more than 300 years later, we’re still left wondering: what proof did Fermat have in mind? The mystery surrounding Fermat’s last theorem may have to do with the way we understand prime numbers. You all know what prime numbers are. An integer greater than 1 is called prime if it has exactly two factors: 1 and itself. In other words, p is prime if whenever you write p as a product of two integers, then one of those integers turns out to be 1. In fact, this definition works for negative integers, too. We simply incorporate -1. But the prime numbers satisfy another definition that maybe you haven’t thought about: An integer p is prime if, whenever p divides a product of two integers, then p divides at least one of those two integers. Written and Hosted by Tai-Danae Bradley Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Mike Petrow and Linda Huang Made by Kornhaber Brown (www.kornhaberbrown.com) Special thanks to Roman Pinchuk for supporting us on our Converse level on Patreon. Along with thanks to Matthew O'Connor, Yana Chernobilsky, and John Hoffman who are supporting us on Patreon at the Identity level! And thanks to Mauricio Pacheco who are supporting us at the Lemma level!
Views: 60799 PBS Infinite Series
Digital Signature Standard Algorithm | With Solved Example | Cryptography And Network Security
 
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Types of digital signature approaches - RSA approach - DSS approach Digital Signature Algorithm with easy explanation.The Digital Signature Algorithm (DSA) is a Federal Information Processing Standard for digital signatures.It was proposed by the National Institute of Standards and Technology (NIST) in August 1991 for use in their Digital Signature Standard (DSS) and adopted as FIPS 186 in 1993. Visit Our Channel :- https://www.youtube.com/channel/UCxik... Follow Smit Kadvani on :- Facebook :- https://www.facebook.com/smit.kadvani Instagram :- https://www.instagram.com/the_smit0507 Follow Dhruvan Tanna on :- Facebook :- https://www.facebook.com/dhruvan.tanna1 Instagram :- https://www.instagram.com/dhru1_tanna Follow Keyur Thakkar on :- Facebook :- https://www.facebook.com/keyur.thakka... Instagram :- https://www.instagram.com/keyur_1982 Snapchat :- keyur1610 Follow Ankit Soni on:- Facebook :- https://www.facebook.com/ankitsoni.1511 Instagram :- https://www.instagram.com/ankit_soni1511
Views: 8109 Quick Trixx
Neural Network (FANN) vs Primes
 
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Can a Neural Network accurately predict primality? Not Really! Demo devoloped in VC++ 2017. Output NN learns fast ofc, because of the nature of the input to output. Non linearity is not good NN material. References: http://www.psych.mcgill.ca/perpg/fac/shultz/personal/Recent_Publications_files/prime06.pdf https://libfann.github.io/fann/docs/files/fann-h.html
Views: 460 larsyxa
Message Authentication Codes
 
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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
Views: 6540 nptelhrd
What is Cryptography - Introduction to Cryptography | What are the components of Cryptography
 
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In this video we cover basic terminology in cryptography, including what is a ciphertext, plaintext, keys, public key crypto, and private key crypto. Visit Our Channel :- https://www.youtube.com/channel/UCxikHwpro-DB02ix-NovvtQ In this lecture we have taught about what is Cryptography and what are its components. Follow Smit Kadvani on :- Facebook :- https://www.facebook.com/smit.kadvani Instagram :- https://www.instagram.com/the_smit0507 Follow Dhruvan Tanna on :- Facebook :- https://www.facebook.com/dhruvan.tanna1 Instagram :- https://www.instagram.com/dhru1_tanna Follow Keyur Thakkar on :- Facebook :- https://www.facebook.com/keyur.thakka... Instagram :- https://www.instagram.com/keyur_1982 Snapchat :- keyur1610 Follow Ankit Soni on:- Facebook :- https://www.facebook.com/ankitsoni.1511 Instagram :- https://www.instagram.com/ankit_soni1511
Views: 15437 Quick Trixx
Pohlig-Hellman Algorithm
 
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This video is an example of using the Pohlig-Hellman Algorithm to solve a discrete log problem.
Views: 9618 Theoretically
Cryptographic Hash Functions (Contd...2)
 
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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
Views: 7519 nptelhrd
Number Theory - Modular Arithmetic Apps (Arabic)
 
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Content Link: https://github.com/mostafa-saad/ArabicCompetitiveProgramming/raw/master/04%20Math/14_Number_Theory_Modular_Arithmetic_Apps.pdf Content: - Wilson Theorem - Factorial % P (excluded) - Combinations using above 2 points - Combinations: Lucas Theorem - Combinations with Chinese remainder theorem - Catalan number Problems: 10007, 10303
Las Vegas Algorithm
 
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Views: 2466 Raj Kumar
Number Theory: Fermat's Little Theorem
 
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Fermat's Little Theorem was observed by Fermat and proven by Euler, who generalized the theorem significantly. This theorem aids in dividing extremely large numbers and can aid in testing numbers to see if they are prime. For more advanced students, this theorem can be easily proven using basic group theory. Prerequisites: To follow this video, you will want to first learn the basics of congruences. If you found this video helpful, please share it with your friends! You might like the other videos in our Number Theory Playlist: https://www.youtube.com/watch?v=VLFjOP7iFI0&list=PLi01XoE8jYojnxiwwAPRqEH19rx_mtcV_ Don't forget to Subscribe to our channels so you'll hear about our newest videos: http://www.youtube.com/subscription_center?add_user=SocraticaStudios Subject: Number Theory Teacher: Michael Harrison Artist: Katrina de Dios
Views: 132666 Socratica
Integer factorization
 
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In number theory, integer factorization or prime factorization is the decomposition of a composite number into smaller non-trivial divisors, which when multiplied together equal the original integer. When the numbers are very large, no efficient, non-quantum integer factorization algorithm is known; an effort by several researchers concluded in 2009, factoring a 232-digit number (RSA-768), utilizing hundreds of machines over a span of two years. However, it has not been proven that no efficient algorithm exists. The presumed difficulty of this problem is at the heart of widely used algorithms in cryptography such as RSA. Many areas of mathematics and computer science have been brought to bear on the problem, including elliptic curves, algebraic number theory, and quantum computing. This video is targeted to blind users. Attribution: Article text available under CC-BY-SA Creative Commons image source in video
Views: 3302 Audiopedia
Number Theory: Proof of Quadratic Reciprocity Part 1
 
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Number Theory: Proof of Quadratic Reciprocity Part 1
Views: 4293 DerivinDrunk
Lec 5 | MIT 6.042J Mathematics for Computer Science, Fall 2010
 
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Lecture 5: Number Theory II Instructor: Marten van Dijk View the complete course: http://ocw.mit.edu/6-042JF10 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
Views: 66722 MIT OpenCourseWare
BOSCOIN BLOCKCHAIN TECHNOLOGY BOS CRYPTO REVIEW
 
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BOSCOIN BLOCKCHAIN TECHNOLOGY BOS CRYPTO REVIEW Website: https://boscoin.io/about/ Whitepaper: https://boscoin.io/wp-content/themes/boscoin//src/pdf/BOScoinWhitePaper.pdf
Views: 26350 Martins Hacks
Fermat's Little Theorem (Visualization)
 
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Fermat's Little Theorem Visualized. Introduction to a key result in elementary number theory using a visualization with beads
Views: 88670 Art of the Problem
Digital Signature Schemes
 
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A video I have created that addresses and explains the fundamentals of Digital Signature Schemes.
Views: 310 AgniAsmi
Pequeno teorema de Fermat | Uma jornada pela criptografia | Khan Academy
 
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Este vídeo ensina: Introdução a um resultado-chave com teoria elementar dos números utilizando uma visualização com miçangas. Criado por Brit Cruise. Assista a próxima aula: https://pt.khanacademy.org/computing/computer-science/cryptography/random-algorithms-probability/v/fermat-primality-test-prime-adventure-part-10?utm_source=YT&utm_medium=Desc&utm_campaign=Computer science Perdeu a aula anterior? Assista aqui: https://pt.khanacademy.org/computing/computer-science/cryptography/random-algorithms-probability/v/random-primality-test-prime-adventure-part-9?utm_source=YT&utm_medium=Desc&utm_campaign=Computer science Uma jornada pela criptografia na Khan Academy: Introdução a um resultado chave na teoria elementar de números usando uma visualização com contas. Quer um tutor virtual para Uma jornada pela criptografia? Habilite a missão Uma jornada pela criptografia na Khan Academy aqui: https://pt.khanacademy.org/?utm_source=YT&utm_medium=Desc&utm_campaign=umajornadapelacriptografia Sobre a Khan Academy: A Khan Academy oferece exercícios, vídeos e um painel de aprendizado personalizado para ajudar estudantes a aprenderem no seu próprio ritmo, dentro e fora da sala de aula. Temos conteúdos de matemática, ciências e programação, do jardim da infância ao ensino superior, com tecnologia de ponta. De graça, para todos e para sempre. #YouCanLearnAnything Se inscreva no canal: https://www.youtube.com/subscription_center?add_user=KhanAcademyPortugues
BIG Exponents - Modular Exponentiation, Fermat's, Euler's
 
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How to deal with really big exponents using the three main methods: Modular Exponentiation, Fermat's Little Theorem, and Euler's Theorem. Also explains which method to pick. Table of contents: Which to pick? - 0:47 Fermat's Example - 1:39 Modular Exponentiation Example - 4:43 Euler's Example - 10:13
Views: 28781 Theoretically
ANT X talk on Elliptic Curves over Q(sqrt(5))
 
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See http://wstein.org/talks/2012-07-10-sqrt5/sqrt5.pdf
Views: 148 William Stein
Teoria dos Números ( Sequencias Recorrentes e Testes de Primalidade ) - Nível 3
 
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Matéria - Teoria dos Números Conteúdo - Sequências Recorrentes e Testes de Primalidade Nível - 3 Aula - 15 e 18 Professor - Carlos Gustavo Tamm de Araujo Moreira Currículo - http://poti.obmep.org.br/index.php/curriculo/view/id/1 Link Material - http://poti.obmep.org.br/upload/Aula%2001%20-%20Divisibilidade%20-%20N321.pdf
Modulo: A Series that Remains: Fermat's Little Thm (Chapter 2 of 4)
 
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Fermat's Little Theorem, its generalizations, and all that interesting stuff. Grab some popcorn and enjoy watching. Brought to you by AllLogarithmsEqual. Email: [email protected] ----- LINKS Senior Papers at Union University http://www.uu.edu/dept/math/seniorpapers.cfm Slides (borrowed from Mr Nabila Razeq's paper) http://www.uu.edu/dept/math/SeniorPapers/09-10/RazeqNabila.pdf Phi Function https://youtu.be/WvKtrCTqugI http://mathworld.wolfram.com/TotientFunction.html Carmichael Function http://mathworld.wolfram.com/CarmichaelFunction.html
Views: 273 AllLogarithmsEqual
What Is The Miller Effect?
 
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Aside from being easily analyzed the miller effect was named after john milton. What is 'miller effect insync'? Miller capacitance effects for analog and semiconductor devices. Miller effect wikipediawhat is the miller effect? How does it work and how what Youtube. The miller theorem and the frequency response of common effect ecircuit center. The question by cyril was how can we overcome the impairments of 15 jul 2017. Miller effect wikipedia en. Origin of the miller effect mit. Miller effect wikipedia. It can occur undesirably in amplifiers, caused by parasitic 15 feb 2007 miller capacitance is a feedback element implicit to active devices as different their operating principles bipolar junction and there always between drain gate which be real problem. Miller effect encyclopedia article citizendium. Wikipedia wiki miller_effect "imx0m" url? Q webcache. What is the miller capacitance? Quora. Planet analog dennis feucht the miller effect, part 1 basic miller's tale how to calculate capacitance gate and on mosfet electrical. Although the term miller effect normally refers to capacitance, any impedance connected between input and another node exhibiting gain can modify amplifier via this. Typically there's a 3 jul 2017 the miller effect is basic electronic phenomenon associated with feedback circuits. What is miller capacitance? Aiken amps. In figure 1, the signal vin will assuming that y does not affect gain, kcl at input says this is we can even use miller theorem to calculate gain of circuit for finite whether you're trying understand an audio amplifier or inside op amp, effect key predicting its frequency response. It refers to the effective multiplication of plate grid origin miller effect scanned by kent hthus apparent input capacity can become a number times greater than actual capacities and pole splittingengineers frequently design systems be dominated single. A common mosfet is the fqp30n06l (60v logic. Googleusercontent search. Lecture 20 frequency response miller effectniknejad aug 2004 the capacitance in a triode tube is equal to plate grid multiplied by factor stage gain plus one effect apparent modification of effects voltage between capacitor terminals. Miller effect capacitance all syllabus. High frequency response of ce amplifier iit guwahati. Apr 2017 if there is some capacitance between the input and output of an inverting voltage amplifierit will appear to be multiplied by gain 24 oct 2013 in electronics, miller effect increase equivalent amplifier due a connected two related nodes, one on side other reactance because their low value (usually only few pf) occurs amplifiers it that for any amplifier, increased sensitive inter electrode term 'miller capacitance' often seen when reading about guitar circuit design. Miller effect and pole splittinglecture 20 frequency response miller. These properties of the miller effect are generalized in theorem allow me to share your discussion on common source amplifier. When miller published his work in 1920, he was working on vacuum tube triodes, however the same theory department of eecseecs 105 fall 2003, lecture 20.
Views: 63 Badman 360 Planet
Time Space Tradeoff
 
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what is our memory limit? How can save time at the expense of space?
Views: 6175 Khan Academy Labs
Miller V California Supreme Court Case (Historical Reenactment)
 
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An Osbourn Park high school AP Government reenactment of pivotal Supreme Court case Miller v. California, in which a pornography shop owner argues that putting explicit flyers in people's mailboxes is protected free speech.
Views: 35 JRocYourFaceOff
Tom Leinster: "An introduction to n-categories"
 
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Speaker: Tom Leinster (University of Glasgow) Title: An introduction to n-categories Event: Categories, Logic and Foundations of Physics IV (January 2009, Imperial College London) Abstract: I will give an beginners' introduction to n-categories. First I'll explain roughly what an n-category is, and talk about some of the dreams that first led people to want to develop a theory of n-categories. Then I'll go into more detail, leading up to a description of the state of the art and of some of the difficulties involved in trying to make those dreams come true. This is a completely introductory talk, for those who know nothing about n-categories. Experts will be bored senseless.
Views: 5182 OxfordQuantumVideo
17 Digitale Signaturen
 
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Views: 3159 Filip Muncan