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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: 3014 dionyziz
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: 928 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: 14286 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: 19626 Quick Trixx
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: 136891 Socratica
What was Fermat’s “Marvelous" Proof? | Infinite Series
 
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Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi If Fermat had a little more room in his margin, what proof would he have written there? 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: 64718 PBS Infinite Series
Best Cryptography and Data Privacy Software 2018 - Semalt
 
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Visit us - https://semalt.com/?ref=y Subscribe to get free educational videos here https://www.youtube.com/channel/UCBAjjiw53lUAm5YR7lgB4sQ?sub_confirmation=1 #data_and, #software, #best, #cryptography, #privacy, #and, #best_best, #data, #privacy_looking, #piechart_data, #jiotrick_best, #prachifam_software, #dyor_privacy, #sorteiotirolplus_data privacy enhancing cryptography software privacy preserving data mining and cryptography privacy cryptography computer security privacy and cryptography software cryptography privacy privacy preserving data mining cryptography best cryptography software cryptography privacy preserving data mining data privacy software cryptography and computer privacy privacy amplification quantum cryptography software cryptography and data horst feistel cryptography and computer privacy software privacy software best best privacy software privacy preserving data mining using cryptography privacy enhancing cryptography implementation cryptography privacy preserving data mining cryptography computer privacy location privacy cryptography cryptography privacy preserving privacy confidentiality cryptography the best cryptography software best free cryptography software best software for cryptography best security and privacy software cryptography and computer privacy pdf privacy enhancing cryptography and network computer security privacy and cryptography feistel cryptography and computer privacy cryptography and computer privacy feistel cryptography data internet privacy software data data privacy security software data privacy software window software data privacy statement software privacy data security data privacy software mac issues data software privacy data cryptography privacy and data data and privacy data privacy and issues in data and software privacy classical cryptography and quantum cryptography software cryptography and data security.ppt cryptography and data integrity cryptography and data security cryptography and data mining cryptography and data security.pdf data security and cryptography cryptography and data encryption cryptography and data compression data compression and cryptography data encryption and cryptography software cryptography privacy and software cryptography software data privacy best practices isogenies and cryptography software primality and cryptography software cryptanalysis and cryptography software best privacy suite software best privacy software 2011 best pc privacy software best web privacy software best privacy cleaner software best privacy software for best privacy protection software best privacy software review best privacy control software privacy software best dat best browsing privacy software best computer privacy software best privacy software 2010 best privacy software mac best privacy software reviews vpn best privacy software best windows privacy software best vpn privacy software best online privacy software best privacy eraser software best privacy software free best privacy software 2008 best ip privacy software best bittorrent privacy software the best privacy software best internet privacy software best software for privacy best privacy software download privacy software best buy best privacy security software best privacy software cnet best p2p privacy software best privacy software 2015 wbr best privacy software best privacy internet software anonymizer privacy software best best free privacy software cryptography privacy public safety privacy enhancing cryptography research cryptography computer privacy feistel privacy enhancing cryptography books privacy enhancing cryptography math privacy enhancing cryptography tools privacy enhancing cryptography history nist privacy enhancing cryptography enforcing privacy with cryptography privacy enhancing cryptography tutorial privacy enhancing cryptography jobs privacy enhancing cryptography puzzles pretty good privacy cryptography privacy enhancing cryptography salary privacy enhancing cryptography 101 privacy enhancing cryptography ppt encryption online privacy cryptography privacy amplification quantum cryptography cryptography maintain receiver privacy visual cryptography biometric privacy privacy enhancing cryptography degree privacy enhancing cryptography games privacy enhancing cryptography definition quantum cryptography privacy amplification computer security privacy and cryptography degree computer security privacy and cryptography research data privacy and data security
Views: 1 Kaustab Kiron
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: 44413 nptelhrd
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: 30510 Theoretically
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: 1988 dionyziz
Key Distribution - 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: 512 Udacity
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: 6629 nptelhrd
17 Digitale Signaturen
 
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Views: 3164 Filip Muncan
Math 706 Sections 6.1 and 6.2
 
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Math 706 Sections 6.1 and 6.2 Primality Testing, Pseudoprimes and Carmichael Numbers
Views: 765 Todd Cochrane
Inverse Using Fermat's Little Theorem | Modulo Arithmatic | Cryptography And Network Security |
 
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In this youtube channel we are going to teach you the basic concepts of Cryptography and Network Security. In this video we have discussed about how to find Inverse using Fermant's Little Theorem. Visit Our Channel :- https://www.youtube.com/channel/UCxik... Programming Interview, Software Interview, Data Structure, Algorithm, modular multiplicative inverse, multiplicative inverse, modular arithmetic, fermats theorem, euler's totient, Euler's Totient Function, Fermat's Little Theorem, Modular Multiplicative Inverse | Fermat's Theorem | Euler's Totient, yt:crop=16:11, 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: 6712 Quick Trixx
Time Space Tradeoff
 
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what is our memory limit? How can save time at the expense of space?
Views: 6245 Khan Academy Labs
Fermat's little theorem made easy
 
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4 typical exam or test questions. For Fermat's LAST Theorem click here https://www.youtube.com/watch?v=TEQrxlcprbY&t=2s
Views: 6834 Randell Heyman
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: 9678 Quick Trixx
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: 89141 Art of the Problem
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: 3389 Audiopedia
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: 19588 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: 540 larsyxa
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: 7554 nptelhrd
Number Theory: Proof of Quadratic Reciprocity Part 1
 
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Number Theory: Proof of Quadratic Reciprocity Part 1
Views: 4446 DerivinDrunk
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
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: 10016 Theoretically
Galois Fields part 6
 
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From the Paar Lectures on cryptography
Views: 642 Project Rhea
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
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: 70265 MIT OpenCourseWare
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
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
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
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: 5664 OxfordQuantumVideo
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