A simple explanation of how prime numbers are used in Public Key Cryptography from ABC1 science program Catalyst

Views: 63319
Simon Pampena

RSA Public Key Encryption Algorithm (cryptography). How & why it works. Introduces Euler's Theorem, Euler's Phi function, prime factorization, modular exponentiation & time complexity.
Link to factoring graph: http://www.khanacademy.org/labs/explorations/time-complexity

Views: 566095
Art of the Problem

How can we estimate the number of primes up to x?
Watch the next lesson: https://www.khanacademy.org/computing/computer-science/cryptography/comp-number-theory/v/time-space-tradeoff?utm_source=YT&utm_medium=Desc&utm_campaign=computerscience
Missed the previous lesson? https://www.khanacademy.org/computing/computer-science/cryptography/comp-number-theory/v/trial-division-primality-test-using-a-sieve-prime-adventure-part-5?utm_source=YT&utm_medium=Desc&utm_campaign=computerscience
Computer Science on Khan Academy: Learn select topics from computer science - algorithms (how we solve common problems in computer science and measure the efficiency of our solutions), cryptography (how we protect secret information), and information theory (how we encode and compress information).
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Views: 84993
Khan Academy Labs

Spies used to meet in the park to exchange code words, now things have moved on - Robert Miles explains the principle of Public/Private Key Cryptography
note1: Yes, it should have been 'Obi Wan' not 'Obi One' :)
note2: The string of 'garbage' text in the two examples should have been different to illustrate more clearly that there are two different systems in use.
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This video was filmed and edited by Sean Riley.
Computer Science at the University of Nottingham: http://bit.ly/nottscomputer
Computerphile is a sister project to Brady Haran's Numberphile. See the full list of Brady's video projects at: http://bit.ly/bradychannels

Views: 428201
Computerphile

This video gives an introduction and motivation about finding large prime numbers for the RSA. General ideas are discussed.

Views: 1712
Leandro Junes

This is a segment of this full video:
https://www.youtube.com/watch?v=YEBfamv-_do
Diffie-Hellman key exchange was one of the earliest practical implementations of key exchange within the field of cryptography. It relies on the discrete logarithm problem. This test clip will be part of the final chapter of Gambling with Secrets!

Views: 449166
Art of the Problem

The history behind public key cryptography & the Diffie-Hellman key exchange algorithm.
We also have a video on RSA here: https://www.youtube.com/watch?v=wXB-V_Keiu8

Views: 627607
Art of the Problem

In this network security video tutorial we will study the working of RSA Algorithm.
RSA Algorithm theory -
1. Ron Rivest, Adi Shamir and Len Adlemen developed the method called as RSA algorithm.
2. Most popular and proven asymmetric key cryptography algorithm
3. Based on the mathematical fact that it is easy to find and multiply large prime numbers together, but it is extremely difficult to factor their product.
RSA Algorithm Steps -
1. Choose two large prime numbers P and Q.
2. Calculate N = P * Q
3. Select the public key (i.e. the encryption key) E such that it is not a factor of [(P – 1) * (Q – 1)].
4. Select the private key (i.e. the decryption key) D such that the following equation is true:
(D * E) mod (P – 1) * (Q – 1) = 1
5. For encryption calculate the cipher text CT from the plain text PT as follows: CT= PT^E mod N
6. Send CT as the cipher text to the receiver
7. For decryption calculate the plain text PT from the cipher text CT as follows: PT = CT^D mod N
Complete Network Security / Information Security Playlist - https://www.youtube.com/watch?v=IkfggBVUJxY&list=PLIY8eNdw5tW_7-QrsY_n9nC0Xfhs1tLEK
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#RSA #RSAalgorithm #NetworkSecurity #AsymmetricCryptography

Views: 1270
Simple Snippets

#breakthroughjuniorchallenge
Background music is not mine. I do not own it. Here's the link to the original video: https://youtu.be/aySvbg_r1RU

Views: 1007
Erika Lustre

This video provides a description of public key cryptography and how asymmetric encryption secures data in a network.

Views: 362
TELEGRID

CS1231 Group 20
To view the presentation only, visit http://youtu.be/Yf3k1c1YEuA?hd=1
Copyright, NUS, 2011
Some people asked about the source code for the C program we used, you can find the original version (not coded by us) here: http://cppgm.blogspot.com/2008/01/rsa-algorithm.html

Views: 27246
xkiller213

Views: 364
Math Forge

Views: 58
Santhana Todatry

Part 3: Introduction to codes and an example or RSA public key encryption.

Views: 1883
MAT 243 Discrete Mathematics

#rsa #deffiehellman #cryptographylectures #lastmomenttuitions
Take the Full Course of Cryptography and Network Security
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Cryptography and System Security Index
Lecture 1 Introduction to Cryptography and Security System
Lecture 2 Security Goals and Mechanism
Lecture 3 Symmetric Cipher
Lecture 4 Substitution Cipher
Lecture 5 Transposition Cipher
Lecture 6 Stream and Block Cipher
Lecture 7 Mono Alphabetic Cipher
Lecture 8 Poly Alphabetic Cipher
Lecture 9 Diffie Hellman
Lecture 10 RSA Algorithm with Solved Example
Lecture 11 IDEA Algorithm Full Working
Lecture 12 SHA-1 Algorithm Full Working
Lecture 13 Blowfish Algorithm Full working
Lecture 14 DES Algorithm Full Working
Lecture 15 Confusion and Diffusion
Lecture 16 AES Algorithm Full working
Lecture 17 Kerberos
Lecture 18 Malicious Software ( Virus and worms )
Lecture 19 DOS and DDOS Attack
Lecture 20 Digital Signature Full working Explained
More videos Coming Soon.

Views: 279834
Last moment tuitions

Introduce concepts of public key crypto, then a detailed example of using RSA. Course material via: http://sandilands.info/sgordon/teaching

Views: 11501
Steven Gordon

Fundamental concepts of Prime Numbers are discussed. Optimization of Private Key operations is presented. RSA Security is Analyzed.

Views: 561
Scholartica Channel

A brief introduction to prime numbers, touching on their use in nature and encryption. If you learnt something new and are feeling generous, please do support the channel at: https://www.patreon.com/bespokeeducation

Views: 179
BespokeEducation

Primes are the building blocks of math. But just how mysterious are they?
Our study of prime numbers dates back to the ancient Greeks who first recognized that certain numbers can't be turned into rectangles, or that they can't be factored into any way.
Over the years prime numbers have only become more and more sought. The Primes are the basis of internet banking and all encryption that allows the internet to exist depends on it. They are the building blocks of numbers themselves.
This video covers what prime numbers are and how mathematicians throughout the globe have been instrumental in discovering a large variety of proofs about them, from the Fundamental Theorem of Arithmetic to Gauss' prime number theorem to touching on the Riemann Hypothesis.
More information on Euclid's proof:
http://www.mathsisgoodforyou.com/conjecturestheorems/euclidsprimes.htm
Music:
Bortex: Gravity
Summer by Bensound | https://www.bensound.com

Views: 130
Kinertia

Please Fill the form - https://docs.google.com/forms/d/1kOxvqvz1IvBMHJ3UeLecLDuK7ePKjHAvHaRcxduHKEE/edit
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Views: 4513
hindi tutorials darshan

finding series and Prime numbers from a logarithmic spiral concept

Views: 1009
ConstructorsCorner

MIT 6.042J Mathematics for Computer Science, Spring 2015
View the complete course: http://ocw.mit.edu/6-042JS15
Instructor: Albert R. Meyer
License: Creative Commons BY-NC-SA
More information at http://ocw.mit.edu/terms
More courses at http://ocw.mit.edu

Views: 18661
MIT OpenCourseWare

This Excellent Video Unravels the Secrets of Prime Numbers.

Views: 235
The Primera

Basics of number theory for public key crypt; divisibility, relative prime, prime numbers; modular addition, subtraction, multiplication and division. Additive inverse .
introduction to number theory for public key crypto. Divisibility, factors, primes, relatively prime. Addition, subtraction, multiplication and division in modular .
CSS441, Semester 2, 2015, Lectures at Sirindhorn International Institute of Technology, Thammasat University, Thailand by Steven Gordon. Course material via: .

Views: 8
Neil Rios

Euclid identified Prime Numbers as building blocks for all numbers. This leads to the discovery of unique factorization. This idea lies at the heart of modern encryption techniques such as RSA.

Views: 17899
Art of the Problem

This video gives an overview of primality tests. Basic ideas on how these tests work are discussed.

Views: 561
Leandro Junes

The Miller-Rabin primality test is described in detail in this video. Number Theory facts and pseudo-code regarding this primality test are explained.

Views: 883
Leandro Junes

Foundations of Arithmetic, Algebra, and Graphing, Part 10. Dividing Integers, Meaning and Application, Part 2. (0:00) Introduction and review problems from last video. (1:08) Another visual way to think about the simpler form of the first problem. (2:07) The integers are NOT closed under division. (3:13) Division is NOT commutative. (4:30) Factoring using prime numbers and factor trees. (6:42) Prime factorizations are important for computer security (RSA codes).

Views: 632
Bill Kinney

Fundamental concepts of Public Key Encryption are discussed. RSA Public Encryption is presented. Optimization of Private Key operations is analyzed.
Public Key Encryption
Symmetric vs. Public-Key
RSA Public Key Encryption
RSA Key Construction
Optimizing Private Key Operations
RSA Security

Views: 1171
Scholartica Channel

Why are prime numbers important? Are there any practical uses of prime numbers or are they taught in school life just for covering academic syllabus! Get familiar with some practical uses of prime numbers in this short animated video.
Do share with us if you know any more real life uses of prime numbers. And what do you think about periodical cicadas, using prime numbers for their existence. Isn't it just amazing. Keep watching for more such curious Tell me why shorts every Monday @ 5PM (IST)
Till then Like and share our videos. Don't forget sharing is caring. Thanks for watching.
Follow us, Like us, be a part of the family:
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Sources and further readings:
http://www.baltimoresun.com/bal-te.ms.cicada10may10-story.html
http://math.stackexchange.com/questions/43119/real-world-applications-of-prime-numbers
To more about RSA encryption visit the wikipedia page:
https://en.wikipedia.org/wiki/RSA_(cryptosystem)
Bckground Music:
Kevin Macleod
incompetech.com

Views: 26411
The Explained Show

For more detail on back substitution go to: http://bit.ly/1W5zJ2g
Here is a link with help on relative primes: http://www.mathsisfun.com/definitions/relatively-prime.html
This is (hopefully) a very simple example of how to calculate RSA public and private keys. Just to be clear: these values should not be used for any real encryption purposes.

Views: 123076
Jenn Janesko

Dr. Soper discusses malicious data interception and public key encryption. Topics covered include wiretapping, defending against message interception, network encryption methods, the key exchange problem, public key encryption, RSA encryption, and key exchange using public key encryption.

Views: 21396
Dr. Daniel Soper

Presenter Matthew Tosh looks at the complex subject of prime numbers, from the theories relating to them, to some of their uses, in an information-packed video for maths teachers. For centuries, mathematicians have been searching for both larger primes and ways of breaking numbers down into their prime factors. Here, we see how prime numbers are used in cryptography algorithms, to help keep our money safe. And starting with Euclid's fundamental theorem of arithmetic, this video explains the role prime numbers play in internet security. Licensed to CPD College Ltd.

Views: 46
CPD College

Prime Adventure: Learn how to build algorithms (and write code!) which solve number theoretic challenges such as prime factorization. Follow the rest of this adventure on Khan Academy: http://www.khanacademy.org/cs/prime-adventure-level-1/1018672065

Views: 21491
Art of the Problem

Here's a second (better) example for how to use the Miller-Rabin primality test.

Views: 38785
Theoretically

This is a class room example of RSA encryption using 3 digit primes and excel for the calculation engine. The video is in three parts. Part 1 describes the initial setup of the algorithm and how to generate exponents of those numbers. This class happened on April 12, 2011 at Eastside Preparatory School in Kirkland.
Download the spreadsheet
https://docs.google.com/open?id=1GLcLhuBUvmC5_YxcILVLnkjhghFa8ABSlMLG7Wm9LZE

Views: 23568
Jonathan Briggs

Previous video: https://youtu.be/xffDdOY9Qa0
Next video: https://youtu.be/uPh6IUhiFUo

Views: 2674
Leandro Junes

From OSCON 2013: What do you need to know about prime numbers, Markov chains, graph theory, and the underpinnings of public key cryptography? Well, maybe more than you think!
In this talk, we'll explore the branch of mathematics that deals with separate, countable things. Most of the math we learn in school deals with real-valued quantities like mass, length, and time. However, much of the work of the software developer deals with counting, combinations, numbers, graphs, and logical statements: the purview of discrete mathematics. Join us for this brief exploration of an often-overlooked but eminently practical area of mathematics.
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Views: 52353
O'Reilly

Explains to algebra students the mathematics needed to perform public-key cryptography.

Views: 5035
Aaron Solt

Basics of number theory for public key crypt; divisibility, relative prime, prime numbers; modular addition, subtraction, multiplication and division. Additive inverse, multiplicative inverse.
Credit: Prof. Steven Gordon

Views: 132
Pritesh Prajapati

In symmetric key encryption the same key is used for both encryption and decryption. In contrast, in asymmetric key encryption a public key (known to everyone) is used for encryption and a private key (known only to the recipient) is used for decryption. Many asymmetric key encryption approaches are based on factoring as a trapdoor function, with the public key being the multiple of the two secret primes and the private key being the two secret primes. Asymmetric key encryption allows one party to encrypt a message to a second party they have never communicated with previously.
Credits: Talking: Geoffrey Challen (Assistant Professor, Computer Science and Engineering, University at Buffalo). Producing: Greg Bunyea (Undergraduate, Computer Science and Engineering, University at Buffalo).
Part of the https://www.internet-class.org online internet course. A blue Systems Research Group (https://blue.cse.buffalo.edu) production.

Views: 923
internet-class

A History of Primes
Manindra Agrawal, American Academy of Arts and Sciences, October 2002
The Clay Mathematics Institute (CMI) 2002 Annual Meeting took place on Wednesday, October 30, 2002, from 2:30 to 5:30 PM, at the American Academy of Arts & Sciences in Cambridge, Massachusetts. The Annual Meeting brought together an international assembly of mathematicians to celebrate the universality of mathematical thought. This meeting provided a public forum for discussion among leading mathematicians and scientists, and it strengthened relations between mathematicians, the public, and the scientific research community.
The meeting began with the presentation of the 2002 Clay Research Award to Oded Schramm (for his work on the Loewner equation) and to Manindra Agrawal (for his work on primality testing). CMI President Arthur Jaffe and Directors Landon Clay and Lavinia Clay gave the awards. This Research Award recognizes major recent breakthroughs in two mathematical directions, and represents the pinnacle of recognition of research achievement by CMI. Each prizewinner becomes a Clay Research Scholar, and receives a bronze model of the CMI logo, an elegant sculpture "Figureight Knot Complement vii/ CMI" by sculptor Helaman Ferguson. Former winners are: Andrew Wiles, Laurent Lafforgue, Alain Connes, Stanislav Smirnov and Edward Witten.
Two talks followed the awards ceremony. Manindra Agrawal of the Indian Institute of Technology surprised all experts in August 2002 by solving an ancient problem (working with two undergraduate students). They showed that one could determine the primality of a number in polynomial time. This was the first talk in the United States by the inventor of the new method. Vladimir Voevodsky from the Institute of Advanced Study gave the second talk. He spoke about the mathematical breakthroughs that led to his receiving the Fields Medal in August 2002.
"We have a very impressive set of ground-breaking mathematicians at this year's meeting as award winners and speakers. The meeting certainly will inspire young mathematicians who attend, as well as all those who read about it or view the meeting on the web," said Arthur Jaffe, President of the Clay Mathematics Institute. "Agrawal will discuss his exciting discovery - the ASK algorithm for primality testing, and Voevodsky will explain his novel approach to the mathematical modeling of shapes known as "motivic homotopy theory."
http://www.claymath.org/annual_meeting/2002_Annual_Meeting/

Views: 13305
PoincareDuality