Home
Search results “Number theory and cryptography problems and solutions”

06:49
For System of Congruence equations - Chinese Remainder Theorem Examples 1 and 2: Example 1: https://www.youtube.com/watch?v=OB1OcmVSWLc Example 2: https://www.youtube.com/watch?v=NSpwIu2xaf4&list=PLsT0BEyocS2JaJZHRyyFcRV2KHyg5OEz8 The Many Solution case video: https://www.youtube.com/watch?v=fxwRrVcddww&t=15s The No Solution Case video: https://www.youtube.com/watch?v=HofgpkQH3-M In this video, I show you an example of a congruence equation that has ONE solution.
Views: 26419 Polar Pi

11:45
Find the least residue (modulo p) using Fermat's Little Theorem; or find the remainder when dividing by p. We start with a simple example, so that we can easily check the answer, then look at much bigger numbers where the answers cannot be directly checked on a calculator.
Views: 232645 Maths with Jay

05:51
CHINESE REMAINDER THEOREM BY B.K. TUTORIALS
Views: 107383 B.K. TUTORIALS

06:11
Linear congruence problems and solutions in hindi easy way to solve linear congruence problems. Problems on linear congruence . Linear congruence problems and solutions in hindi. NUMBER THEORY. LINEAR CONGRUENCE. Real Analysis - Integral Equations and Boundary Value Problems https://www.amazon.in/dp/8121928052?ref=yo_pop_ma_swf Ode and pde {differential equation} - Ordinary and Partial Differential Equations https://www.amazon.in/dp/9352535863?ref=yo_pop_ma_swf Intregral equation and boundary value problems - Integral Equations and Boundary Value Problems https://www.amazon.in/dp/8121928052?ref=yo_pop_ma_swf Please subscribe the chanel for more vedios and please support us.
Views: 21065 Mathematics Analysis

51:44
Modular arithmetic especially the properties of congruence are an important tool in arriving at quick solutions to a variety of problems. In this video Mayank unravels this concept of Congruence starting with the basic concepts and then explaining the 5 key properties of Congruence (≡): a+c ≡ (b+d)mod N (Remainder of Sums ≡ Sum of Remainders) a-c ≡ (b-d)mod N (Remainder of Difference ≡ Difference of Remainders) ac ≡ (bd)mod N (Remainder of Products ≡ Products of Remainders) a^e ≡ b^e mod N (Remainder of Exponent ≡ Exponent of Remainders) a/e ≡ b/e (mod N/gcd(N,e)) (However, don’t do division without writing basic equation Mayank applies these concepts to arrive at quick solutions for 7 representative problems - reducing seemingly impossible math involving large numbers to mere seconds. Some example problems from the video: Find the remainder 6^(6^(6^6 ) )/7 Find the last digit of (17)^16 There are 44 boxes of chocolates with 113 chocolates in each box. If you sell the chocolates by dozens, how many will be leftover? More Motivations – Reducing Big Number @0:08 Why Bother? – Shortcuts to Several Problems @1:10 Face of a Clock @2:05 Face of a Clock Replace 12 with 0 – Module 12 @4:38 What Happens with 7 Days? @6:20 Running the Clock Backwards @8:37 Addition and Subtraction of Congruence’s @10:54 Application of Addition – Example-1 @14:30 Multiplication in Congruence’s @18:46 Application of Multiplication – Example -2/3 @22:15 Exponentiation in Congruence’s @26:08 Application of Exponentiation Example -4/5 @27:58 Division of Congruence’s: Never Divide, Think from Basics @33:37 Combining Congruence’s @38:43 Example – 6 @40:36 Concept of Multiplicative Inverse @48:33 Summary @49:30 Next – Faster Solutions to Exponent Problems @51:05 #Inverse #Exponentiation #Dozens #Subtraction #Happen #Congruence #Arithmetic #Reducing #Motivations #Delayed #Mayank #Examrace
Views: 54634 Examrace

18:51
Learn more math and science with brilliant.org, https://brilliant.org/blackpenredpen/ , first 200 people to sign up will get 20% off your subscription, and you can also support my channel! Thank you! Read more about CRT: https://brilliant.org/wiki/chinese-remainder-theorem/ Solution to the question: https://brilliant.org/problems/thursday-birthday/ a classic modular arithmetic problem, solving system of congruences, must know number theory basic, blackpenredpen, math for fun, https://blackpenredpen.com/bprplive, https://twitter.com/blackpenredpen, [email protected]
Views: 59317 blackpenredpen

18:21

08:08
If you missed part 1: https://www.youtube.com/watch?v=eSFA1Fp8jcU ►Support the Channel Patreon: https://patreon.com/majorprep PayPal: https://www.paypal.me/majorprep Join Facebook Group: https://www.facebook.com/groups/majorprep/ Follow MajorPrep on Twitter: https://twitter.com/MajorPrep1 ►Check out the MajorPrep Amazon Store: https://www.amazon.com/shop/majorprep *************************************************** ► For more information on math, science, and engineering majors, check us out at https://majorprep.com Best Ways to Contact Me: Facebook, twitter, or email ([email protected])
Views: 58057 MajorPrep

03:55
For System of Congruence equations - Chinese Remainder Theorem Examples 1 and 2: Example 1: https://www.youtube.com/watch?v=OB1OcmVSWLc Example 2: https://www.youtube.com/watch?v=NSpwIu2xaf4&list=PLsT0BEyocS2JaJZHRyyFcRV2KHyg5OEz8 The Many Solution case video: https://www.youtube.com/watch?v=fxwRrVcddww&t=15s The One Solution Case: https://www.youtube.com/watch?v=kXL9UKujxJo In this video, I show you an example of a congruence equation that has ONE solution. In this video, I show you an example of a congruence equation that has no solutions. I also prove why it has no solutions.
Views: 1103 Polar Pi

12:43
We construct a small RSA cryptography system using basic number theoretic results, including linear congruences, Euler's function and Euler's Theorem.

09:43
Once you know how to solve diophantine equations with a single variable, the next step in complexity is to consider equations with two variables. The simplest such equations are linear and take the form ax+by=c. Before we solve this equation generally, we need a preliminary result. We show that you can solve the equation ax+by=GCD(a,b) by performing the Euclidean algorithm, and then reverse-substituting to arrive at a single solution. Subject: Elementary Number Theory Teacher: Michael Harrison
Views: 96258 Socratica

07:20
A solution to a typical exam question. See my other videos https://www.youtube.com/channel/UCmtelDcX6c-xSTyX6btx0Cw/.
Views: 303441 Randell Heyman

10:17
Find integer solutions a^2+b^2=4c+3 , a number theory proof or disproof. blackpenredpen, math for fun, https://blackpenredpen.com/bprplive, https://twitter.com/blackpenredpen, [email protected]
Views: 84631 blackpenredpen

05:13
Views: 62 AsTonyShinFin

06:06

14:13
Let's acquaint ourselves with two of the most important theorems in elementary number theory (and competition math like AMC/AIME) by solving an interesting problem. The only prerequisite is the basic knowledge of modular arithmetic (what it is, how it behaves under addition/multiplication, some intuition on number theory). Congratulations to Essentials of Math, Gustavo Exel, Devansh Sehta, Minh Cong Nguyen, Prathmesh, Eliot Argüello, Jack Miller, NoName, Daulian Doge, and Benjamin Wang for successfully solving this challenge question! Essentials of Math was the first person to solve the question. Your support is truly a huge encouragement. Please take a second to subscribe in order to send us your valuable support and receive notifications for new videos! Every subscriber and every like are wholeheartedly appreciated. For more Weekly Math Challenges: https://www.youtube.com/playlist?list=PLpoKXj-PWCbaDXYHES37_zX4O-kCWxguM
Views: 8803 LetsSolveMathProblems

09:54
Views: 55528 Quick Trixx

06:16
B.K. TUTORIALS SOLUTION OF CONGRUENCE EQUATION
Views: 34253 B.K. TUTORIALS

06:28
Congruence, Modular Arithmetic, 3 ways to interpret a ≡ b (mod n), Number theory, discrete math, how to solve congruence, blackpenredpen, math for fun, https://blackpenredpen.com/bprplive, https://twitter.com/blackpenredpen, [email protected]
Views: 94263 blackpenredpen

17:12
Introduction to congruence and the terminology used. Fairly basic with emphasis on the arithmetic of remainders. Examples of the addition and multiplication rules for congruence. Powers and Fermat’s little theorem. Lastly an example solved using Fermat’s little theorem.
Views: 91469 DLBmaths

17:57
This video clearly explains the concept of modulo in modular example. Several examples involving positive and negative dividends were given. Enjoy!!! www.modular-arithmetic.appspot.com www.samuelchukwuemeka.com
Views: 189879 Samuel Chukwuemeka

10:02
Views: 38833 Iqbal Shahid

14:23
How to solve 17x ≡ 3 (mod 29) using Euclid's Algorithm. If you want to see how Bézout's Identity works, see https://www.youtube.com/watch?v=9PRPr6J_btM
Views: 211959 Maths with Jay

08:42
BA BSC 1ST YEAR NUMBER THEORY TRIGONOMETRY EXERCISE 2.2 MODULO M LINEAR CONGRUENCE UNIQUE SOLUTION CHAPTER 2 EXERCISE 2.2 #BABSCMATHEMATICS#LINEAR CONGRUENCE# A+ JULANA EDUCATION HUB EDUCATING FOR BETTER FUTURE A PLUS INSTITUTE OF SCIENCE APJ INSTITUTE OF SCIENCE
Views: 5977 A Plus Julana - APJ

04:12

10:43

06:46

01:51
Congratulations to Hizami Anuar, staffehn, Laura Kuttnig, Minh Cong Nguyen, FaTalCaT FL, Prof Bits, and attyfarbuckle for successfully solving the last week's math challenge question! Hizami Anuar was the first person to solve the question. Your support is truly a huge encouragement. Please take a second to subscribe in order to send us your valuable support and receive notifications for new videos! Every subscriber and every like are wholeheartedly appreciated. Welcome, everyone! My channel hosts one weekly math challenge question per week (made by either myself, my family, or my friends), which will be posted every Wednesday. Please comment your proposed answer and explanation below! If you are among the first ten people with the correct answer, you will be recognized in the next math challenge video. The solution to this question and new question will be posted next Wednesday.
Views: 5313 LetsSolveMathProblems

08:40
Views: 212781 Eddie Woo

03:55
Solving congruences, 3 introductory examples, Number Theory, Modular Arithmetic, blackpenredpen, math for fun, https://blackpenredpen.com/bprplive, https://twitter.com/blackpenredpen, [email protected]
Views: 35604 blackpenredpen

08:09

02:21
How to solve 6x ≡ 4 (mod 10) If you want to see how to solve a linear congruence using Euclid's Algorithm, see https://youtu.be/4-HSjLXrfPs
Views: 67950 Maths with Jay

13:42
#rsa #deffiehellman #cryptographylectures #lastmomenttuitions Take the Full Course of Cryptography and Network Security What we Provide 1) 20 Videos (Index is given down) + More Update will be Coming Before final exams 2)Hand made Notes with problems for your to practice 3)Strategy to Score Good Marks in Cryptography and Network Scurity To buy the course click https://goo.gl/mpbaK3 if you have any query email us at [email protected] Sample Notes : https://goo.gl/Ze1FpX or Fill the form we will contact you https://goo.gl/forms/2SO5NAhqFnjOiWvi2 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: 315993 Last moment tuitions

41:17
Innovations in Algorithmic Game Theory May 23rd, 2011 Hebrew University of Jerusalem First session: Micheal O. Rabin - Cryptography and Solutions for Matching Problems Session Chair: Noam Nisan.

02:16
Here we find a remainder using the powerful Fermat's Little Theorem.
Views: 12742 Joshua Helston

03:34
In the Department of Mathematical Sciences at Keio University, the Bannai Group, led by Professor Kenichi Bannai, is conducting research in number theory. Number theory, which deals with the properties of integers, is known as the "Queen of Mathematics." The Bannai Group is focused especially on arithmetic geometry. Arithmetic geometry utilizes methods and results from algebraic geometry. In this field, number theoretical problems are investigated via the geometric properties of geometric objects defined by algebraic equations. Q. "Humans perceive things in two ways, logically and intuitively. Logic involves calculating things precisely. On the other hand, when using intuition, especially geometric intuition, we look at a problem in a certain geometric way and immediately "know" the answer. If one asks how this can be applied to problems in number theory, for example, consider the problem of finding rational solutions of the equation x2 + y2 = 1. The problem of seeking rational solutions of an algebraic equation is a number theoretical problem. Geometry comes into the picture if one thinks of the equation x2 + y2 = 1 as expressing a unit circle. When I use the word geometric intuition, what I mean is, it is much easier to solve this problem if one thinks that the equation x2 + y2 = 1 is not simply an algebraic equation but also that it represents a circle." Using methods from arithmetic geometry, Andrew Wiles in 1995 solved the Fermat's Last Theorem, which had puzzled mathematicians for 300 years. Number theory can be applied for example to cryptography, which is an important practical application of number theory to society. Q. "Because number theory concerns integers s -- 1, 2, 3, and so on -- one might think it's a very narrow field. At first, I also imagined that number theory was a very narrow topic; I wanted to do mathematics, but number theory did not seem all that interesting. But when I learned that problems in number theory were deeply related to geometry and also to analysis through various interesting analytic functions, I realized that number theory was a very deep field related to a wide range of areas in mathematics. That's what's fascinating about number theory. Rather than being superficial, because number theory deals with integers, which is a very fundamental object of study, it is deeply related to many interesting theories in the forefront of mathematics." Since the dawn of civilization, numbers and equations were used to better understand natural phenomena. Through abstraction, mathematics has greatly expanded its range of application. The Bannai Group will continue to do research, in order to understand through logic and intuition abstract phenomena appearing in number theory.

01:25:50
Views: 35101 matsciencechannel

01:19:41
Views: 5205 matsciencechannel

00:21
Views: 27 Rose Holt

17:57

10:26
Views: 78223 KNOWLEDGE GATE

23:42
This video covers the definitions for some basic algebraic structures, including groups and rings. I give examples of each and discuss how to verify the properties for each type of structure.
Views: 53113 James Hamblin

17:32
This video will explain you in detail how caesar cipher encryption and decryption technique works. This video includes solved example for caesar cipher encryption and decryption algorithm on whiteboard. I had explained in detail about difficulties student might face while solving example related to caesar cipher in their examination. More videos about encryption algorithms, computer tips and tricks, ethical hacking are coming very soon so share this video with your friends. Subscribe to my youtube channel so that you can know when I upload any new video. See you all very soon in next video, have great days ahead. Thanks for watching my video. #caesar #encryption #decryption
Views: 33058 SR COMPUTER EDUCATION

11:22
This video shows you how to calculate the order of integers and how to find primitive roots.
Views: 19032 Cathy Frey

02:38
This video is part of an online course, Applied Cryptography. Check out the course here: https://www.udacity.com/course/cs387.
Views: 10815 Udacity

04:21
Views: 21239 Quick Trixx

10:08