PPT-Data encryption with big prime numbers

Daniel FreemaN SLU Old school codes Full knowledge of the code is needed to both encrypt messages and to decrypt messages The code can only be used between a small number of trusted people. Integers and Modular Arithmetic . Fall 2010. Sukumar Ghosh. Preamble. Historically, . number theory . has been a beautiful area of . study in . pure mathematics. . However, in modern times, . number theory is very important in the . Prime numbers and factors.. Prime numbers. Prime numbers divide by themselves and one.. So… 3=3*1…or… 13=13*1. But 16 divides 16*1 and 8*2 and 4*4. So you see that prime numbers are very specific.. Prime and Composite Numbers. Prime Number. A prime number is any whole number that has only two factors, itself and 1. . Example:. 5. It only has two factors, 5 and 1. 5 x 1= 5. What are other examples of prime numbers?. History, theories and applications. By Kim . Wojtowicz. Definition of a Prime Number. A Prime number is a number that has exactly 2 Distinct factors: itself and 1. . Smallest prime number is 2, it is also the only even prime number.. Remember to Silence Your Cell . Phone and Put It In Your Bag!. Definition of Prime and Composite Numbers. A natural number that has exactly two distinct (positive) factors is called a . prime. . number. Integers and Modular Arithmetic . Fall 2010. Sukumar Ghosh. Preamble. Historically, . number theory . has been a beautiful area of . study in . pure mathematics. . However, in modern times, . number theory is very important in the . There are many different ways that we can . categorise. /label/group . numbers.. What are some of the ways you that that we can categorise numbers?. Types of Numbers. There are many different ways that we can . Learning Goals. We will use our divisibility rules so that we can decompose numbers into prime factors.. We’ll know we understand when we can identify the prime factors that are used to form a number.. NANDAN GOEL. HISTORY. THE STUDY OF SURVIVING RECORDS OF EGYPTIANS SHOW THAT THEY HAD KNOWLEDGE OF PRIMES.. THE GREEK MATHEMATICIAN . “. EUCLID PERFORMED. ”. SOME EXCEPTIONAL WORK .. HIS WORK . “. What’s a Prime Number?. Lots of definitions out there. My Favorite (recursive): . “an integer greater than 1, that is not divisible by any smaller primes”. Note: The above is equivalent to (but feels less restrictive than) the more standard: . by Carol Edelstein. Definition. Product. – An answer to a multiplication problem.. . 7 x 8 = 56. Product. Definition. Factor. – a number that is multiplied by another to give a product.. . 7 x 8 = 56. Seth Futrell, Matthew Ritchie, . Dakota Perryman, Mark Thompson . (Tag’s Tots). Background History . Prime numbers have fascinated the human race for millennia with solutions to finding primes predating the times of euclid. Primes continue to amaze mathematicians and theoretical thinkers daily. Research of these fascinating numbers continues in present day with the continuing growth of the field of number theory and encryption protocols .. 1. Recap. Number Theory Basics. Abelian Groups. . for distinct primes p and q.  . 2. RSA Key-Generation. KeyGeneration. (1. n. ). Step 1: Pick two random n-bit primes p and q. . Step 2: Let N=. Maria Murphy. Central Florida Math Circle. University of Central Florida . Department of Mathematics . What is a Palindrome? . A palindrome is a word or phrase that reads the same forwards and backwards. .