PPT-Cryptography CS 555 Topic 24: Finding Prime Numbers, RSA

1 Recap Number Theory Basics Abelian Groups for distinct primes p and q   2 RSA KeyGeneration KeyGeneration 1 n Step 1 Pick two random nbit primes p and q Step 2 Let N. 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.. 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. 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. ICS 6D. Sandy . Irani. Cryptography Intro. Alice wants to send a message to Bob so that even if Eve can see the transmitted information, she does not learn the true message.. message. message. message. sit down. get . out homework. &quietly work on . bellringer. Solve. -4^2 (-2)^3 (-3)^4. Solve. -4^2 (-2)^3 (-3)^4. -16. -8. 81. Get papers . sit down. get . out homework. &quietly work on . 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 . “. 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.. 1. Administrative Note. Professor Blocki is traveling and will be back on Wednesday. . E-mail: . jblocki@purdue.edu. . Thanks to Professor Spafford for covering the first lecture!. 2. https://www.cs.purdue.edu/homes/jblocki/courses/555_Spring17/index.html. 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. When Will I Ever Use Prime and Composite Numbers?. If you are baking cupcakes for a birthday party, you will be able to know if the amount you baked can be divided evenly between your friends. . Will you have leftovers? If it is a prime number, you know there will be leftovers!. 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 .. Encryption is the key to information security. The main idea- by using only . public. information, a sender can lock up their information in such a way that it can only be unlocked (. privately. ) by the intended recipient.. What is a composite number?. Give an example of each.. Greatest Common Factor. Mr. . Haupt. CC.2.1.8.E.1. Greatest Common Factor. The Greatest Common Factor, or GCF, is the largest number that goes in to every number given..