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Consider a consequence of Euclid's Lemma: a,b,c Z, gcd (a,b) =1 Aa | bca | b and Fermat's Little Theorem: If p is any prime number and a is any integer such that p Xa⇒a=¹= 1 (mod p). Show how these statements are used to show an RSA cypher will work. It is possible in RSA cryptog- raphy to encode a cypher with (pq, e) as public key, by using C=Me (mod pq) and then decode the cypher with d=-e (mod (p-1) (q-1)), using M = Cd (mod pq)

Consider a consequence of Euclid's Lemma: a,b,c Z, gcd (a,b) =1 Aa | bca | b and Fermat's Little Theorem: If p is any prime number and a is any integer such that p Xa⇒a=¹= 1 (mod p). Show how these statements are used to show an RSA cypher will work. It is possible in RSA cryptog- raphy to encode a cypher with (pq, e) as public key, by using C=Me (mod pq) and then decode the cypher with d=-e (mod (p-1) (q-1)), using M = Cd (mod pq)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider a consequence of Euclid's Lemma: V a,b,c € Z, gcd (a,b) =1 ^ a | bca | b and Fermat's Little Theorem: If p is any prime number and a is any integer such that p Xa ap=1= 1 (mod p). Show how these statements are used to show an RSA cypher will work. It is possible in RSA cryptog- raphy to encode a cypher with (pq, e) as public key, by using C-Me (mod pq) and then decode the cypher with d=-e (mod (p-1) (q-1)), using M = Cd (mod pq)
Transcribed Image Text:Consider a consequence of Euclid's Lemma: V a,b,c € Z, gcd (a,b) =1 ^ a | bca | b and Fermat's Little Theorem: If p is any prime number and a is any integer such that p Xa ap=1= 1 (mod p). Show how these statements are used to show an RSA cypher will work. It is possible in RSA cryptog- raphy to encode a cypher with (pq, e) as public key, by using C-Me (mod pq) and then decode the cypher with d=-e (mod (p-1) (q-1)), using M = Cd (mod pq)
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