Lecture 4 part 2.ppt - RSA Encryption What is an RSA Number An RSA number n is a number s.t n=pq Where p and q are distinct large prime integers totient

# Lecture 4 part 2.ppt - RSA Encryption What is an RSA Number...

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RSA Encryption

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What is an RSA Number? An RSA number n is a number s.t. n=pq Where p and q are distinct, large, prime integers.
totient function φ(n) In number theory, Euler's totient function counts the positive integers up to a given integer n that are relatively prime to n. For example, the totatives of n = 9 are the six numbers 1, 2, 4, 5, 7 and 8

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Let’s Make a Key, Shall We? 1. Let’s use small prime numbers for the example: p=2 q=5 n=pq=10 2. Compute the totient: φ(n) = (p-1)(q-1) = 1*4 = 4 Observe that the number of integers less than n that are coprime to n is 4: (1, 3, 7, 9) 3. Choose an integer

Unformatted text preview: e s.t. 1 &lt; e &lt; φ( n ), and e and φ( n ) are coprime (1 &lt; e &lt; 4) e = 3 (e is used as the public key exponent) 4. Compute d s.t. d*e = 1 + kφ(n) for some integer k (k=2,5) . d*3 = 1 + k*4 OR e*d=1 mod ø(N) 3*d=1 mod 4 d = 7 ( d is used as the private key exponent) Let’s Make a Key, Shall We? 5-So then, the public key will be: c=m e mod n c=m 3 mod 10 6-And the private key will be: m=c d mod n m=c 7 mod 10 example We use the public key to encrypt and the private key to decrypt If we want to encrypt m=8 we use c=8 3 mod 10 = 2 In order to decrypt c=2 we use m=2 7 mod 10 = 8...
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