- 19500596 Then n = p * q = 5 * 7 = 35. Select primes: p=17 ;q=11 2. p =17, q = 11 n = 187, e= 7 & d = 23 After sufring on internet i found this command to generate the public,private key pair : openssl genrsa -out mykey.pem 1024. Select e: GCD(e,160) =1;choose e=7 Now, we need to compute d = e-1 mod f(n) by using backward substitution of GCD algorithm: According to GCD: 60 = 17 * 3 + 9. Then, nis used by all the users. For this example we can use p = 5 & q = 7. What is the encryption of the message M = 41? CIS341 . 17 = 9 * 1 + 8. Select primes: p =17 & q =11 2. Next the public exponent e is generated so that the greatest common divisor of e and PHI is 1 (e is relatively prime with PHI). Is there any changes in the answers, if we swap the values of p and q? RSA Example - Key Setup 1. RSA Calculator JL Popyack, October 1997 This guide is intended to help with understanding the workings of the RSA Public Key Encryption/Decryption scheme. Choose n: Start with two prime numbers, p and q. RSA Example - Key Setup 1. Select e: gcd(e,160)=1; choose e =7 5. RSA Key Construction: Example Select two large primes: p, q, p ≠q p = 17, q = 11 n = p×q = 17×11 = 187 Calculate = (p-1)(q-1) = 16x10 = 160 Select e, such that gcd( , e) = 1; 0 < e < say, e = 7 Calculate d such that de mod = 1 Use Euclid’s algorithm to find d=e-1mod 160k+1 = 161, 321, 481, 641 Calculate n=pq =17 x11 =187 3. No provisions are made for high precision arithmetic, nor have the algorithms been encoded for efficiency when dealing with large numbers. Publish public … Using RSA, p= 17 and q= 11. Answer: n = p * q = 7 * 11 = 77 . Consider the following textbook RSA example. Examples Question: We are given the following implementation of RSA: A trusted center chooses pand q, and publishes n= pq. What is the max integer that can be encrypted? Calculate F (n): F (n): = (p-1)(q-1) = 4 * 6 = 24 Choose e & d: d & n must be relatively prime (i.e., gcd(d,n) = 1), and e & d must be multiplicative inverses mod F (n). Consider an RSA key set with p = 17, q = 23, N = 391, and e = 3 (as in Figure 1.9). Calculate ø(n )=(p –1)(q -1) =16 x10 =160 4. What numbers (less than 25) could you pick to be your enciphering code? Give a general algorithm for calculating d and run such algorithm with the above inputs. What value of d should be used for the secret key? He gives the i’th user a private key diand a public key ei, such that 8i6=jei6=ej. Example 1 Let’s select: P =11 Q=3 [Link] The calculation of n and PHI is: n=P × Q = 11 × 3 =33 PHI = (p-1)(q-1) = 20 The factors of PHI are 1, 2, 4, 5, 10 and 20. So, the public key is {3, 55} and the private key is {27, 55}, RSA encryption and decryption is following: p=7; q=11; e=17; M=8. But I want to generate private key corresponding to d = 23 and public key corresponding to e = 7. Compute ø(n)=(p – 1)(q-1)=16 x 10=160 4. How can i give these numbers as input. Thus, the smallest value for e … Sample of RSA Algorithm. f(n) = (p-1) * (q-1) = 6 * 10 = 60. 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