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. Consider the following textbook RSA example. No provisions are made for high precision arithmetic, nor have the algorithms been encoded for efficiency when dealing with large numbers. Then, nis used by all the users. RSA Calculator JL Popyack, October 1997 This guide is intended to help with understanding the workings of the RSA Public Key Encryption/Decryption scheme. … Thus, the smallest value for e … Then n = p * q = 5 * 7 = 35. Answer: n = p * q = 7 * 11 = 77 . RSA Example - Key Setup 1. Examples Question: We are given the following implementation of RSA: A trusted center chooses pand q, and publishes n= pq. Show that if two users, iand j, for which gcd(ei;ej) = 1, receive the same Give a general algorithm for calculating d and run such algorithm with the above inputs. CIS341 . Is there any changes in the answers, if we swap the values of p and q? Compute ø(n)=(p – 1)(q-1)=16 x 10=160 4. Determine d: d.e= 1 mod 160 and d < 160 Value is d=23 since 23x7=161= 1x160+1 6. 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. What is the encryption of the message M = 41? 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 - 19500596 Consider an RSA key set with p = 17, q = 23, N = 391, and e = 3 (as in Figure 1.9). Calculate n=pq =17 x11 =187 3. 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). Let be p = 7, q = 11 and e = 3. But I want to generate private key corresponding to d = 23 and public key corresponding to e = 7. Choose n: Start with two prime numbers, p and q. Solution- Given-Prime numbers p = 13 and q = 17; Public key = 35 . Compute n = pq =17 x 11=187 3. What numbers (less than 25) could you pick to be your enciphering code? f(n) = (p-1) * (q-1) = 6 * 10 = 60. What value of d should be used for the secret key? If the public key of A is 35, then the private key of A is _____. What is the max integer that can be encrypted? Select e: GCD(e,160) =1;choose e=7 Publish public … PRACTICE PROBLEMS BASED ON RSA ALGORITHM- Problem-01: In a RSA cryptosystem, a participant A uses two prime numbers p = 13 and q = 17 to generate her public and private keys. For this example we can use p = 5 & q = 7. Select e: gcd(e,160)=1; choose e =7 5. Using RSA, p= 17 and q= 11. Calculate ø(n )=(p –1)(q -1) =16 x10 =160 4. 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). 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. I tried to apply RSA … How can i give these numbers as input. 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 primes: p =17 & q =11 2. Sample of RSA Algorithm. 17 = 9 * 1 + 8. Select primes: p=17 ;q=11 2. RSA Example - Key Setup 1. A general algorithm for calculating d and run such algorithm with the above inputs ) * ( )... To generate private key corresponding to e = 7, q =,. A is 35, then the private key diand A public key = 35 1 mod 160 d. = ( p – 1 ) ( q -1 ) =16 x 10=160 4 p =17 & q 2! 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