# rsa example p=17 q=11

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 CIS341 . f(n) = (p-1) * (q-1) = 6 * 10 = 60. Consider the following textbook RSA example. Select e: gcd(e,160)=1; choose e =7 5. How can i give these numbers as input. - 19500596 Calculate n=pq =17 x11 =187 3. 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. 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. Choose n: Start with two prime numbers, p and q. RSA Example - Key Setup 1. Compute ø(n)=(p – 1)(q-1)=16 x 10=160 4. What value of d should be used for the secret key? Compute n = pq =17 x 11=187 3. I tried to apply RSA … What is the encryption of the message M = 41? Then n = p * q = 5 * 7 = 35. He gives the i’th user a private key diand a public key ei, such that 8i6=jei6=ej. 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). Show that if two users, iand j, for which gcd(ei;ej) = 1, receive the same Determine d: d.e= 1 mod 160 and d < 160 Value is d=23 since 23x7=161= 1x160+1 6. Calculate ø(n )=(p –1)(q -1) =16 x10 =160 4. Answer: n = p * q = 7 * 11 = 77 . Using RSA, p= 17 and q= 11. Select primes: p =17 & q =11 2. … Solution- Given-Prime numbers p = 13 and q = 17; Public key = 35 . 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). Consider an RSA key set with p = 17, q = 23, N = 391, and e = 3 (as in Figure 1.9). Thus, the smallest value for e … 17 = 9 * 1 + 8. Select primes: p=17 ;q=11 2. What numbers (less than 25) could you pick to be your enciphering code? No provisions are made for high precision arithmetic, nor have the algorithms been encoded for efficiency when dealing with large numbers. For this example we can use p = 5 & q = 7. Examples Question: We are given the following implementation of RSA: A trusted center chooses pand q, and publishes n= pq. Is there any changes in the answers, if we swap the values of p and q? Sample of RSA Algorithm. Select e: GCD(e,160) =1;choose e=7 Give a general algorithm for calculating d and run such algorithm with the above inputs. Then, nis used by all the users. Let be p = 7, q = 11 and e = 3. 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. But I want to generate private key corresponding to d = 23 and public key corresponding to e = 7. 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. Publish public … 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. RSA Example - Key Setup 1. If the public key of A is 35, then the private key of A is _____. What is the max integer that can be encrypted? RSA Calculator JL Popyack, October 1997 This guide is intended to help with understanding the workings of the RSA Public Key Encryption/Decryption scheme. With the above inputs numbers p = 7 ; public key = 35 implementation of RSA A. That if two users, iand j, for which gcd ( )... 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