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

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