Question

In: Computer Science

Consider an RSA system with p = 7109 and q = 7919. Generate a public and...

Consider an RSA system with p = 7109 and q = 7919. Generate a public and private key pair based on the given p and q. Show the STEPS

Solutions

Expert Solution

Given:

p = 7109 and q = 7919

Public and Private keys can be find using belwo steps:

  • Find Derived Number (e)

    • Number e must be greater than 1 and less than (p − 1)(q − 1).

    • There must be no common factor for e and (p − 1)(q − 1) except for 1. In other words two numbers e and (p – 1)(q – 1) are coprime.

Let n = p * q = 7109 * 7919 = 56,296,171

Let m = (p-1) * (q-1) = 56,281,144

now, e = 3

  • Form the public key

    • The pair of numbers (n, e) form the RSA public key and is made public.

    • public key = (56296171 , 3)

  • Generate the private key

    • Private Key d is calculated from p, q, and e. For given n and e, there is unique number d.

    • Number d is the inverse of e modulo (p - 1)(q – 1). This means that d is the number less than (p - 1)(q - 1) such that when multiplied by e, it is equal to 1 modulo (p - 1)(q - 1).

    • This relationship is written mathematically as follows −

ed = 1 mod (p − 1)(q − 1)

Related Solutions

QUESTION 26 Consider RSA with p = 7 and q = 11. What are n and...
QUESTION 26 Consider RSA with p = 7 and q = 11. What are n and z? n z 4 points    QUESTION 27 Put the following wireless encryption protocols in order from most secure to least secure.       -       1.       2.       3.          WPA       -       1.       2.       3.          WEP       -       1.       2.   ...
Computer Security Sara is using RSA crypto-system with the following setup: p = 11 and q...
Computer Security Sara is using RSA crypto-system with the following setup: p = 11 and q = 3. Sara publish his Public Key: (n, e) = (33, 3). a. Find n, Ф(n). b. Calculate Sara’s private key. c. Nora wants to send the message M = 13 to Sara. Using Sara’s public and private keys, calculate the ciphertext C, and the value for Message R, when Sara recovers the message. d. Deem wants to set up his own public and...
a) In a public-key system using RSA, n=77 and its public key is e=23. What is...
a) In a public-key system using RSA, n=77 and its public key is e=23. What is the private key d? Show your steps of calculation. b) Let M=3. Compute its cipher text under the above RSA. Please use the divide conquer algorithm to compute the exponential function for the cipher text.
RSA system ( cryptology)
What is the original message encrypted using the RSA system with n = 53 * 61 and e = 17 if the encrypted message is 3185 2038 2460 2550
Write C program for RSA encryption and decryptin, where: p = 11,q = 5, e =...
Write C program for RSA encryption and decryptin, where: p = 11,q = 5, e = 7
RSA: Alice wishes to send Bob the message POET. Suppose Bob chooses P = 29, Q...
RSA: Alice wishes to send Bob the message POET. Suppose Bob chooses P = 29, Q = 31, E = 47, and D = 143. Show the steps that Alice uses to encrypt the message POET (use the ascii values of the letters P, O, E, and T), and how Bob decrypts the message he receives from Alice. You will be generating very large numbers, and will find the following calculator helpful: https://www.calculator.net/big-number-calculator.html
Please perform encryption and decryption given the following values of an RSA public key cryptosystem; p=17,...
Please perform encryption and decryption given the following values of an RSA public key cryptosystem; p=17, q=31, e=7 and M=2
IN PYTHON Generate valid keys (e, n) for the RSA cryptosystem.
IN PYTHON Generate valid keys (e, n) for the RSA cryptosystem.
(c) (¬p ∨ q) → (p ∧ q) and p (d) (p → q) ∨ p...
(c) (¬p ∨ q) → (p ∧ q) and p (d) (p → q) ∨ p and T I was wondering if I could get help proving these expressions are logically equivalent by applying laws of logic. Also these 2 last questions im having trouble with. Rewrite the negation of each of the following logical expressions so that all negations immediately precede predicates. (a) ¬∀x(¬P(x) → Q(x)) (b) ¬∃x(P(x) → ¬Q(x))
import math print("RSA ENCRYPTION/DECRYPTION") print("*****************************************************") #Input Prime Numbers print("PLEASE ENTER THE 'p' AND 'q' VALUES BELOW:")...
import math print("RSA ENCRYPTION/DECRYPTION") print("*****************************************************") #Input Prime Numbers print("PLEASE ENTER THE 'p' AND 'q' VALUES BELOW:") p = int(input("Enter a prime number for p: ")) q = int(input("Enter a prime number for q: ")) print("*****************************************************") #Check if Input's are Prime '''THIS FUNCTION AND THE CODE IMMEDIATELY BELOW THE FUNCTION CHECKS WHETHER THE INPUTS ARE PRIME OR NOT.''' def prime_check(a): if(a==2): return True elif((a<2) or ((a%2)==0)): return False elif(a>2): for i in range(2,a): if not(a%i): return false return True check_p =...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT