Discrete math 1 1) In RSA algorithm, suppose the public key n = 55 (11*5) and e = 17. Please find a private key d which ed = 1 (mod 40) (40 = (11-1)(5-1)) 2) From the previous problem, suppose we have a message "one" (Letter A to Z are coded as 00 to 25), what will be the ciphered message? 3)Rewrite the classic Binary Search method as a Recursive Function (just the pseudocode.) 4)Deduce that, if A ⊆ B,...
Using RSA algorithm, if p=3 and q=11, k=3, then the public key is equal to (You may use the formulas below): Select two large prime numbers P, 9 Compute n = pxq v = (p-1) (q-1) • Select small odd integer k relatively prime to v gcd(k, v) = 1 Compute d such that (d k)%v = (k d)%v = 1 Public key is (k, n) Private key is (d, n) . . . Select one: a. (3,11) b. (33,3)...
Consider the RSA algorithm. Let the two prime numbers, p=11 and q=41. You need to derive appropriate public key (e,n) and private key (d,n). Can we pick e=5? If yes, what will be the corresponding (d,n)? Can we pick e=17? If yes, what will be the corresponding (d,n)? (Calculation Reference is given in appendix) Use e=17, how to encrypt the number 3? You do not need to provide the encrypted value.
Discrete Structures problem Suppose we use p = 7 and q = 5 to generate keys for RSA. a) What is n ? b) What is on)? c) One choice of e is 5. What are the other choices for e? d) Explain how you got your answer for part c. e) For the choice of e = 5 what is d? Show work. f) Using the public key (n, e), what is the message 3 encrypted as? Show work...
p=3, q=7 Suppose that Bob wants to create an example of an RSA public-key cryptosystem by using the two primes p ??? and q ???. He chooses public encryption key e He was further supposed to compute the private decryption key d such that ed 1 mod A(pq)). However, he confuses A and and computes instead d' such that ed' =1 (mod P(pq)). (i) Prove that d' works as a decryption key, even though it is not necessarily the same...
CIPHER THAT LETS LOOK PA RSA AT USES Two PRIMES p=23 AND q=17 PUBLIC KEY e=3 A) PRIVATE DECRYPTING KEY d. FIND IN B) DESCRIBE STEPS HOW TO FIND IS c=165. PLAIN TEXT CIPHERTEXTI IF
In a public key encryption system, the values p = 7, q = 11, s = 53 are selected. A numerical message x is then encrypted using the function y=x' mod pg. What was the original message x if the received message is y = 67? You may leave your answer in terms of an exponent. Explain why it is necessary in public key encryption to choose s to be relatively prime to (p-1)(9 – 1).
Discrete math problems: 9. Show that p = 10. Show that p = q and ( q p = n are logically equivalent. ) and q = (p V r) are logically equivalent. r
Discrete Math 1. Use the primes P1 = 3 and P2 = 17 and the value E = 3 with the RSA algorithm to compute the values below needed to get the keys: What is the value of N? What is the value of Z? What is the value of D? (ABET 5) Using the values from the problem 9) above, show how to encrypt the message, M = 44. Do NOT simplify, just show the computation needed to encrypt...
QUESTION 4 137 and 151 are assigned to p and q respectively to generate a pair of public and private keys. What is the modulus n? What is the value of the totient function ? If 11 is assigned to public key e, what is the value of the private key d? Choose from 1854, 1880, 16691, 16699