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Discrete math 1 1) In RSA algorithm, suppose the public key n = 55 (11*5) and...
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...
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...
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...
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 ??? an...
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...
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 =...
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 (...
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
Perform encryption using the RSA algorithm. Given p=5, q=11, e=3, M=9, determine the following: modulus n...
Perform encryption using the RSA algorithm. Given p=5, q=11, e=3, M=9, determine the following: modulus n = , t = , private key d = , ciphertext c = (Note: Choose the smallest value "d" that works) If M is changed to M=40, the new ciphertext value becomes c =
QUESTION 4 137 and 151 are assigned to p and q respectively to generate a pair...
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
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)...
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
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
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