Crypotography Question 1. A message m was encrypted using the RSA algorithm with n=899 and e=13....
Crypotography Question 1. A message m was encrypted using the RSA algorithm with n=899 and e=13. The ciphertext is 706. Find the message m. Show all the work from the scratch, including finding 1/e(using the extended Euclidean algorithm) and the resulting modular exponentiation...
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Crypotography Question 1. A message m was encrypted using the
RSA algorithm with n=899 and e=13....
For the RSA encryption algorithm , do the following (a) Use p=257,q=337(n=pq=86609),b=(p-1)(q-1)=86016. Gcd(E,b)=1, choose E=17, find...
For the RSA encryption algorithm , do the following (a) Use p=257,q=337(n=pq=86609),b=(p-1)(q-1)=86016. Gcd(E,b)=1, choose E=17, find D, the number which has to be used for decryption, using Extended Euclidean Algorithm (b) One would like to send the simple message represented by 18537. What is the message which will be sent? (c) Decrypt this encrypted message to recover the original message.
Computing RSA by hand. Let p = 13, q = 23, e = 17 be your...
Computing RSA by hand. Let p = 13, q = 23, e = 17 be your initial parameters. You may use a calculator for this problem, but you should show all intermediate results. Key generation: Compute N and Phi(N). Compute the private key k_p = d = e^-1 mod Phi(N) using the extended Euclidean algorithm. Show all intermediate results. Encryption: Encrypt the message m = 31 by applying the square and multiply algorithm (first, transform the exponent to binary representation)....
Exercise 1 (2 pts). In an RSA cryptosystem, Bob's public key is (n = 253, e...
Exercise 1 (2 pts). In an RSA cryptosystem, Bob's public key is (n = 253, e = 3), Alice uses this public key to encrypt a message M for Bob. The resulting ciphertext is 110. Recover the message M. (You can use online modular calculators available at the Web.)
O-8. (15 points) Bob's simple toy RSA eryptosystem has public key kyub(n, e) (65,5), where n =p,-...
o-8. (15 points) Bob's simple toy RSA eryptosystem has public key kyub(n, e) (65,5), where n =p,-5x13-65 and e-5. I. Describe the key pair generation procedure for Bob to generate his private key kor- d. With the above given parameters, use EEA to calculate d 2. Describe RSA encryption procedure that Alice uses to encrypt her plaintext message x to its above given parameters, what will be y? ciphertext y before sending the message to Bob. Suppose Alice's message x-...
(8) In an RSA cryptosystem, Bob’s public key is (n = 629, e = 43). Alice...
(8) In an RSA cryptosystem, Bob’s public key is (n = 629, e = 43). Alice uses this public key to encrypt the word “MARCH” and send the ciphertext to Bob. First, she represents this word in ASCII where the capital letters A, B, C, . . . , X, Y, Z are represented by integers 65, 66, 67, . . . , 88, 89, 90 respectively. Then she encrypts the five integers that represent M, A, R, C, H...
Problem 4. The plaintext P has been encrypted with RSA n = 65, e = 29...
Problem 4. The plaintext P has been encrypted with RSA n = 65, e = 29 to yield the ciphertext C = 3 = P29 mod 65. Find P using the decryption key d, and prove the congruence class of P that solves this congruence is unique.
You intercept a message “2206 0755 0436 1165 1737”, which you know was encrypted using RSA...
You intercept a message “2206 0755 0436 1165 1737”, which you know was encrypted using RSA with modulus n= 2747 and encrypting exponent e= 13.Crack the message (You do not need to bother converting it into letters)
If a public key has the value (e, n)-(13,77) (a) what is the totient of n,...
If a public key has the value (e, n)-(13,77) (a) what is the totient of n, or (n)? (b) Based on the answer from part (a), what is the value of the private key d? (Hint: Remember that d * e-1 mod (n), and that d < ф(n)) You may use an exhaustive search or the Modified Euclidean Algorithm for this. Show all steps performed. For both (c) and (d), use the Modular Power Algorithm, showing all steps along the...
in RSA e= 13 and n = 100 encrypt message HOW ARE YOU DOING using 00...
in RSA e= 13 and n = 100 encrypt message HOW ARE YOU DOING using 00 to 25 letter A to Z and 26 for space use different blocks to make p < n
(d) Decrypt the ciphertext message LEWLYPLUJL PZ H NYLHA ALHJOLY that was encrypted with the shift cipher f(p) (p+7) mod 26. [10 points] (e) [Extra Credit - 5 points] Encrypt the message "BA"...
(d) Decrypt the ciphertext message LEWLYPLUJL PZ H NYLHA ALHJOLY that was encrypted with the shift cipher f(p) (p+7) mod 26. [10 points] (e) [Extra Credit - 5 points] Encrypt the message "BA" using the RSA cryptosystem with key (ne) = (35,5), where n = p . q 5-7 and ged(e, (p-1) 1)) (5, 24) 1. 6. [5 points each (a) Is 2 a primitive root of 11? (b) Find the discrete logarithm of 3 modulo 11 to the base...
Computing RSA by hand. Let p = 13, q = 23, e = 17 be your initial parameters. You may use a calculator for this problem, but you should show all intermediate results. Key generation: Compute N and Phi(N). Compute the private key k_p = d = e^-1 mod Phi(N) using the extended Euclidean algorithm. Show all intermediate results. Encryption: Encrypt the message m = 31 by applying the square and multiply algorithm (first, transform the exponent to binary representation)....
Exercise 1 (2 pts). In an RSA cryptosystem, Bob's public key is (n = 253, e = 3), Alice uses this public key to encrypt a message M for Bob. The resulting ciphertext is 110. Recover the message M. (You can use online modular calculators available at the Web.)
o-8. (15 points) Bob's simple toy RSA eryptosystem has public key kyub(n, e) (65,5), where n =p,-5x13-65 and e-5. I. Describe the key pair generation procedure for Bob to generate his private key kor- d. With the above given parameters, use EEA to calculate d 2. Describe RSA encryption procedure that Alice uses to encrypt her plaintext message x to its above given parameters, what will be y? ciphertext y before sending the message to Bob. Suppose Alice's message x-...
Problem 4. The plaintext P has been encrypted with RSA n = 65, e = 29 to yield the ciphertext C = 3 = P29 mod 65. Find P using the decryption key d, and prove the congruence class of P that solves this congruence is unique.
If a public key has the value (e, n)-(13,77) (a) what is the totient of n, or (n)? (b) Based on the answer from part (a), what is the value of the private key d? (Hint: Remember that d * e-1 mod (n), and that d < ф(n)) You may use an exhaustive search or the Modified Euclidean Algorithm for this. Show all steps performed. For both (c) and (d), use the Modular Power Algorithm, showing all steps along the...
(d) Decrypt the ciphertext message LEWLYPLUJL PZ H NYLHA ALHJOLY that was encrypted with the shift cipher f(p) (p+7) mod 26. [10 points] (e) [Extra Credit - 5 points] Encrypt the message "BA" using the RSA cryptosystem with key (ne) = (35,5), where n = p . q 5-7 and ged(e, (p-1) 1)) (5, 24) 1. 6. [5 points each (a) Is 2 a primitive root of 11? (b) Find the discrete logarithm of 3 modulo 11 to the base...
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