RSA basics
Explain an attack that can break RSA for ?=3 (Hint: Read Chinese Remainder Theorem, and explain how it is used to attack e=3)
RSA basics Explain an attack that can break RSA for ?=3 (Hint: Read Chinese Remainder Theorem,...
Problem 3. Use the Chinese Remainder Theorem to find all congruence classes that satisfy x2 = 1 mod 77.
Problem 2.6.1. We have 7*6* 55 = 2310. Extend the technique of the Chinese remainder theorem to find the solutions in Z2310 of the equations. 2x => 3 X 564 5x 355 50 Hint: There will be 5 solutions because the last equation has 5 solutions. You may use the Mathematica command ExtendedGCD.
can you please help me with these
Use u U 6. Use the Chinese remainder theorem to find all of the solutions to r? +1 = 0, modulo 1313. 7. What are the last two digits of 31000 ? 8. Find a positive integer x such that the last three digits of 77* are 007
3. (16 points) Solve the system of linear congruences using the Chinese Remainder Theorem. 4 (mod 11) a 11 (mod 12) x=0 (mod 13) b. (6 pts) Find the inverses n (mod 11), n21 (mod 12), and nz1 (mod 13). Using these ingredients find the common solution a (mod N) to the system. c. (4 pts) 4. (8 points) What is 1!+ 23+50! congruent to modulo 14?
9. Use the construction in the proof of the Chinese remainder theorem to find a solution to the system of congruences X 1 mod 2 x 2 mod 3 x 3 mod 5 x 4 mod 11 10. Use Fermats little theorem to find 712 mod 13 11. What sequence of pseudorandom numbers is generated using the linear congruential generator Xn+1 (4xn + 1) mod 7 with seed xo 3?
9. Use the construction in the proof of the Chinese...
In RSA, it is desirable to select a small encryption exponent, "e", in order to improve the efficiency of encryption. However, a small encryption exponent should not be used if the same message is sent to many entities, because an eavesdropper can recover the plaintext "m", without knowing the private key, "k" Explain how the eavesdropper can recover the plaintext "m". Describe a practical countermeasure for thwarting the attack described above, assuming that a small encryption exponent is used and...
Explain how it would give a potential intruder an additional advantage if he can spend a week stealthily watching the behaviors of the users on a computer he plans to attack. (Hint: consider what such information is worth if the network had an Intrusion Detection System)
Briefly explain each attack scenario performed by Trudy
with a proper diagram which
on the protocol.
Q4 (Authentication Protocol) [3 Marks] The following mutual authentication protocol is proposed based on a symmetric-key cryptography algorithm. We assume that the cryptography algorithm that is used here is secure. Given that the following protocol does not provide mutual authentication. Give two different attack scenarios where Trudy can convince Bob that she is Alice. Briefly explain each attack scenario performed by Trudy with proper...
Suppose we use p = 7 and q = 5 to generate keys for RSA. a) What is n ? ___________________ b) What is φ(n) ? _______________________ 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?...
3) Out of the following, name which kind of attack you carried out in part 1 and part2: a. ciphertext only, b. known plaintext, c. chosen plaintext, d. chosen ciphertext. Explain your answer Problem 3 10 points] A 4-bit long message was encrypted using one-time pad to yield a cipher-text “1010” Assuming the message space consists of all 4-bit long messages, what is the probability that the corresponding plaintext was “1001”? Explain your answer. Problem 4 Assume we perform a...