COMP3334 Computer Systems Security 2021/22 Semester 2
Tutorial 3 Public-Key Cryptography Question 1 Extended Euclidean Algorithm
Suppose m and b are integers. If GCD(b, m) = 1, b has a multiplicative inverse modulo m. That is, (b * b-1) mod m = 1. Below is an algorithm, named Extended Euclidean Algorithm, for finding the inverse of b:
EXTENDED EUCLID(b, m)
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1. (A1, A2, A3) = (1, 0, m); (B1, B2, B3) = (0, 1, b);
return A3 which is GCD(m, b) and there is no inverse;
return B3 which is GCD(m, b) and B2 which is the inverse of b;
4. Q=A3divB3;//Qisthequotient
5. (T1,T2,T3)=(A1–Q*B1,A2–Q*B2,A3–Q*B3);
6. (A1, A2, A3) = (B1, B2, B3);
7. (B1, B2, B3) = (T1, T2, T3);
8. goto 2;
Using the algorithm, calculate the inverse of 33 mod 35.
COMP3334 Computer Systems Security 2021/22 Semester 2
Question 2 RSA Keys
Let p = 11 and q = 13. If the public key e = 7, what is the private key d?
Question 3 RSA Encryption
In a public-key system using RSA, you intercept the ciphertext C = 10 sent to a user whose public key is e = 5, n = 35. What is the plaintext M? Can you break it?
COMP3334 Computer Systems Security 2021/22 Semester 2
Question 4 RSA Security
In the RSA public-key encryption scheme, each user has a public key, e, and a private key, d. Suppose Bob leaks his private key d. Rather than generating a new modulus, he decides to generate a new public key and a new private key. Is this safe? Explain.
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