Exam 1 (Fri Mar 14, in class, PHSC 809)

This exam will cover material discussed in lecture, lab and homework through Wed Mar 12. Expect some True/False questions, short answer questions, calculations, Python questions and simple proof problems. In particular, you should be able to do the following

• Perform encryption/decryption given the encryption key and plaintext/ciphertext for classical cryptosystems (shift, affine, vigenere, substitution, columnar transposition).
• Break shift, affine, vigenere and substitution cryptosystems.
• Write code in Python to accomplish simple tasks
• Determine what simple Python code does
• Answer basic group theory questions (as in Homework 4)
• Solve number theory problems (as in Chapter 3, find gcd, extended Euclidean algorithm, inverses mod n, Fermat's little theorem, Euler's theorem)

Exam 2 (Fri Apr 25, in class, PHSC 809)

This exam will cover material discussed in lecture, lab and homework through Wed Apr 23. Expect some True/False questions, short answer questions, calculations, Python questions and simple proof problems. In particular, you should be able to do the following

• Solve number theory problems (as in Chapter 3, find gcd, extended Euclidean algorithm, inverses mod n, Fermat's little theorem, Euler's theorem)
• Explain/carry out RSA (including key generation). Explain how RSA is implemented both for key/message exchange and for digital signatures.
• Carry out simple primality tests and factorization algorithms (trial division, Fermat test, Miller-Rabin test, Pollard p-1).
• Find points on an elliptic curve mod p. State Hasse's bound.
• Add points on an elliptic curve (over R or mod p).
• Factor with elliptic curves (if we get to this in time).
• Write code in Python to accomplish simple tasks