These files are for the use of students in CS 555 Spring, 2018, at Purdue University

Instructor: Samuel S. Wagstaff, Jr.

Phone: 49-46022; E-mail: ssw@cerias.purdue.edu

Prerequisites: CS 251, CS 381, CS 426 and MA 351.

Class web page: https://www.cs.purdue.edu/homes/ssw/cs555/index.html

The real prerequisites for CS 555.

Text: Introduction to Modern Cryptography, second edition, by J. Katz and Y. Lindell, Chapman and Hall/CRC Press, 2015, ISBN 978-1-4665-7026-9. See also the errata here.

Recommended additional reading: Applied Cryptography (2nd edition), by Bruce Schneier, Wiley, 1996. See also the errata here.

See also here for the new Advanced Encryption Standard algorithm Rijndael.

The overall course policies are the same as Spaf's.

Link to a list of web sources on cryptography and security.

Location and Time: LWSN B134, Tue-Thu 1:30 PM - 2:45 PM.

Office: LWSN 1167; Office hours: Monday 2-3 PM, Thursday 3-4 PM.

Grading: Homework: 20%; Midterm exam 20%; Project 20%; Final exam 40%.

Day-by-day list of topics covered.

Solution to homework and a summary of your grades on the midterm.

Sample Final exam. Try to do it in 50 minutes with no references.

Homework # 1, due Tuesday, January 23, 2018, 1:30 PM, on paper, in class. In question 2, your reasoning is much more important than the numbers you give as the answers. Unsupported guesses are worthless, even if correct. Text of the questions.

Homework # 2, due Tuesday, January 30, 2018, 1:30 PM, on paper, in class. In question 1, your reasoning is much more important than the numbers you give as the answers. Unsupported guesses are worthless. Text of the questions.

Homework # 3, due Tuesday, February 6, 2018, 1:30 PM, on paper, in class. Text of the questions.

Homework # 4, due Tuesday, February 13, 2018, 1:30 PM, on paper, in class. Text of the questions.

Homework # 5, due Tuesday, February 20, 2018, 1:30 PM, on paper, in class. Text of the questions.

Homework # 6, due Tuesday, February 27, 2018, 1:30 PM, on paper, in class. Text of the questions.

Homework # 7, due Tuesday, April 3, 2018, 1:30 PM, on paper, in class. Text of the questions.

Homework # 8, due Tuesday, April 10, 2018, 1:30 PM, on paper, in class. Text of the questions.

Homework # 9, due Tuesday, April 17, 2018, 1:30 PM, on paper, in class. Text of the questions.

Homework # 10, due Tuesday, April 24, 2018, 1:30 PM, on paper, in class. Text of the questions.

Please sign up for your project demonstration using this doodle. All members of each team should put their names on one entry for one time. The demonstrations will be held on April 15-17 and should take about 15 minutes. Thanks.

Review 1: Basic probability and hash.

Review 2: Remainders, arithmetic, divisibility, gcd, primes.

Review 3: primes, congruences, Caesar cipher.

Review 4: Fermat, Euler, fast exponentiation, public-key ciphers.

Review 5: CRT, solving quadratic congruences, oblivious transfer.

Block, stream ciphers, LFSRs, meet-in-the-middle attacks.

Divisibility, Arithmetic with large integers, GCD.

Examples of the Extended Euclidean Algorithm and the Chinese Remainder Theorem

Congruences: Definition and single linear ones.

2009 slides, part 3, congruences, Fermat, Euler.

Congruences for fun and profit.

Fermat, Euler, fast exponentiation, finding large primes.

2009 slides, part 4, more about RSA.

2009 slides, part 5, groups and DLP.

Much more about discrete logs.

More about zero-knowledge proofs.

Example of a letter with many variations.

Hash and other one-way functions.

Threshold schemes, Digital Signature Standard and Subliminal Channels.

Large primes via Pocklington-Lehmer.

Construction of large primes (2).

Transposition ciphers and substitution ciphers, IC.

Substitution ciphers, product ciphers.

P-H, RSA, ElGamal, Massey-Omura ciphers, signatures.

ElGamal public-key cryptosystem.

Diffie-Hellman key exchange, discrete logs.

Mental poker and quadratic residues.

Euler's Criterion, Legendre symbol.

Quadratic congruences, Oblivious transfer, Zero-knowledge proofs.

Subliminal channels; the one in DSA.

Some old slides you might enjoy.

Information theory: Definition of entropy.

Information theory: Rate, perfect secrecy.

Key equivocation, unicity distance.

Transposition ciphers and substitution ciphers, IC.

Synchronous and self-synchronous stream ciphers, CBC.

Congruences: CSR, XEuclid, multiplicative inverses.

Fermat, Euler, fast exponentiation, finding large primes.

Entropy question and proposed solution.

Substitution ciphers, product ciphers.

Send e-mail to Sam Wagstaff