## Applied Cryptography - CSCI 531, Fall 2008

General Information
 Time : Fri 9:00am - 11:50am Location : OHE 132 Instructor : Bill Cheng, Office Hours: TuTh 11:00am - 12:00pm and Fri 12:00pm - 1:00pm, in SAL 228, E-mail: or    (Please do not send HTML-only e-mails. They will not be read.) TA : (none) Grader : Hou-Lun Chang, E-mail: Midterm Exam : during class, Fri, 10/31/2008 (firm) Final Exam : 11am-1pm, Mon, 12/15/2008 (firm)

Class Resources
 Description : textbooks, topics covered, grading policies, additional resources, etc. Papers : required technical papers Lectures : slides from lectures in HTML and PDF formats Homeworks : homework assignments (please also see important information about programming assignments at the bottom of this page.) Discussion Group : Google Group for discussing course materials and programming assignments.

News
(in reversed chronological order)
• 12/5/2008: The final exam will be closed book, closed notes, and closed everything (and no "cheat sheet"). Also, no calculators, cell phones, or any electronic gadgets are allowed. Please bring a photo ID. Your ID will be collected at the beginning of the exam and will be returned to you when you turn in your exam. There will be assigned seating.

The final exam will cover everything from AES (slide 1 of lecture 10) to the end of the last lecture. Here is a quick summary of the topics (not all topics covered are listed):

• Block Ciphers
• AES
• math for Rijndael
• xtime()
• multiplication in GF(28)
• multiplicative inverse in GF(28)
• extended Euclidean algorithm
• table method
• multiplication of polynomials with coefficients in GF(28)
• components and structure of Rijndael
• SubBytes() and InvSubBytes()
• ShiftRows() and InvShiftRows()
• MixColumns() and InvMixColumns()
• key expansion
• equivalent inverse cipher
• security of Rijndael
• Generating Primes
• math background
• square root
• Legendre and Jacobi symbols
• pseudosquares
• Blum integers
• integer factorization
• Pollard's rho factoring algorithm
• primality proving algorithms
• using the factorization of n-1
• Pocklington's theorem
• probabilistic primality tests
• Fermat's test
• Carmichael number
• Solovey-Strassen test
• Miller-Rabin test
• generating probable primes
• RANDOM-SEARCH(k,t)
• incremental search
• generating provable primes
• Maurer's algorithm
• Public-key Encryption
• background
• extended Euclidean algorithm
• modular exponentiation algorithm
• Chinese remainder theorem
• residue number system
• Garner's algorithm
• RSA
• the RSA problem
• key generation
• security of RSA
• small exponent problem
• forward search attack
• multiplicative properties
• common modulus attack
• cycling attack
• message concealing
• Diffie-Hellman
• the Diffie-Hellman problem
• ElGamal
• key generation
• encryption/decryption
• randomized encryption
• Rabin
• key generation
• encryption/decryption
• finding square roots
• Stream Ciphers
• synchronous vs. self-synchronizing stream ciphers
• LFSR
• connection polynomial
• linear complexity
• Berlekamp-Massey algorithm
• Non-linear FSR
• de Bruijn FSR
• Hash Functions
• keyed hash functions
• MACs
• unkeyed hash functions
• MDCs
• OWHF
• CRHF
• hash function properties
• compression
• ease of computation
• preimage resistance
• 2nd-preimage resistance
• collision resistance
• computational resistance for MACs
• Yuval's birthday attack
• one-way functions
• compression functions
• DES-based one-way functions
• other one-way functions
• iterated hash functions
• Merkle's meta-method for hashing
• Merkle Damgard strengthening
• MD5 & SHA-1 seriously broken
• HW6, HW7

• 11/24/2008: If your usc e-mail address is <hveera@usc.edu>, your mailbox is over quota and is bouncing e-mail messages! Please fix it as soon as possible.

• 11/19/2008: The online course evaluations for DEN students are now available. Please click here for the instructions (in PDF). These online evaluations are available for DEN students only.

• 10/24/2008: The midterm exam will be held in OHE 132 between 9am and 10:20am. It is closed book, closed notes, and closed everything (and no "cheat sheet"). Also, no calculators, cell phones, or any electronic gadgets are allowed. Please bring a photo ID. Your ID will be collected at the beginning of the exam and will be returned to you when you turn in your exam. There will be assigned seating.

The midterm exam will cover everything from the beginning of the semester till the end of math background for AES (last slide of lecture 9 on 10/24/2008).

Here is a quick summary of the topics (not all topics covered are listed):

• overview
• functions
• bi-jections and inverses
• one-way functions and trapdoor one-way functions
• permutations
• encryption schemes
• max number of permutations
• model of communication and channels
• types of cryptanalysis
• symmetric-key encryption
• model of communication and channels
• block ciphers
• substitution ciphers
• mono-alphabetic substitution cipher
• homophonic substitution cipher
• polyalphabetic substitution cipher
• transposition ciphers
• composition of ciphers and product ciphers
• stream ciphers
• Vernam ciphers and one-time pad
• key space issues
• digital signatures
• signing and verification transformations
• authentication and identification
• entity vs. data origina authentication
• public-key cryptography
• necessity of authentication
• digital signature from reversible public-key encryption
• cryptographic hash functions
• one-wayness
• weak collision-resistance
• strong collision-resistance
• keyed vs. unkeyed hash functions
• protocols and mechanisms
• protocol failures
• key management
• symmetric-key and trusted third party
• public-key and certificate authority
• attacks
• ciphertext-only
• known-plaintext
• chosen-plaintext
• chosen-ciphertext
• security models
• unconditional security
• complexity-theoretic security
• provable security
• computational security
• pseudorandom bit generators
• linear congruential generator
• polynomial-time statistical tests
• statistics background
• normal distribution
• chi-square distribution
• five basic tests
• frequency (mono-bit) test
• serial (two-bit) test
• poker test
• runs test
• autocorrelation test
• cryptographically secure PRBG
• RSA pseudorandom bit generator
• Blum-Blum-Shub pseudorandom bit generator
• block ciphers
• attacks
• complexity of attacks
• modes of operation
• ECB
• CBC
• CFB
• OFB
• cascade cipher and multiple encryption
• meet-in-the-middle attacks
• known-plaintext unicity distance
• DES
• product ciphers
• Fiestel
• DES algorithm
• P
• S
• E
• DES key scheduling
• V
• PC1
• PC2
• DES properties
• DES weak and semi-weak keys
• cryptanalysis of DES
• classical ciphers
• simple transposition ciphers
• mono-alphabetic substitution cipher
• polygram substitution cipher
• homophonic substitution cipher
• cryptographic codes
• polyalphabetic substitution cipher
• Vigenere cipher and variants
• Jefferson cylinders and rotors and the Enigma machine
• cryptanalysis of classical ciphers
• unicity distance
• language statistics
• method of Kasiski
• index of coincidences
• HW1, HW2, HW4, HW5

• 8/29/2008: Office hours today been canceled. Sorry about the inconvenience.

• 8/15/2008: Watch this area for important announcements.

Prerequisites
CS 102L (Data Structures) or graduate standing. It is assumed that you know how to write programs, and how to debug them and make them work correctly.