Lecture 7: AES & Hash Functions (10 Feb)

In today's lecture, Dr. Gunes ,first, went over the RSA. Then, we began discussing Advanced Encryption Standard(AES) in more detail. He gave brief information about how the first AES is implemented and why DES was not sufficient. Then, he explained the architecture of AES and its requirements. In AES, each round consists of four main operations: byte substitution, shift row, mix columns and add round key. And the number of rounds needed is different for each bit length. He explained these four main steps with examples. Then, he compared DES and AES. One interesting thing was that DES still widely used around the world to protect sensitive online applications. Finally, he mentioned about cryptographic hash functions: Message Digest Functions(MDFs) and Message Authentication Codes(MACs).

Colloquium talk

There is a speaker from the Department of Homeland Security this Friday at 11 am in Ansari Business Building room 107. Dr. Lesley Blancas and Jalal Mapar will talk about "Research Funding Opportunities at the U.S. Department of Homeland Security".

Especially graduate students should plan to attend the talk.
See CSE Colloquia & Symposia page for details

Lecture 6: RSA (Feb 8)

This lecture we talked about RSA, which is a public key encryption algorithm that uses the problem of factoring large numbers to its advantage. This is a strong algorithm as it is said that is does not reside in the domain of NP-Complete, meaning the best known algorithm that can break this encryption is exponential. This encryption is based on two key numbers, which need to both be fairly large prime numbers, which are then multiplied together to get "N". We can derive the first of the two keys by finding a relatively prime number greater than one less than each of the two primes that were selected. We then can find the second key by finding the number that you can multiply with the first key that results in a 1 when the modulus of the product of the two primes each with one subtracted from it. A weakness of this encryption was pointed out, and that was if someone was ever able to factor "N", which is available to the public along with one of the two keys, the other key would be fairly easy to compute. We were then shown that encryption and decryption of a message using RSA was rather simple, take the message, raise it to the power of one of the keys, then take the modulus using "N". Decryption is the same process except the other key is used. It was pointed out that if we directly raise the message to the power of one of the keys, the result would be a fairly large number, however a method of "repeated squaring" can be used to achieve the same result without ever having to compute a large number. For example, say one of the keys is "20", which can be broken down into 2*10, the "10" can be broken down into 2*5, then 5=2*2+1, and finally 2=1*2. Starting with the smallest exponent (as the numbers just listed correspond to what the values should be) and using exponent rules calculating the final solution by repeated applying the modulus of "N" while building the exponent back up to "20" in this case results in never having to deal with any large numbers. We ended that day with a final note of the fact that RSA has no set key length and only RSA-140,155,160, and 200 have been cracked so far.

Student presentations

I have uploaded the link for class presentation schedule on WebCT under announcements.
Indicate your preferred date and topic on the spread sheet.

Homework 1

Ch 2, Q 19: The question is mainly about key lengths. You may take any computer in production and estimate the number of operations for DES and AES in calculations.

Ch 12, Q 13: The question is asking which of the keys should be used.

Lecture 5:DES & Rivest-Shamir-Adelman (Feb 3)

We began the lecture by discussing how DES came to be unreasonable for encrypting messages when it was easy enough to crack it. Then, triple DES was introduced to cover this weakness. Triple DES is used with two separate keys. The first is used to encrypt, the second is used to decrypt, and finally the first is used to encrypt again. This creates a better encryption because these two keys need to be ordered the right way to decrypt the message, creating an exponential increase in the encryption. We then went over computational complexity and what P, NP, NP-Hard, and NP-Complete problems. Finally, we went over what is behind the Rivest-Shamir-Adelman encryption which uses two large prime numbers.

Lecture 4: Data Encryption Standard (DES) (Feb 1)

In today’s lecture we discussed the Data Encryption Standard. The DES algorithm is a combination of substitutions and transpositions. Product ciphers are created by the combination of two weaker ciphers. DES uses an initial permutation followed by 16 cycles of different shifts and swaps that increase the cipher texts security. Most of the class was spent diving into the granular details of the steps in the algorithm. The algorithm uses a series of look up tables that are all published. DES is used on 64 bit blocks with 56 bit keys. Decryption is just the inverse of the encryption by applying the 16 cycles in reverse order. For more in depth information about the DES algorithm see the Lecture 4 Ppt. Also Wikipedia has a ton of great information about the standard.