2008 REU Program Information

NSF‐sponsored participants:

Damon Alexander, University of Wisconsin

Jeremy Erickson, Taylor University

Brad Fox, Transylvania University

Brian Nixon, University of Michigan

Amber Rogers, Northern Kentucky University

Sean Simmons, University of Texas

University of Cincinnati‐sponsored participant:

Zachary Vance, University of Cincinnati

2008 REU in Mathematical Cryptology Problems

There were five major problems explored by the participants.  Various groups of participants worked on each problem.

KeeLoq: Amber Rogers and Brad Fox (assisted with programming by Jeremy Erickson) worked on attacking the KeeLoq cipher. KeeLoq is the cipher that is commonly used on remote entry systems for automobiles. Amber and Brad were able to break 64 rounds of the 238‐round cipher. Participants are continuing this work during Fall 2008. Another interesting question about KeeLoq was investigated by Brian Nixon – how random are the permutations generated by KeeLoq?

Algebraic attacks on standard encryption algorithms: Damon Alexander and Sean Simmons applied algebraic attacks to two simplified ciphers – S‐DES and S‐AES. Damon also explored an algebraic attack on “full‐strength” DES.

SMS4: SMS4 is a Chinese wi‐fi cipher. Jeremy Erickson, Brian Nixon, and Zachary Vance attacked SMS4. Participants are continuing this work during Fall 2008.

X^2: Damon Alexander, Jeremy Erickson, Brian Nixon, and Zachary Vance attacked the X^2 cryptosystem that was proposed by Ding.

Hidden Field Equations public key cryptosystems: Sean Simmons examined the bijectivity of the polynomials used for Hidden Field Equation cryptosystems. Sean’s work shows that the hidden field equation polynomials cannot be distinguished from random by examining bijectivity.