Honors Students' Abstracts
Data Encryption Over Elliptic Curves
Alyssa Bowden, Andrew Kimball, Kameryn Williams
The Data Encryption Standard (DES) is a symmetric key encryption algorithm that was published by the National Bureau of Standards in 1977. Symmetric key encryption algorithms transform strings of characters into encrypted strings of the same length, which requires a user-provided secret key. DES and DES-like encryptions are commonly used in electronic financial transactions, secure data communications, and the protection of passwords and PIN's against unauthorized access. DES has been the model for all successive symmetric key encryption systems, but it has been implemented only over the set {0,1} with addition modulo 2 as the group operation. In this research project, we developed a new simplified version of DES (called E-DES) by replacing the usual operation with elliptic curve addition. Though mathematically more complex, elliptic curves allow smaller key sizes and higher speeds to produce equivalent security. We also developed software that implements the cryptosystem, which allowed us to analyze the security of E-DES and confirm our results through computation. As in the original DES, the structure of E-DES includes an expander function, a key schedule, and an initial and final permutation. E-DES is designed with two Feistel rounds and three substitution boxes (S-boxes), which are the cryptosystem’s main source of security. For E-DES we constructed S-boxes with specific properties that allow them to mimic the behavior of the S-boxes used in the original DES. In this way E-DES has become both a practical and an educational tool.