A digital signature is like a handwritten signature for a file, such that it ensures the identity of the person responsible for the file and prevents any unauthorized changes to the original file. Digital signatures use the same technology as most public key cryptosystems in which there is a public and private key. Most mathematical operations are done over a field Zp where p is some large prime. It is possible to do the same operations over other finite fields. My project explains and studies the different finite fields that can be used as well as ways to implement and experiment with them. It turns out that operations over Zp run the fastest, but with polynomial basis in a close second. Normal basis did not prove to be efficient at all. These results turned out to be against most claims of others, especially in hardware implementations. Large integer libraries are so efficient and fast that is was hard to beat the times with custom bit manipulation structures. Various secure signature schemes have proven to be practical and it is likely that they will be used much more in the near future in many applications.
Department, Program, or Center
Computer Science (GCCIS)
Radzizsowski, Stanislaw - Chair
Nealon, Gerard, "ElGamal-type signature schemes in modular arithmetic and Galois fields" (2005). Thesis. Rochester Institute of Technology. Accessed from
RIT – Main Campus