Paper Info
Title
An overview of trace based public key cryptography over finite fields.
Abstract
The Discrete Log Problem (DLP), that is computing x, given y=@a^x and =G@?F"q^*, based Public Key Cryptosystem (PKC) have been studied since the late 1970's. Such development of PKC was possible because of the trapdoor function f:Z"@?-G=@?F"q^*, f(m)=@a^m is a group homomorphism. Due to this fact we have; Diffie Hellman (DH) type key exchange, ElGamal type message encryption, and Nyberg-Rueppel type digital signature protocols. The cryptosystems based on the trapdoor f(m)=@a^m are well understood and complete. However, there is another trapdoor function f:Z"@?-G, f(m)-Tr(@a^m), where G=@?F"q"^"k^*,k=2, which needs more attention from researchers from a cryptographic protocols point of view. In the above mentioned case, although f is computable, it is not clear how to produce protocols such as Diffie Hellman type key exchange, ElGamal type message encryption, and Nyberg-Rueppel type digital signature algorithm, in general. It would be better, of course if we can find a more efficient algorithm than repeated squaring and trace to compute f(m)=Tr(@a^m) together with these protocols. In the literature we see some works for a more efficient algorithm to compute f(m)=Tr(@a^m) and not wondering about the protocols. We also see some works dealing with an efficient algorithm to compute Tr(@a^m) as well as discussing the cryptographic protocols. In this review paper, we are going to discuss the state of art on the subject.
Year
DOI
Venue
2014
10.1016/j.cam.2013.10.022
J. Computational Applied Mathematics
Keywords
Field
DocType
diffie hellman type key,type key exchange,digital signature algorithm,cryptographic protocols point,diffie hellman,efficient algorithm,cryptographic protocol,public key cryptography,finite field,trapdoor function,elgamal type message encryption,nyberg-rueppel type,discrete logarithm problem
Discrete mathematics,Key exchange,Mathematical analysis,Arithmetic,Encryption,Digital signature,Cryptosystem,Trapdoor function,ElGamal encryption,Public-key cryptography,Mathematics,Diffie–Hellman key exchange
Journal
Volume
ISSN
Citations 
259
0377-0427
2
PageRank 
References 
Authors
0.40
9
2
Name
Order
Citations
PageRank
Ersan Akyıldız120.40
Muhammad Ashraf274.62