TY - JFULL
AU - Markus Kaiser and Johannes Buchmann
PY - 2007/1/
TI - Computer Verification in Cryptography
T2 - International Journal of Computer, Electrical, Automation, Control and Information Engineering
SP - 4147
EP - 4153
EM -
VL - 1
SN - 1307-6892
UR - http://waset.org/publications/2218
PU - World Academy of Science, Engineering and Technology
NX - International Science Index 12, 2007
N2 - In this paper we explore the application of a formal proof system to verification problems in cryptography. Cryptographic properties concerning correctness or security of some cryptographic algorithms are of great interest. Beside some basic lemmata, we explore an implementation of a complex function that is used in cryptography. More precisely, we describe formal properties of this implementation that we computer prove. We describe formalized probability distributions (o--algebras, probability spaces and condi¬tional probabilities). These are given in the formal language of the formal proof system Isabelle/HOL. Moreover, we computer prove Bayes' Formula. Besides we describe an application of the presented formalized probability distributions to cryptography. Furthermore, this paper shows that computer proofs of complex cryptographic functions are possible by presenting an implementation of the Miller- Rabin primality test that admits formal verification. Our achievements are a step towards computer verification of cryptographic primitives. They describe a basis for computer verification in cryptography. Computer verification can be applied to further problems in crypto-graphic research, if the corresponding basic mathematical knowledge is available in a database.
ER -