Using decision problems in public key cryptography

Details Using decision problems in public key cryptography Using decision problems in public key cryptography

2007-03-22

arxiv.org/abs/math/0703656v1

Mathematics

Group Theory

12 pages

Scientific paper

There are several public key establishment protocols as well as complete public key cryptosystems based on allegedly hard problems from combinatorial (semi)group theory known by now. Most of these problems are search problems, i.e., they are of the following nature: given a property P and the information that there are objects with the property P, find at least one particular object with the property P. So far, no cryptographic protocol based on a search problem in a non-commutative (semi)group has been recognized as secure enough to be a viable alternative to established protocols (such as RSA) based on commutative (semi)groups, although most of these protocols are more efficient than RSA is. In this paper, we suggest to use decision problems from combinatorial group theory as the core of a public key establishment protocol or a public key cryptosystem. By using a popular decision problem, the word problem, we design a cryptosystem with the following features: (1) Bob transmits to Alice an encrypted binary sequence which Alice decrypts correctly with probability "very close" to 1; (2) the adversary, Eve, who is granted arbitrarily high (but fixed) computational speed, cannot positively identify (at least, in theory), by using a "brute force attack", the "1" or "0" bits in Bob's binary sequence. In other words: no matter what computational speed we grant Eve at the outset, there is no guarantee that her "brute force attack" program will give a conclusive answer (or an answer which is correct with overwhelming probability) about any bit in Bob's sequence.

Affiliated with

Also associated with

No associations

Rating

Using decision problems in public key cryptography does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Using decision problems in public key cryptography, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Using decision problems in public key cryptography will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-168475