## Paper: Weak Bounded Arithmetic, the Diffie-Hellman Problem and Constable's Class K (at LICS 1999)

**Jan Johannsen**

### Abstract

The bounded arithmetic theory \mathof Johannsen and Pollett (LICS'98), which is closely related to the complexity class DLogTime- uniform \math, is extended by a function symbol and axioms for integer division, which is not known to be in DLogTime-uniform \math. About this extended theory \math, two main results are proved:1. The \math-definable functions of \math[div]$ are exactly Constable's class K, a function algebra whose precise complexity- theoretic nature is yet to be determined. This also yields the new upper bound \mathuniform \math.2. The \math-theorems of \math[div]$ do not have Craig-interpolants of polynomial circuit size, unless the Diffie-Hellman key exchange protocol is insecure.

### BibTeX

@InProceedings{Johannsen-WeakBoundedArithmet, author = {Jan Johannsen}, title = {Weak Bounded Arithmetic, the Diffie-Hellman Problem and Constable's Class K}, booktitle = {Proceedings of the Fourteenth Annual IEEE Symposium on Logic in Computer Science (LICS 1999)}, year = {1999}, month = {July}, pages = {268--274}, location = {Trento, Italy}, publisher = {IEEE Computer Society Press} }