## On the Foundations of Oblivious Transfer

### Christian Cachin

We show that oblivious transfer can be based on a very general notion of asymmetric information difference. We investigate a *Universal Oblivious Transfer*, denoted UOT$(X, Y)$, that gives Bob the freedom to access Alice's input $X$ in an arbitrary way as long as he does not obtain full information about $X$. Alice does not learn which information Bob has chosen. We show that oblivious transfer can be reduced to a single execution of UOT$(X, Y)$ with Bob's knowledge $Y$ restricted in terms of Rényi entropy of order $\alpha > 1$. For independently repeated UOT the reduction woks even if only Bob's Shannon information is restricted, i.e. $H(X|Y) > 0$ in every UOT$(X, Y)$. Our protocol requires that honest Bob obtains at least half of Alice's information $X$ without error.

## BibTeX Citation

@inproceedings{Cachin98, author = {Christian Cachin}, title = {On the Foundations of Oblivious Transfer}, editor = {Kaisa Nyberg}, booktitle = {Advances in Cryptology --- EUROCRYPT~'98}, pages = 361--374, series = {Lecture Notes in Computer Science}, volume = 1403, year = 1998, month = 5, publisher = {Springer-Verlag}, }