Advances in Cryptology — CRYPTO '98
Volume 1462 of the series Lecture Notes in Computer Science pp 283298
Manytoone trapdoor functions and their relation to publickey cryptosystems
 Mihir BellareAffiliated withDept. of Computer Science & Engineering, University of California at San Diego
 , Shai HaleviAffiliated withT. J. Watson Research Center, IBM
 , Amit SahaiAffiliated withMIT Laboratory for Computer Science
 , Salil VadhanAffiliated withMIT Laboratory for Computer Science
Abstract
The heart of the task of building public key cryptosystems is viewed as that of“making trapdoors;” in fact, public key cryptosystems and trapdoor functions are often discussed as synonymous. How accurate is this view? In this paper we endeavor to get a better understanding of the nature of“trapdoorness” and its relation to public key cryptosystems, by broadening the scope of the investigation: we look at general trapdoor functions; that is, functions that are not necessarily injective (ie., onetoone). Our first result is somewhat surprising: we show that noninjective trapdoor functions (with superpolynomial preimage size) can be constructed from any oneway function (and hence it is unlikely that they suffice for public key encryption). On the other hand, we show that trapdoor functions with polynomial preimage size are sufficient for public key encryption. Together, these two results indicate that the preimage size is a fundamental parameter of trapdoor functions. We then turn our attention to the converse, asking what kinds of trapdoor functions can be constructed from public key cryptosystems. We take a first step by showing that in the randomoracle model one can construct injective trapdoor functions from any public key cryptosystem.
 Title
 Manytoone trapdoor functions and their relation to publickey cryptosystems
 Book Title
 Advances in Cryptology — CRYPTO '98
 Book Subtitle
 18th Annual International Cryptology Conference Santa Barbara, California, USA August 23–27, 1998 Proceedings
 Pages
 pp 283298
 Copyright
 1998
 DOI
 10.1007/BFb0055735
 Print ISBN
 9783540648925
 Online ISBN
 9783540684626
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 1462
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
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 Editors
 Authors

 Mihir Bellare ^{(1)}
 Shai Halevi ^{(2)}
 Amit Sahai ^{(3)}
 Salil Vadhan ^{(3)}
 Author Affiliations

 1. Dept. of Computer Science & Engineering, University of California at San Diego, 9500 Gilman Drive, 92093, La Jolla, CA, USA
 2. T. J. Watson Research Center, IBM, P.O. Box 704, 10598, Yorktown Heights, NY, USA
 3. MIT Laboratory for Computer Science, 545 Technology Square, 02139, Cambridge, MA, USA
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