Complexity-Theoretic One-Way Functions, Cryptography, and Pseudorandom Generators
This project studies complexity-theoretic one-way functions,
cryptography, and pseudorandom generators.
One central focus is
seeking characterizations regarding the existance of various types of
one-way functions, such as one-way permutations and polynomial-to-one
one-way functions. For example, for each of the 81 ways one can
require, forbid, or be oblivious to the four attributes ``strong,''
``total,'' ``commutative,'' and ``associative,'' we have completely
characterized in terms of the separation of complexity classes the
issue of whether one-way functions with those properties exist. We
have, relatedly, shown that one-way functions exist if and only if
strong, total, commutative, associative one-way functions exist.
of interest in this project is the extent to which queries can be made
without leaking information, and
learning more about the connection between
and whether all pseudorandom generators are insecure.
This is a list of selected journal (except when the work has not yet
appeared in journal/book form, plus in some cases some conference articles)
papers, from or related to this project, by University of Rochester authors.
Essentially all the papers listed below can be found, in their full technical
report versions, in the UR-CS Technical Report Archive's
theory section. Here is
Lane's complete publication
and links to
essentially all his conference and journal papers (and also his arXiv.org
technical reports) can be found via the ``EE'' (electronic edition) links at
Lane's entry at the DBLP
M. Abadi, E. Allender, A. Broder, J. Feigenbaum, and L. Hemachandra.
On generating solved instances of computational problems.
In Advances in Cryptology--CRYPTO '88, pages 297-310.
Springer-Verlag Lecture Notes in Computer Science #403, 1990.
J. Hartmanis and L. Hemachandra.
One-way functions and the non-isomorphism of NP-complete sets.
Theoretical Computer Science, 81(1):155-163, 1991.
J. Goldsmith, L. Hemachandra, and K. Kunen.
Computational Complexity, 2(1):18-39, 1992.
E. Hemaspaandra and L. Hemaspaandra.
Theoretical Computer Science, 123(2):407-413, 1994.
Y. Han and L. Hemaspaandra.
Pseudorandom generators and the frequency of simplicity.
Journal of Cryptology, 9(4):251-261, 1996.
How to privatize random bits.
Technical Report TR-616, Department of Computer Science, University
of Rochester, Rochester, NY, April 1996.
Y. Han, L. Hemaspaandra, and T. Thierauf.
Threshold computation and cryptographic security.
SIAM Journal on Computing, 26(1):59-78, 1997.
L. Hemaspaandra, J. Rothe, and G. Wechsung.
Easy sets and hard certificate schemes.
Acta Informatica, 34(11):859-879, 1997.
L. Hemaspaandra, Z. Jiang, J. Rothe, and O. Watanabe.
Boolean operations, joins, and the extended low hierarchy.
Theoretical Computer Science, 205(1-2):317-327, 1998.
A. Beygelzimer, L. Hemaspaandra, C. Homan, and J. Rothe.
One-way functions in worst-case cryptography: Algebraic and
security properties are on the house.
SIGACT News, 30(4):25-40, 1999.
L. Hemaspaandra and J. Rothe.
Creating strong, total, commutative, associative one-way functions
from any one-way function in complexity theory.
Journal of Computer and System Sciences, 58(3):648-659, 1999.
L. Hemaspaandra and J. Rothe.
Characterizing the existence of one-way permutations.
Theoretical Computer Science, 244(1-2):257-261, 2000.
J. Rothe and L. Hemaspaandra.
On characterizing the existence of partial one-way permutations.
Information Processing Letters, 82(3):165-171, 2002.
C. Homan and M. Thakur.
One-way permutations and self-witnessing languages.
Journal of Computer and System Sciences, 67(3):608-622,
Tight lower bounds on the ambiguity in strong, total, associative,
Journal of Computer and System Sciences, 68(3):657-674, 2004.
E. Hemaspaandra, L. Hemaspaandra, and H. Hempel.
All superlinear inverse schemes are coNP-hard.
Theoretical Computer Science, 345(2-3):345-358, 2005.
L. Hemaspaandra, K. Pasanen, and J. Rothe.
If P NP then some strongly noninvertible functions are
Theoretical Computer Science, 362(1-3):54-62, 2006.
Exploring and eliminating redundancy in computation.
Technical Report TR-921, Department of Computer Science, University
of Rochester, Rochester, NY, August 2007.
This is the technical report version, available on the web at
cs.rochester.edu/trs/theory-trs.html, of Christopher Homan's Ph.D.
L. Hemaspaandra, J. Rothe, and A. Saxena.
Enforcing and defying associativity, commutativity, totality, and
strong noninvertibility for one-way functions in complexity theory.
Theoretical Computer Science, 401(1-3):27-35, 2008.
(Last modified: February 1, 2012.)
Lane A. Hemaspaandra