Zapiski Nauchnykh Seminarov POMI
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Zap. Nauchn. Sem. POMI:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Zap. Nauchn. Sem. POMI, 2008, Volume 358, Pages 54–76 (Mi znsl2145)  

Time hierarchies for cryptographic function inversion with advice

E. A. Hirscha, D. Yu. Grigor'evb, K. V. Pervyshevcd

a St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
b Institute of Mathematical Research of Rennes
c Saint-Petersburg State University
d University of California, San Diego, Department of Computer Science and Engineering

Abstract: We prove a time hierarchy theorem for inverting functions computable in a slightly non-uniform polynomial time. In particular, we prove that if there is a strongly one-way function then for any $k$ and for any polynomial $p$, there is a function $f$ computable in linear time with one bit of advice such that there is a polynomial-time probabilistic adversary that inverts $f$ with probability $\ge1/p(n)$ on infinitely many lengths of input while all probabilistic $O(n^k)$-time adversaries with logarithmic advice invert $f$ with probability less than $1/p(n)$ on almost all lengths of input.
We also prove a similar theorem in the worst-case setting, i.e., if $\mathbf P\neq\mathbf{NP}$, then for every $l>k\ge1$
$$ (\mathbf{DTime}[n^k]\cap\mathbf{NTime}[n])/1\subsetneq(\mathbf{DTime}[n^l]\cap\mathbf{NTime}[n])/1. $$
Bibl. – 16 titles.

Full text: PDF file (310 kB)
References: PDF file   HTML file

English version:
Journal of Mathematical Sciences (New York), 2009, 158:5, 633–644

UDC: 510.52
Received: 11.05.2007

Citation: E. A. Hirsch, D. Yu. Grigor'ev, K. V. Pervyshev, “Time hierarchies for cryptographic function inversion with advice”, Studies in constructive mathematics and mathematical logic. Part XI, Zap. Nauchn. Sem. POMI, 358, POMI, St. Petersburg, 2008, 54–76; J. Math. Sci. (N. Y.), 158:5 (2009), 633–644

Citation in format AMSBIB
\Bibitem{HirGriPer08}
\by E.~A.~Hirsch, D.~Yu.~Grigor'ev, K.~V.~Pervyshev
\paper Time hierarchies for cryptographic function inversion with advice
\inbook Studies in constructive mathematics and mathematical logic. Part~XI
\serial Zap. Nauchn. Sem. POMI
\yr 2008
\vol 358
\pages 54--76
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl2145}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2009
\vol 158
\issue 5
\pages 633--644
\crossref{https://doi.org/10.1007/s10958-009-9403-5}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-67349115686}


Linking options:
  • http://mi.mathnet.ru/eng/znsl2145
  • http://mi.mathnet.ru/eng/znsl/v358/p54

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Записки научных семинаров ПОМИ
    Number of views:
    This page:195
    Full text:59
    References:24

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021