Electrical Engineering
      and Computer Sciences

Electrical Engineering and Computer Sciences

COLLEGE OF ENGINEERING

UC Berkeley

Discrete Logarithms and Factoring

Eric Bach

EECS Department
University of California, Berkeley
Technical Report No. UCB/CSD-84-186
June 1984

http://www.eecs.berkeley.edu/Pubs/TechRpts/1984/CSD-84-186.pdf

This note discusses the relationship between the two problems of the title. We present probabilistic polynomial-time reductions that show:
1) To factor n, it suffices to be able to compute discrete logarithms modulo n.
2) To compute a discrete logarithm modulo a prime power p^(e), it suffices to know it mod p.
3) To compute a discrete logarithm modulo any n, it suffices to be able to factor and compute discrete logarithms modulo primes.

To summarize: solving the discrete logarithm problem for a composite modulus is exactly as hard as factoring and solving it modulo primes.


BibTeX citation:

@techreport{Bach:CSD-84-186,
    Author = {Bach, Eric},
    Title = {Discrete Logarithms and Factoring},
    Institution = {EECS Department, University of California, Berkeley},
    Year = {1984},
    Month = {Jun},
    URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/1984/5973.html},
    Number = {UCB/CSD-84-186},
    Abstract = {This note discusses the relationship between the two problems of the title.  We present probabilistic polynomial-time reductions that show:  <br />1) To factor <i>n</i>, it suffices to be able to compute discrete logarithms modulo <i>n</i>.  <br />2) To compute a discrete logarithm modulo a prime power <i>p^(e)</i>, it suffices to know it mod <i>p</i>.  <br />3) To compute a discrete logarithm modulo any <i>n</i>, it suffices to be able to factor and compute discrete logarithms modulo primes.  <p>To summarize: solving the discrete logarithm problem for a composite modulus is exactly as hard as factoring and solving it modulo primes.}
}

EndNote citation:

%0 Report
%A Bach, Eric
%T Discrete Logarithms and Factoring
%I EECS Department, University of California, Berkeley
%D 1984
%@ UCB/CSD-84-186
%U http://www.eecs.berkeley.edu/Pubs/TechRpts/1984/5973.html
%F Bach:CSD-84-186