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