Francois,
I haven't followed the latest thinking on breaking algorithms such as RSA, so
I'll take your word for the fact that the Number Field Sieve is currently the
most efficient algorithm. But isn't it at least possible that there might be
other methods that although less efficient than the NFS on a single machine,
might be more well-suited to a distributed attack? Likewise, would other
algorithms be less constrained by a 64-bit addressing limitation?
Interesting point, though, in any case.
Regards,
Bob
Robert R. Jueneman
Security Architect
Novell, Inc.
<FRousseau(_at_)chrysalis-its(_dot_)com> 12/13/00 10:36PM >>>
I am sorry for the multiple postings, but I thought this particular subject,
although probably quite controversial, might be of interest to the many peoples
following these mailing lists, especially because of the upcoming adoption of
the AES algorithm by many IETF protocols.
As symmetric keys grow, they can be attacked by more processors without a
change in processor technology since the memory requirements for breaking
symmetric keys remain trivial. However, for the Number Field Sieve (NFS)
algorithm, which is currently the most efficient method to break RSA keys, this
is not true. Based on this premise, the "time and space" based RSA key size
equivalents previously published in the RSA Labs Bulletin #13 of April 2000 by
Robert Silverman (http://www.rsalabs.com/bulletins/) have recently been
extended to cover all the AES symmetric key sizes in the latest draft of ANSI
X9.44, which will eventually become the ANSI standard for RSA key transport:
Time and Space
Symmetric Equivalent
Key Size RSA Key Size
(in bits) (in bits)
64 450
128 1620
192 2500
256 4200
These "time and space" based key sizes equivalents assume that both time and
memory are binding constraints in order to break RSA keys. This same draft
also indicates that beyond RSA key sizes of 768 bits one can no longer
effectively utilize 32-bit processors with the NFS algorithm because the
required memory exceeds what can be addressed in 32 bits; one is forced to use
64-bit machines. Beyond RSA key sizes of about 2500 bits, the memory
requirements for the NFS algorithm exceed what can be addressed even on 64 bit
machines.
For your information, here are also the estimated "time" only based RSA key
size equivalents for solving the NFS problem from the same ANSI draft:
Time Only
Symmetric Equivalent
Key Size RSA Key Size
(in bits) (in bits)
64 512
128 2550
192 6700
256 13500
Note that either of these sets of RSA key size equivalents could be used with
Diffie-Hellman for solving the value of "p" since the NFS algorithm is also the
most efficient method to break Diffie-Hellman algorithm today. Note also that
these time only equivalents numbers are slightly smaller than those from ANSI
X9.42 for Diffie-Hellman (i.e. 2550 vs 3072 for 128 bits, 6700 vs 7680 for 192
bits and 13500 vs 15360 for 256 bits) and the numbers in Hilarie Orman's
Internet Draft (i.e. draft-orman-public-key-lengths-01.txt).
Shouldn't IETF standards mention these new "time and space" based key size
equivalents in addition to existing "time" only based key size equivalents, and
possibly even suggest that "time and space" based key size equivalents be used
for RSA and Diffie-Hellman? Why mandate larger equivalent key sizes when
smaller equivalent key sizes can probably suffice?
Food for thought!
Cheers,
Francois
___________________________________
Francois Rousseau
Director of Standards and Conformance
Chrysalis-ITS
1688 Woodward Drive
Ottawa, Ontario, CANADA, K2C 3R7
frousseau(_at_)chrysalis-its(_dot_)com Tel. (613) 723-5076 ext. 419
http://www.chrysalis-its.com Fax. (613) 723-5078