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09/14/1999
More Bits and Bytes
My wife has been complaining that my columns are much too
long. Now she''s made sure that this one will be short by having
major surgery about a week ago. As a result, I''ve been nurse,
cook, and shopper and have been doing all those chores that I''ve
been told we men take for granted. We have, and I''m exhausted!
I''m indebted to our artist-in-residence, Harry Trumbore, for
taking time off his Lamb-creating activity to call my attention to
an article on Internet code-cracking in the September 7th New
York Times Business Day section. This article provides the
substance of my shorter column this week.
Two weeks ago, I discussed encryption of data and the fact that a
standard method of encrypting data involves so-called public and
private keys. This method of encryption depends on the
difficulty encountered by an interloper trying to factor very large
numbers derived from the products of prime numbers. I noted
that if someone developed a way to do this factoring for a given
Web site''s public key, it would compromise the security of all
transactions made on that site.
Well, according to the Times article, factoring a 155-digit
number has been accomplished! An international team of
workers, including one from Citigroup, accomplished the feat.
Although the effort required computing power available
generally only to governments or large corporations, Arjen
Lenstra of Citigroup is quoted as saying it was insignificant
compared to the computing power dedicated to other code-
cracking efforts. The article pointed out that, thanks to the
continuing validity of Moore''s Law, it is likely that such
computing power will become available to individuals in the near
future.
The factoring of such a large number brings into question the
security of the R.S.A. 512-bit encryption code that is standard for
financial transactions on a large number of Internet Web sites.
R.S.A. are the initials of the three men who developed the code,
but what interested me were the 512 bits. Just last week, we
talked about the fact that there were 8 bits in a byte. Dividing
512 by 8 gives 64 bytes. Remember that one byte could handle
the storage of 256 numbers and that 2 bytes could store 256 x
256 numbers. If my back-of-the-envelope calculation is correct,
64 bytes could store numbers up to a value of 256 times itself 64
times. I was pleasantly surprised to find that this corresponds to
a 155-digit number, just the size number factored by the
researchers in the Times article. Forgive me for bragging about
my mathematical achievement but I was thrilled to get this
answer. It made me feel that I actually understood what I''ve
been writing about. It really doesn''t take much to make my day!
The Times article mentioned that today some companies or
individuals are paying extra to encode their communications
using a 1,024-bit (128-byte) encryption code. I calculate this
code could handle numbers up to 309 digits. Until recently the
government wouldn''t allow manufacturers to build in software
capable of handling 1024-bit encryption but it apparently is
easing off this stance. The government, of course, wants to keep
the ability to crack the codes for fighting terrorism and other
criminal activities.
An interesting feature of the public 512-bit key for an individual
Web site is that, according to the article, it typically stays the
same for a year. This makes the payoff for a code cracker quite
lucrative since he or she would then have access to a whole
year''s worth of transactions on that site, assuming it was
monitored continuously.
Strangely enough, another article (this time in the Star Ledger, a
New Jersey newspaper) discussed degrees of separation. You
may recall that in one of my earlier columns I linked Brian
Trumbore to the Clintons by only 2 or 3 degrees of separation.
The Star Ledger article reported a study in the journal Nature by
a Notre Dame professor and colleagues who found that if you
picked any two pages on the Web, they would be on average 19
clicks or degrees of separation away from each other. Of the 800
million documents on the Web, the best search engines only
cover about 34% according to this article. The hope is that this
study will help software writers to design more efficient search
engines that will find whatever it is you''re looking for. I sure
could have used one last week in a fruitless search for a small
plastic Kelley clamp for a Foley catheter at our local pharmacies.
If I have the time, next week''s column will include a bit on
micro-orgasms.
Allen F. Bortrum
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