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Using deterministic programs to select private RSA keys.
Much has been said recently here about how to produce truly random primes.
Suppose you are selecting a secret key to be used by a bank to sign its
documents. Short of examining the code very closely, or writing your own,
you are vulnerable to a program that selects primes from a vastly reduced
set. If this program behavior is known then discovering the secret primes
may be vastly easier. Writing your own code, or examining other's code, is
error-prone and requires trusting someone who knows more math than most
programmers. Here is an alternative that requires only simple high school
math to understand.
I define a simple protocol and commission several independent programmers
to implement it. The protocol is to accept a sequence of key strokes for
printable ASCII characters. Whitespace is ignored except that two
successive newlines terminate the input. MD5 is applied to the input stream
and the result is used to start the search for the prime.
The required entropy must come from the keyboard. Each of these programs
are used with the same input and the yields are compared. It is even better
if the programs are bought on the open market. The more divers the
interests of the programmers, the less likely there can be an undetected
The naive objection to this is that the keyboard input will be less than
perfectly random. That is certainly true. The input need not be random--it
is only necessary that there be sufficient entropy. There is a real hazard
that the user does not understand the issues and will merely type in the
first paragraph of the Gettysburg address, having heard that there is about
one bit of entropy per character in the English language.
If several bank officers trust each other but not the other's grasp of
entropy they can each enter text since the accumulated entropy only
increases. (They need not hide the text from each other.)
MD5 only produces 128 bits. It might be wise to require more than 128 bits
of entropy. The scheme as described can only ever produce 2^128 distinct
primes. That is small compared with the number of 1K primes. But having to
test 2^128 primes seems hard enough. Are there other attacks?
You might argue that trusting a program to choose secret keys is no worse
than trusting your operational signing software. True. You can confine that
operational software and compare the yields of programs by different
programmers. (The software of the Space Shuttle uses such redundancy.) The
confinement program must supply any required random salt or padding.