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From: don@allegra.UUCP
Newsgroups: net.crypt,net.math
Subject: Arnold Arnold
Message-ID: <2232@allegra.UUCP>
Date: Mon, 23-Jan-84 15:21:29 EST
Article-I.D.: allegra.2232
Posted: Mon Jan 23 15:21:29 1984
Date-Received: Fri, 27-Jan-84 06:14:04 EST
Organization: AT&T Bell Laboratories, Murray Hill
Lines: 63

I found this article in my latest issue of the Manchester Guardian:

			CODES RISK IN MATHS ADVANCE

    Secret codes on which national and international security rest appear
    to have been broken wide open by an advance in mathematical analysis
    that, so far, has been ignored by the government.

    The mathematical system, which involves multi-dimensional vectors is
    claimed by its author, the cyberneticist Arnold Arnold, to have solved a
    famous mathematical problem known as Fermat's Last Theorem.

    Although this appears to be remote from matters of security, the
    system has the power to find with ease prime numbers of any magnitude
    and to factor, very rapidly, large numbers that are themselves products
    of prime numbers (prime numbers are those which can be divided by only
    themselves and one).

    Although governments maintain a very high security wall around their
    coding techniques, it is widely known that many high level codes
    including those which control the "interlocks" governing procedural
    progression up Nato's nuclear ladder in the event of war, make use of
    prime numbers.

    Nuclear triggers themselves are in many cases, prime number sequences,
    and the highest level diplomatic codes make use of numerical structures
    which ultimately rest on prime numbers.

    The reason for making use of prime numbers is that the pattern of the
    series--although recently described in a huge polynomial equation--has
    hitherto seemed inpenetrable.  This in turn has meant that attempts to
    break codes have demanded huge computers and extremely long computing
    times.

    Only a couple of years ago, when academic interest in factoring and in
    cryptography began it embarrass the US Government, experts were claiming
    that a 60 digit number that was itself the product of prime numbers
    could form a secure basis for cryptography because it would take
    hundreds of years of computing time to resolve it.

    Conventional techniques of number crunching, in which almost every step
    of arithmetic has to be tried have advanced to the point at which a
    number of that size can probably be factored in a day.

    It is believed that the difficulty of factoring grows exponentially with
    the number of digits and that, for example, a number of 100 digits
    would still require many years of analysis before it could be
    factored.

    According to Mr. Arnold, who points out that the cracking of Fermat is
    merely a sideshoot of the development of much more powerful techniques,
    the number of digits is now irrelevant to the level of security.

    Using his technique, it should be possible to go directly to any level
    of prime numbers, including numbers which are many thousands of times
    larger than any examined hitherto, and to analyse in seconds the key
    components of prime number codes.

    Since the techniques he uses are known to have been under investigation
    by Russian mathematicians for several years but have been virtually
    ignored in the West the position of the Government and its cypher staff
    at its communications centre at Cheltenham and elsewhere, could be
    embarrassing.