Cryptography-Digest Digest #436, Volume #14 Fri, 25 May 01 12:13:00 EDT
Contents:
Cryptography FAQ (10/10: References) ([EMAIL PROTECTED])
Quantum Computers and the M-N Theory Interface - Doctorow ("Osher Doctorow")
----------------------------------------------------------------------------
Crossposted-To: talk.politics.crypto,sci.answers,news.answers,talk.answers
Subject: Cryptography FAQ (10/10: References)
From: [EMAIL PROTECTED]
Reply-To: [EMAIL PROTECTED]
Date: 25 May 2001 15:45:30 GMT
Archive-name: cryptography-faq/part10
Last-modified: 94/06/13
This is the tenth of ten parts of the sci.crypt FAQ. The parts are
mostly independent, but you should read the first part before the rest.
We don't have the time to send out missing parts by mail, so don't ask.
Notes such as ``[KAH67]'' refer to the reference list in this part.
The sections of this FAQ are available via anonymous FTP to rtfm.mit.edu
as /pub/usenet/news.answers/cryptography-faq/part[xx]. The Cryptography
FAQ is posted to the newsgroups sci.crypt, talk.politics.crypto,
sci.answers, and news.answers every 21 days.
Contents
10.1. Books on history and classical methods
10.2. Books on modern methods
10.3. Survey articles
10.4. Reference articles
10.5. Journals, conference proceedings
10.6. Other
10.7. How may one obtain copies of FIPS and ANSI standards cited herein?
10.8. Electronic sources
10.9. RFCs (available from [FTPRF])
10.10. Related newsgroups
10.1. Books on history and classical methods
[FRIE1] Lambros D. Callimahos, William F. Friedman, Military Cryptanalytics.
Aegean Park Press, ?.
[DEA85] Cipher A. Deavours & Louis Kruh, Machine Cryptography and
Modern Cryptanalysis. Artech House, 610 Washington St.,
Dedham, MA 02026, 1985.
[FRIE2] William F. Friedman, Solving German Codes in World War I.
Aegean Park Press, ?.
[GAI44] H. Gaines, Cryptanalysis, a study of ciphers and their
solution. Dover Publications, 1944.
[HIN00] F.H.Hinsley, et al., British Intelligence in the Second
World War. Cambridge University Press. (vol's 1, 2, 3a, 3b
& 4, so far). XXX Years and authors, fix XXX
[HOD83] Andrew Hodges, Alan Turing: The Enigma. Burnett Books
Ltd., 1983
[KAH91] David Kahn, Seizing the Enigma. Houghton Mifflin, 1991.
[KAH67] D. Kahn, The Codebreakers. Macmillan Publishing, 1967.
[history] [The abridged paperback edition left out most
technical details; the original hardcover edition is
recommended.]
[KOZ84] W. Kozaczuk, Enigma. University Publications of America, 1984
[KUL76] S. Kullback, Statistical Methods in Cryptanalysis. Aegean
Park Press, 1976.
[SIN66] A. Sinkov, Elementary Cryptanalysis. Math. Assoc. Am. 1966.
[WEL82] Gordon Welchman, The Hut Six Story. McGraw-Hill, 1982.
[YARDL] Herbert O. Yardley, The American Black Chamber. Aegean Park
Press, ?.
10.2. Books on modern methods
[BEK82] H. Beker, F. Piper, Cipher Systems. Wiley, 1982.
[BRA88] G. Brassard, Modern Cryptology: a tutorial.
Spinger-Verlag, 1988.
[DEN82] D. Denning, Cryptography and Data Security. Addison-Wesley
Publishing Company, 1982.
[KOB89] N. Koblitz, A course in number theory and cryptography.
Springer-Verlag, 1987.
[KON81] A. Konheim, Cryptography: a primer. Wiley, 1981.
[MEY82] C. Meyer and S. Matyas, Cryptography: A new dimension in
computer security. Wiley, 1982.
[PAT87] Wayne Patterson, Mathematical Cryptology for Computer
Scientists and Mathematicians. Rowman & Littlefield, 1987.
[PFL89] C. Pfleeger, Security in Computing. Prentice-Hall, 1989.
[PRI84] W. Price, D. Davies, Security for computer networks. Wiley, 1984.
[RUE86] R. Rueppel, Design and Analysis of Stream Ciphers.
Springer-Verlag, 1986.
[SAL90] A. Saloma, Public-key cryptography. Springer-Verlag, 1990.
[SCH94] B. Schneier, Applied Cryptography. John Wiley & Sons, 1994.
[errata avbl from [EMAIL PROTECTED]]
[WEL88] D. Welsh, Codes and Cryptography. Claredon Press, 1988.
10.3. Survey articles
[ANG83] D. Angluin, D. Lichtenstein, Provable Security in Crypto-
systems: a survey. Yale University, Department of Computer
Science, #288, 1983.
[BET90] T. Beth, Algorithm engineering for public key algorithms.
IEEE Selected Areas of Communication, 1(4), 458--466,
1990.
[DAV83] M. Davio, J. Goethals, Elements of cryptology. in Secure
Digital Communications, G. Longo ed., 1--57, 1983.
[DIF79] W. Diffie, M. Hellman, Privacy and Authentication: An
introduction to cryptography. IEEE proceedings, 67(3),
397--427, 1979.
[DIF88] W. Diffie, The first ten years of public key cryptography.
IEEE proceedings, 76(5), 560--577, 1988.
[FEI73] H. Feistel, Cryptography and Computer Privacy. Scientific
American, 228(5), 15--23, 1973.
[FEI75] H. Feistel, H, W. Notz, J. Lynn Smith. Some cryptographic
techniques for machine-to-machine data communications,
IEEE IEEE proceedings, 63(11), 1545--1554, 1975.
[HEL79] M. Hellman, The mathematics of public key cryptography.
Scientific American, 130--139, 1979.
[LAK83] S. Lakshmivarahan, Algorithms for public key
cryptosystems. In Advances in Computers, M. Yovtis ed.,
22, Academic Press, 45--108, 1983.
[LEM79] A. Lempel, Cryptology in transition, Computing Surveys,
11(4), 285--304, 1979.
[MAS88] J. Massey, An introduction to contemporary cryptology, IEEE
proceedings, 76(5), 533--549, 1988.
[SIM91] G. Simmons (ed.), Contemporary Cryptology: the Science of
Information Integrity. IEEE press, 1991.
10.4. Reference articles
[AND83] D. Andelman, J. Reeds, On the cryptanalysis of rotor and
substitution-permutation networks. IEEE Trans. on Inform.
Theory, 28(4), 578--584, 1982.
[BEN87] John Bennett, Analysis of the Encryption Algorithm Used in
the WordPerfect Word Processing Program. Cryptologia 11(4),
206--210, 1987.
[BER91] H. A. Bergen and W. J. Caelli, File Security in WordPerfect
5.0. Cryptologia 15(1), 57--66, January 1991.
[BIH91] E. Biham and A. Shamir, Differential cryptanalysis of
DES-like cryptosystems. Journal of Cryptology, vol. 4, #1,
3--72, 1991.
[BI91a] E. Biham, A. Shamir, Differential cryptanalysis of Snefru,
Khafre, REDOC-II, LOKI and LUCIFER. In Proceedings of CRYPTO
'91, ed. by J. Feigenbaum, 156--171, 1992.
[BOY89] J. Boyar, Inferring Sequences Produced by Pseudo-Random
Number Generators. Journal of the ACM, 1989.
[BRI86] E. Brickell, J. Moore, M. Purtill, Structure in the
S-boxes of DES. In Proceedings of CRYPTO '86, A. M. Odlyzko
ed., 3--8, 1987.
[BRO89] L. Brown, A proposed design for an extended DES, Computer
Security in the Computer Age. Elsevier Science Publishers
B.V. (North Holland), IFIP, W. J. Caelli ed., 9--22, 1989.
[BRO90] L. Brown, J. Pieprzyk, J. Seberry, LOKI - a cryptographic
primitive for authentication and secrecy applications.
In Proceedings of AUSTCRYPT 90, 229--236, 1990.
[CAE90] H. Gustafson, E. Dawson, W. Caelli, Comparison of block
ciphers. In Proceedings of AUSCRYPT '90, J. Seberry and J.
Piepryzk eds., 208--220, 1990.
[CAM93] K. W. Campbell, M. J. Wiener, Proof the DES is Not a Group.
In Proceedings of CRYPTO '92, 1993.
[CAR86] John Carrol and Steve Martin, The Automated Cryptanalysis
of Substitution Ciphers. Cryptologia 10(4), 193--209, 1986.
[CAR87] John Carrol and Lynda Robbins, Automated Cryptanalysis of
Polyalphabetic Ciphers. Cryptologia 11(4), 193--205, 1987.
[ELL88] Carl M. Ellison, A Solution of the Hebern Messages. Cryptologia,
vol. XII, #3, 144-158, Jul 1988.
[EVE83] S. Even, O. Goldreich, DES-like functions can generate the
alternating group. IEEE Trans. on Inform. Theory, vol. 29,
#6, 863--865, 1983.
[GAR91] G. Garon, R. Outerbridge, DES watch: an examination of the
sufficiency of the Data Encryption Standard for financial
institutions in the 1990's. Cryptologia, vol. XV, #3,
177--193, 1991.
[GIL80] Gillogly, ?. Cryptologia 4(2), 1980.
[GM82] Shafi Goldwasser, Silvio Micali, Probabilistic Encryption and
How To Play Mental Poker Keeping Secret All Partial Information.
Proceedings of the Fourteenth Annual ACM Symposium on Theory of
Computing, 1982.
[HUM83] D. G. N. Hunter and A. R. McKenzie, Experiments with
Relaxation Algorithms for Breaking Simple Substitution
Ciphers. Computer Journal 26(1), 1983.
[KAM78] J. Kam, G. Davida, A structured design of substitution-
permutation encryption networks. IEEE Trans. Information
Theory, 28(10), 747--753, 1978.
[KIN78] P. Kinnucan, Data encryption gurus: Tuchman and Meyer.
Cryptologia, vol. II #4, 371--XXX, 1978.
[KIN92] King and Bahler, Probabilistic Relaxation in the
Cryptanalysis of Simple Substitution Ciphers. Cryptologia
16(3), 215--225, 1992.
[KIN93] King and Bahler, An Algorithmic Solution of Sequential
Homophonic Ciphers. Cryptologia 17(2), in press.
[KOC87] Martin Kochanski, A Survey of Data Insecurity Packages.
Cryptologia 11(1), 1--15, 1987.
[KOC88] Martin Kochanski, Another Data Insecurity Package.
Cryptologia 12(3), 165--177, 1988.
[KRU88] Kruh, ?. Cryptologia 12(4), 1988.
[LAI90] X. Lai, J. Massey, A proposal for a new block encryption
standard. EUROCRYPT 90, 389--404, 1990.
[LUB88] C. Rackoff, M. Luby, How to construct psuedorandom
permutations from psuedorandom functions. SIAM Journal of
Computing, vol. 17, #2, 373--386, 1988.
[LUC88] Michael Lucks, A Constraint Satisfaction Algorithm for the
Automated Decryption of Simple Substitution Ciphers. In
CRYPTO '88.
[MAS88] J. Massey, An introduction to contemporary cryptology.
IEEE proceedings, 76(5), 533--549, 1988.
[ME91a] R. Merkle, Fast software encryption functions. In Proceedings
of CRYPTO '90, Menezes and Vanstone ed., 476--501, 1991.
[MEY78] C. Meyer, Ciphertext/plaintext and ciphertext/key
dependence vs. number of rounds for the Data Encryption
Standard. AFIPS Conference proceedings, 47, 1119--1126,
1978.
[NBS77] Data Encryption Standard. National Bureau of Standards,
FIPS PUB 46, Washington, DC, January 1977.
[PEL79] S. Peleg and A. Rosenfeld, Breaking Substitution Ciphers
Using a Relaxation Algorithm. CACM 22(11), 598--605, 1979.
[REE77] J. Reeds, `Cracking' a Random Number Generator.
Cryptologia 1(1), 20--26, 1977.
[REE84] J. A. Reeds and P. J. Weinberger, File Security and the UNIX
Crypt Command. AT&T Bell Laboratories Technical Journal,
Vol. 63 #8, part 2, 1673--1684, October, 1984.
[SHA49] C. Shannon, Communication Theory of Secrecy Systems. Bell
System Technical Journal 28(4), 656--715, 1949.
[SHE88] B. Kaliski, R. Rivest, A. Sherman, Is the Data Encryption
Standard a Group. Journal of Cryptology, vol. 1, #1,
1--36, 1988.
[SHI88] A. Shimizu, S. Miyaguchi, Fast data encipherment algorithm
FEAL. EUROCRYPT '87, 267--278, 1988.
[SHI92] K. Shirriff, C. Welch, A. Kinsman, Decoding a VCR Controller
Code. Cryptologia 16(3), 227--234, 1992.
[SOR84] A. Sorkin, LUCIFER: a cryptographic algorithm.
Cryptologia, 8(1), 22--35, 1984.
[SPI93] R. Spillman et al., Use of Genetic Algorithms in
Cryptanalysis of Simple Substitution Ciphers. Cryptologia
17(1), 31--44, 1993.
10.5. Journals, conference proceedings
CRYPTO
Eurocrypt
IEEE Transactions on Information Theory
Cryptologia: a cryptology journal, quarterly since Jan 1977.
Cryptologia; Rose-Hulman Institute of Technology; Terre Haute
Indiana 47803 [general: systems, analysis, history, ...]
Journal of Cryptology; International Association for Cryptologic
Research; published by Springer Verlag (quarterly since
1988).
The Cryptogram (Journal of the American Cryptogram Association);
18789 West Hickory Street; Mundelein, IL 60060; [primarily
puzzle cryptograms of various sorts]
Cryptosystems Journal, Published by Tony Patti, P.O. Box 188,
Newtown PA, USA 18940-0188 or [EMAIL PROTECTED]
Publisher's comment: Includes complete cryptosystems with
source and executable programs on diskettes. Tutorial. The
typical cryptosystems supports multi-megabit keys and Galois
Field arithmetic. Inexpensive hardware random number
generator details.
Computer and Communication Security Reviews, published by Ross Anderson.
Sample issue available from various ftp sites, including
black.ox.ac.uk. Editorial c/o [EMAIL PROTECTED] Publisher's
comment: We review all the conference proceedings in this field,
including not just Crypto and Eurocrypt, but regional gatherings
like Auscrypt and Chinacrypt. We also abstract over 50 journals,
and cover computer security as well as cryptology, so readers can
see the research trends in applications as well as theory.
Infosecurity News, MIS Training Institute Press, Inc. 498 Concord Street
Framingham MA 01701-2357. This trade journal is oriented toward
administrators and covers viruses, physical security, hackers,
and so on more than cryptology. Furthermore, most of the articles
are written by vendors and hence are biased. Nevertheless, there
are occasionally some rather good cryptography articles.
10.6. Other
Address of note: Aegean Park Press, P.O. Box 2837, Laguna Hills, CA
92654-0837. Answering machine at 714-586-8811. Toll Free at 800 736-
3587, and FAX at 714 586-8269.
The ``Orange Book'' is DOD 5200.28-STD, published December 1985 as
part of the ``rainbow book'' series. Write to Department of Defense,
National Security Agency, ATTN: S332, 9800 Savage Road, Fort Meade, MD
20755-6000, and ask for the Trusted Computer System Evaluation
Criteria. Or call 301-766-8729.
The ``Orange Book'' will eventually be replaced by the U.S. Federal
Criteria for Information Technology Security (FC) online at the NIST
site [FTPNS], which also contains information on other various proposed
and active federal standards.
[BAMFD] Bamford, The Puzzle Palace. Penguin Books, 1982.
[GOO83] I. J. Good, Good Thinking: the foundations of probability and
its applications. University of Minnesota Press, 1983.
[KNU81] D. E. Knuth, The Art of Computer Programming, volume 2:
Seminumerical Algorithms. Addison-Wesley, 1981.
[KUL68] Soloman Kullback, Information Theory and Statistics.
Dover, 1968.
[YAO88] A. Yao, Computational Information Theory. In Complexity in
Information Theory, ed. by Abu-Mostafa, 1988.
10.7. How may one obtain copies of FIPS and ANSI standards cited herein?
Many textbooks on cryptography contain complete reprints of the FIPS
standards, which are not copyrighted.
The following standards may be ordered from the
U.S. Department of Commerce, National Technical Information Service,
Springfield, VA 22161.
FIPS PUB 46-1 Data Encryption Standard (this is DES)
FIPS PUB 74 Guidelines for Implementing as Using the NBS DES
FIPS PUB 81 DES Modes of Operation
FIPS PUB 113 Computer Data Authentication (using DES)
[Note: The address below has been reported as invalid.]
The following standards may be ordered from the
American National Standards Institute Sales Office,
1430 Broadway, New York, NY 10018.
Phone 212.642.4900
ANSI X3.92-1981 Data Encryption Algorithm (identical to FIPS 46-1)
ANSI X3.106-1983 DEA Modes of Operation (identical to FIPS 113)
Notes: Figure 3 in FIPS PUB 46-1 is in error, but figure 3 in X3.92-1981
is correct. The text is correct in both publications.
10.8. Electronic sources
Anonymous ftp:
[FTPAL] kampi.hut.fi:alo/des-dist.tar.Z
[FTPBK] ftp.uu.net:bsd-sources/usr.bin/des/
[FTPCB] ftp.uu.net:usenet/comp.sources.unix/volume10/cbw/
[FTPCP] soda.berkeley.edu:/pub/cypherpunks
[FTPDF] ftp.funet.fi:pub/unix/security/destoo.tar.Z
[FTPDQ] rsa.com:pub/faq/
[FTPEY] ftp.psy.uq.oz.au:pub/DES/
[FTPMD] rsa.com:?
[FTPMR] ripem.msu.edu:pub/crypt/newdes.tar.Z
[FTPNS] csrc.nist.gov:/bbs/nistpubs
[FTPOB] ftp.3com.com:Orange-Book
[FTPPF] prep.ai.mit.edu:pub/lpf/
[FTPPK] ucsd.edu:hamradio/packet/tcpip/crypto/des.tar.Z
[FTPPX] ripem.msu.edu:pub/crypt/other/tran-and-prngxor.shar
[FTPRF] nic.merit.edu:documents/rfc/
[FTPSF] beta.xerox.com:pub/hash/
[FTPSO] chalmers.se:pub/unix/des/des-2.2.tar.Z
[FTPTR] ripem.msu.edu:pub/crypt/other/tran-and-prngxor.shar
[FTPUF] ftp.uu.net:usenet/comp.sources.unix/volume28/ufc-crypt/
[FTPWP] garbo.uwasa.fi:pc/util/wppass2.zip
World Wide Web pages:
[WWWQC] http://www.quadralay.com/www/Crypt/Crypt.html
Quadralay Cryptography archive
[WWWVC] ftp://furmint.nectar.cs.cmu.edu/security/README.html
Vince Cate's Cypherpunk Page
10.9. RFCs (available from [FTPRF])
[1424] B. Kaliski, Privacy Enhancement for Internet Electronic Mail:
Part IV: Key Certification and Related Services. RFC 1424,
February 1993.
[1423] D. Balenson, Privacy Enhancement for Internet Electronic Mail:
Part III: Algorithms, Modes, and Identifiers. RFC 1423,
February 1993.
[1422] S. Kent, Privacy Enhancement for Internet Electronic Mail:
Part II: Certificate-Based Key Management. RFC 1422, February
1993.
[1421] J. Linn, Privacy Enhancement for Internet Electronic Mail:
Part I: Message Encryption and Authentication Procedures. RFC
1421, February 1993.
10.10. Related newsgroups
There are other newsgroups which a sci.crypt reader might want also to
read. Some have their own FAQs as well.
alt.privacy.clipper Clipper, Capstone, Skipjack, Key Escrow
alt.security general security discussions
alt.security.index index to alt.security
alt.security.pgp discussion of PGP
alt.security.ripem discussion of RIPEM
alt.society.civil-liberty general civil liberties, including privacy
comp.compression discussion of compression algorithms and code
comp.org.eff.news News reports from EFF
comp.org.eff.talk discussion of EFF related issues
comp.patents discussion of S/W patents, including RSA
comp.risks some mention of crypto and wiretapping
comp.society.privacy general privacy issues
comp.security.announce announcements of security holes
misc.legal.computing software patents, copyrights, computer laws
sci.math general math discussion
talk.politics.crypto politics of cryptography
------------------------------
From: "Osher Doctorow" <[EMAIL PROTECTED]>
Subject: Quantum Computers and the M-N Theory Interface - Doctorow
Date: Fri, 25 May 2001 09:42:50 -0700
From: Osher Doctorow [EMAIL PROTECTED], Fri. May 25, 6:46AM
M (Memory) Theory, from May 12, refers to events which depend on two or more
previous events, while N Theory refers to events which depend on 0 or 1
previous events. When there is dependence on one previous event, I also
refer to S (Semi-Memory) Theory.
The binomial coefficient and the gamma function bring us to the interface of
M and N or M and N and S Theories. Yet there is no interface between 1 and
2 previous events - or is there? Notice that I did not specify *integer*
versus *real* time dependence. Time is not discrete as we understand it
(the Sub-Planck level being an open question). It is continuous. Events
when depend on two or more previous events are ordinarily continuous, and
the times are ordinarily any two specified real (non-negative) past times so
that in this sense there is *continuous dependence*. When we restrict
times to (nonnegative) integer values, then the gamma function gives us a
remarkable clue. If G(n+1) is the gamma function at the time or domain
value n + 1, then G(n + 1) = n! for n = 0, 1, 2, .... As L. C. Andrews
(1998, SPIE and Oxford Science Publications: Oxford) points out (p. 63), the
gamma function generalizes the factorial function f(n) = n! from the
positive (or 0) integers to all real numbers except that /G(-n)/ = infinity
or 1/G(-n) = 0 for n= 0, 1, 2, .... But n! = 1 times 2 times ... times n
for n a nonnegative integer. Independent events (which have no time
dependence) obey the multiplication law of probability and the
multiplication law of combinatorics (one multiplies the number of ways of
doing the first event times the number of ways of doing the second event to
obtain the number of ways of doing both). Events with dependence. Now, in a
sense the number of ways of doing things relates to the number of paths or
*sum of histories* approach (which again has discrete versus continuous
parts). This becomes slightly different in form (although with even clearer
relevance) with events that depend discretely on one previous integer time
or on one integer step. In that case, the multiplicative law holds with a
change: instead of multiplying the number of events, we multiply the number
of events given each prior event in time, or even
N(An/An-1)N(An-1/An-2)...N(A1) where the slash / indicates *given the prior
event* and A1, A2, ..., An is a sequence of events (possibly the same
spatially) in times 1 to n.
The distinction between N(A1), the number of ways that A1 can occur, and
N(A2/A1), the number of ways that A2 can occur given that A1 has occurred,
is very important. The second has a certain quality of *ghost* events in
that it *freezes* the prior event A1. It says in different language:
freeze the prior event A1 at time 1 and regard it as having occurred but
being non-variable, and then, in this *frozen universe* consisting of the
event A1, calculate the number of ways that the later event A2 at time 2 can
occur. This is exactly the philosophy of Bayesian (conditional)
probability/statistics (BCP for short), except that it takes the ratio of
N(A2/A1) to N(A1) and calls it P(A2/A1), the probability of A2 given A1. It
then claims to generalize this to the continuous level and uses the
terminology P(At/As) for arbitrary events At at time t and As at time s or
even P(B/A) = P(AB)/P(A) where AB is the intersection of events A and B and
/ on the right hand side refers to real division if P(A) is not 0, while /
on the left hand side means *given*.
What is hidden by these symbols is the fact that when moving from M Theory
to N or S Theory, we have lost the concept of influence and causation and
have gone into another *phase* which can be referred to as *frozen
combinatorics/probability*. The M Theory probable influence of A on B is
P(A-->B) = P(AB')' = P(A' U B) = P(A') + P(AB) = P(AB) - P(AB) + 1 which is
precisely the proximity function p(x, y) = 1 + y - x for y = P(AB) and x =
P(A) that tells us the (probable or deterministic) influence of A on B.
The BCP analogue is P(B/A) defined as P(AB)/P(A) when P(A) is not 0, or y/x
when x is not 0. The first measures (probable) influence through time (or
space, etc.), the second acts like a probability in a frozen universe of the
past. This is not just analogy language. For finite integer time events
A1, A2, ..., An, if you calculate P(A2/A1), you get the actual probability
that A2 will occur when you find yourself in the condition or situation (a
non-variable frozen situation but nonetheless one that we subjectively
experience) that A1 has occurred. Likewise for N(A2/A1). However, you
have no indication of how A1 influences A2 except with P(A1 --> A2). If
you tried to find that out from P(A2/A1), you would have to consider all
possible frozen scenarios, and even then you would have trouble deciding
what to do with them. For discrete but infinite events, not to mention
continuous events, the trouble is compounded remarkably.
Contributors to sci.crypt might argue that computers are finite and not
infinite, and therefore that everything has to reduce to BCP and N(A2/A1)
type calculations. This is not what happens in quantum computers, and in
fact it is not what happens in the real world including even human memory
where to remember event At at time t and event As at time s, you do not
calculate all possible finite combinations or permutations or concatenations
of one-step paths from time t to time s. In fact, quantum computers make
use of waves, which are continuous and not discrete. If anything, they
resemble analog computers more than digital computers, but they go beyond
analog computers to superpositions.
In moving from M Theory to N or S Theory, it is the passage to the discrete
case and with it the one-step nature of influence or 0 step nature that is
decisive. We pass from (probable) influence to calculation of frozen
probabilities or numbers. We are used to thinking in this way in card
games and scientific applications, but dropping influence/causality is a
terrible price to pay. When in addition we try to drop the discrete case
and use its ideas for continuous events and continuous dependence, we fail
because even when 1, 2, ..., are replaced by times s, t, u, v, ..., the BCP
probabilities and their N(B/A) analogues implicitly assume that the s, t, u,
v, ... are discrete even if they are not integers - they assume that there
is no step in between s and t, which is not true in a continuous universe
and in time as we understand it.
This whole process may seem to run against the quantum mechanical results
that energy levels are discrete and quanta are discrete, and this is a topic
for intensive analysis, but quantum computers are not based on these
discrete aspects but on the continuous wave entanglement aspects. In this
sense, they are more advanced than Schrodinger's equation as we now
interpret it (with its discrete energy levels, etc.) and more accurately
reflect the real world. The macroscopic world in which we live looks
continuous, but when we calculate probabilities and number of events we
assume discete models in which we add up all possible discrete one-step
paths (when using Bayesian methods or even our unguided *intuition*). It
is much more likely that the macroscopic world is actually discrete in these
relevant aspects in at least an idealized sense and that the quantum world
is continuous in its deepest aspects (via waves). From this viewpoint, I
personally suspect that the sub-Planck level is also continuous, contrary to
mainstream physics.
Osher Doctorow Ph.D.
Doctorow Consultants
There is something else hidden by these symbols.
------------------------------
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