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TUCoPS :: Crypto :: pgpatack.txt

The PGP Attack FAQ, beta v.10 on the theoretical possibility of cracking RSA

    As before, comments, suggestions and corrections are WELCOMED.

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BETABETA          This is NOT done.                                 BETABETA
BETABETA    There are entire sections unfinished.  The elipsis      BETABETA
BETABETA    indicates a section is underconstruction...             BETABETA
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            [ The Feasibility of Breaking PGP ]
            [ The PGP attack FAQ ]

          12/95     v.10 [beta]

          by infiNity [ /]

       -- [Brief introduction] --

    This FAQ is a small side project I have decided to undertake.
    It was originally just going to be a rather lengthy spur-of-the
    moment post to alt.2600 in order to clear up some incorrect
    assumptions and perceptions people had about the security of
    PGP.  It has grown well beyond that...

    There are a great many misconceptions out there about how
    vulnerable Pretty Good Privacy is to attack.  This FAQ is designed
    to shed some light on the subject.  It is not an introduction to
    PGP or cryptography.  If you are not at least conversationally
    versed in either topic, readers are directed to The Infinity Concept
    issue 1, and the sci.crypt FAQ.  Both documents are available via
    ftp from  This document can be found there
    as well (/pub/Philes/Cryptography/PGPattackFAQ.txt.gz).

    PGP is a hybrid cryptosystem.  It is made up of 4 crytpographic
    elements: It contains a symmetric cipher (IDEA), an asymmetric cipher
    (RSA), a one-way hash (MD5), and a random number generator (Which is
    two-headed, actually:  it samples entropy from the user and then
    uses that to seed a PRNG).  Each is subject to a different form of

       1 -- [The Symmetric Cipher] -- 1

    IDEA, finalized in 1992 by Lai and Massey is a block cipher that
    operates on 64-bit blocks of data.  There have be no advances
    in the cryptanalysis of standard IDEA that are publically known.
    (I know nothing of what the NSA has done, nor does most anyone.)
    The only method of attack, therefore, is brute force.

    -- Brute Force of IDEA --

    As we all know the keyspace of IDEA is 128-bits.  In base 10
    notation that is:


    To recover a particular key, one must, on average, search half the
    keyspace.  That is 127 bits:


    If you had 1,000,000,000 machines that could try 1,000,000,000
    keys/sec, it would still take all these machines longer than the
    universe as we know it has existed and then some, to find  the key.
    IDEA, as far as present technology is concerned, is not vulnerable to
    attack, pure and simple.

    -- Other attacks against IDEA --

    If we cannot crack the cipher, and we cannot brute force the
    key-space, what if we can find some weakness in the PRNG used
    by PGP to generate the psuedo-random IDEA session keys?  This
    topic is covered in more detail in section 4.

       2 -- [The Asymmetric Cipher] -- 2

    RSA, the first full fledged public key cryptosystem was designed
    by Rivest, Shamir, and Adleman in 1977.  RSA gets it's security from
    the apparent difficulty in factoring very large composites.
    However, nothing has been proven with RSA.  It is not proved
    that factoring the public modulous is the only (best) way to
    break RSA.  There may be an as yet undiscovered way to break it.
    It is also not proven that factoring *has* to be as hard as it is.
    There exists the possiblity that an advance in number theory may lead
    to the discovery of a polynomial time factoring algorithm.  But, none
    of these things has happened, and no current research points in that
    direction.  However, 3 things that are happening and will continue
    to happen that take away from the security of RSA are: the advances
    in factoring technique, computing power and the decrease in the
    cost of computing hardware.  These things, especially the first one,
    work against the security of RSA.  However, as computing power
    increases, so does the ability to generate larger keys.  It is *much*
    easier to multiply very large primes than it is to factor the
    resulting composite (given today's understanding of number theory).

    -- The math of RSA in 7 fun-filled steps --

    To understand the attacks on RSA, it is  important to understand
    how RSA works.  Briefly:

      - Find 2 very large primes, p and q.
      - Find n=pq (the public modulous).
      - Choose e, such that e<n and relatively prime to (p-1)(q-1).
      - Compute d=e^-1 mod[(p1-)(q-1)]  OR  ed=1[mod (p-1)(q-1)].
      - e is the public exponent and d is the private one.
      - The public-key is (n,e), and the private key is (n,d).
      - p and q should never be revealed, preferably destroyed (PGP
        keeps p and q to speed operations by use of the Chinese Remainder
        Theorem, but they are kept encrypted)

      Encryption is done by dividing the target message into blocks
      smaller than n and by doing modular exponentiation:

       c=m^e mod n

      Decryption is simply the inverse operation:

       m=c^d mod n

    -- Brute Force RSA Factoring --

    An attacker has access to the public-key.  In other words, the
    attacker has e and n.  The attacker wants the private key.  In
    other words the attacker wants d.  To get d, n needs to be
    factored (which will yield p and q, which can then be used to
    calculate d).  Factoring n is the best known attack against RSA to
    date.  (Attacking RSA by trying to deduce (p-1)(q-1) is no easier
    than factoring n, and executing an exhaustive search for values of d
    is harder than factoring n.)  Some of the algorithms used for
    factoring are as follows:

    - Trial division:  The oldest and least efficient.  Exponential
    running time.  Try all the prime numbers <= sqrt(n).

    - Quadratic Sieve (QS):  The fastest algorithm for numbers smaller
    than 110 digits.

    - Multiple Polynomial Quadratic Sieve (MPQS):  Faster version of QS.

    - Double Large Prime Variation of the MPQS:  Faster still.

    - Number Field Sieve (NFS):  Currently the fastest algorithm known for
    numbers larger than 110 digits.  Was used to factor the ninth Fermat

    These algorithms represent the state of the art in warfare against
    large composite numbers (therefore agianst RSA).  The best algorithms
    have a super-polynomial (sub-exponential) running time, with the NFS
    having an asypmtotic time estimate closest to polynomial behaivior.

    Still, factoring large numbers is hard.  However, with the advances
    in number theory and computing power, it is getting easier.  In 1977
    Ron Rivest said that factoring a 125-digit number would take
    40 quadrillion years.  In 1994 RSA129 was factored using about
    5000 MIPS-years of effort from idle CPU cycles on computers across
    the Internet for eight months.  In 1995 the Blacknet key (116 digits)
    was factored using about 400 MIPS-years of effort (1 MIPS-year is
    a 1,000,000 instruction per second computer running for one year)
    from several dozen workstations and a MasPar for about three months.
    Given current trends the keysize that can be factored will only
    increase as time goes on.  The table below estimates the effort
    required to factor some common PGP-based RSA public-key modulous
    lengths using the General Number Field Sieve:

      KeySize       MIPS-years required to factor
      512           30,000
      768           200,000,000
      1024          300,000,000,000
      2048          300,000,000,000,000,000,000

    The next chart shows some estimates for the equivalences in brute
    force key searches of symmetric keys and brute force factoring
    of asymmetric keys, using the NFS.

      Symmetric        Asymmetric
      56-bits          384-bits
      64-bits          512-bits
      80-bits          768-bits
      112-bits        1792-bits
      128-bits        1304-bits

    It was said by the 4 men who factored the Blacknet key that
    "Organizations with 'more modest' resources can almost certainly
    break 512-bit keys in secret right now."  This is not to say
    that such an organization would be interested in devoting so
    much computing power to break just anyone's messages.  However, most
    people using cryptography do not rest comfortably knowing the
    system they trust their secrets to can be broken...

    My advice as always is to use the largest key allowable by the
    implementation.  If the implementation does not allow for large
    enough keys to satisfy your paranoia, do not use that implementation.

    -- Esoteric RSA attacks --

    These attacks do not exhibit any profound weakness in RSA itself,
    just in certian implementations of the protocol.  Most are not
    issues in PGP.

    -- Choosen cipher-text attack --

    An attacker listens in on the insecure channel in which RSA
    messages are passed.  The attacker collects an encrypted message
    c, from the target (destined for some other party).  The attacker
    wants to be able to read this message without having to mount a
    serious factoring effort.  In other words, she wants m=c^d.

    To recover m, the attacker first chooses a random number, r<n.
    (The attacker has the public-key (e,n).)  The attacker computes:

      x=r^e mod n (She encrypts r with the target's public-key)

      y=xc mod n (Multiplies the target ciphertext with the temp)

      t=r^-1 mod n (Multiplicative inverse of r mod n)

    The attacker counts on the fact property that:

      If x=r^e mod n, Then r=x^d mod n

    The attacker then gets the target to sign y with her private-key,
    (which actually decyrpts y) and sends u=y^d mod n to the
    attacker.  The attacker simply computes:

    tu mod n = (r^-1)(y^d) mod n = (r^-1)(x^d)(c^d) mod n = (c^d) mod n

            = m

    To foil this attack do not sign some random document presented to
    you.  Sign a one-way hash of the message instead.

    -- Low encryption exponent e --

    As it turns out, e being a small number does not take away from the
    security of RSA.  If the encryption exponent is small (common values
    are 3,17, and 65537) then public-key operations are significantly
    faster.  The only problem in using small values for e  as a public
    exponent is in encrypting small messages.  If we have 3 as our e
    and we have an m smaller than the cubic root of n, then the message
    can be recovered simply by taking the cubic root of m beacuse:

      m [for m<= 3rdroot(n)]^3 mod n will be equivalent to m^3

      and therefore:

      3rdroot(m^3) = m.

    To defend against this attack, simply pad the message with a nonce
    before encryption, such that m^3 will always be reduced mod n.

    PGP uses a small e for the encryption exponent, by default it tries
    to use 17.  If it cannot compute d with e being 17, PGP will iterate
    e to 19, and try again...  PGP also makes sure to pad m with a random
    value so m > n.

    -- Timing attack against RSA --

    A very new area of attack publically discovered by Paul Kocher deals
    with the fact that different crytpographic operations (in this case
    the modular exponentiation operations in RSA) take discretely different
    amounts of time to process.  If the RSA computations are done without
    the Chinese Remainder theorem, the following applies:

    An attacker can exploit slight timing differences in RSA computations
    to, in many cases, recover d.  The attack is a passive one that where
    the attacker sits on a network and is able to observe the RSA

    The attacker passively observes k operations measuring the time t
    it takes to compute each modular exponentation operation:
    m=c^d mod n.  The attacker also knows c and n.  The psuedo code of
    the attack:

    Algorithm to compute m=c^d mod n:

    Let m0 = 1.
    Let c0 = x.
    For i=0 upto (bits in d-1):
      If (bit i of d) is 1 then
       Let mi+1 = (mi * ci) mod n.
       Let mi+1 = mi.
      Let di+1 = di^2 mod n.

    This is very new (the public announcement was made on 12/7/95)
    and intense scrutiny of the attack has not been possible.  However,
    Ron Rivest had this to say about countering it:

-------------------------------------------BEGIN INCLUDED TEXT---------------

From: Ron Rivest <rivest>
Newsgroups: sci.crypt
Subject: Re: Announce: Timing cryptanalysis of RSA, DH, DSS
Date: 11 Dec 1995 20:17:01 GMT
Organization: MIT Laboratory for Computer Science

The simplest way to defeat Kocher's timing attack is to ensure that the
cryptographic computations take an amount of time that does not depend on the
data being operated on.  For example, for RSA it suffices to ensure that
a modular multiplication always takes the same amount of time, independent of
the operands.

A second way to defeat Kocher's attack is to use blinding: you "blind" the
data beforehand, perform the cryptographic computation, and then unblind
afterwards.  For RSA, this is quite simple to do.  (The blinding and
unblinding operations still need to take a fixed amount of time.) This doesn't
give a fixed overall computation time, but the computation time is then a
random variable that is independent of the operands.
Ronald L. Rivest  617-253-5880  617-253-8682(Fax)

---------------------------------------------END INCLUDED TEXT---------------

    PGP is not vulnerable to the timing attack as it uses the CRT to
    speed RSA operations.  Also, since the timing attack requires an
    attacker to observe the cryptographic operations in real time (ie:
    snoop the decryption process from start to finish) and most people
    encrypt and decrypt off-line, it is further made inpractical.

    -- Other RSA attacks --

    There are other attacks against RSA, such as the common modulous
    attack in which several users share n, but have different values
    for e and d.  Sharing a common modulous with several users, can
    enable an attacker to recover a message without factoring n.  PGP
    does not share public-key modulous' among users.

    If d is up to one quarter the size of n and e is less than n, d
    can be recovered without factoring.  PGP does not choose small
    values for the decryption exponent.  (If d were too small it might
    make a brute force sweep of d values feasible which is obviously a
    bad thing.)

    -- Keysizes --

    It is pointless to make predictions for recommended keysizes.
    The breakneck speed at which technology is advancing makes it
    difficult and dangerous.  Respected cryptographers will not make
    predictions past 10 years and I won't embarass myself trying to
    make any.  For today's secrets, a 1024-bit is probably safe and
    a 2048-bit key definitely is.  I wouldn't trust these numbers
    past the end of the century.  However, it is worth mentioning that
    RSA would not have lastest this long if it was as fallible as some
    crackpots with middle initials would like you to believe.

       3 -- [The one-way hash] -- 3

    MD5 is the one-way hash used to hash the passphrase into the IDEA
    key and to sign documents.  Message Digest 5 was designed by Rivest
    as a sucessor to MD4 (which was found to be weakened with reduced
    rounds).  It is slower but more secure.  Like all one-way hash
    functions, MD5 takes an arbitrary-length input and generates a unique

    -- Brute Force of MD5 --

    The strength of any one-way hash is defined by how well it can
    randomize an arbirary message and produce a unique output.  There
    are two types of brute force attacks against a one-way hash
    function, pure brute force (my own terminolgy) and the birthday

    -- Pure Brute Force Attack against MD5 --

    The output of MD5 is 128-bits.  In a pure brute force attack,
    the attacker has access to the hash of message H(m).  She wants
    to find another message m' such that:

       H(m) = H(m').

    To find such message (assuming it exists) it would take a machine
    that could try 1,000,000,000 messages per second about 1.07E22
    years.  (To find m would require the same amount of time.)

    -- The birthday attack against MD5 --

    Find two messages that hash to the same value is known as a collision
    and is exploited by the birthday attack.

    The birthday attack is a statistical probability problem.  Given
    n inputs and k possible outputs, (MD5 being the function to take
    n -> k) there are n(n-1)/2 pairs of inputs.  For each pair, there
    is a probability of 1/k of both inputs producing the same output.
    So, if you take k/2 pairs, the probability will be 50% that a
    matching pair will be found.  If n > sqrt(k), there is a good chance
    of finding a collision.  In MD5's case, 2^64 messages need to be
    tryed.  This is not a feasible attack given today's technology.  If
    you could try 1,000,000 messages per second, it would take 584,942
    years to find a collision. (A machine that could try 1,000,000,000
    messages per second would take 585 years, on average.)

    For a successful account of the birthday against crypt(3), see:

    -- Other attacks against MD5 --

    Differential cryptanalysis has proven to be effective against one
    round of MD5, but not against all 4 (differential cryptanalysis
    looks at ciphertext pairs whose plaintexts has specfic differences
    and analyzes these differences as they propagate through the cipher).

    There was successful attack at compression function itself that
    produces collsions, but this attack has no practical impact the
    security.  If your copy of PGP has had the MD5 code altered to
    cause these collisions, it would fail the message digest
    verification and you would reject it as altered... Right?

    -- Passphrase Length and Information Theory --

    According to conventional information theory, the English language
    has about 1.3 bits of entropy (information) per 8-bit character.
    If the pass phrase entered is long enough, the reuslting MD5 hash will
    be statiscally random.  For the 128-bit output of MD5, a pass phrase
    of about 98 characters will provide a random key:

      (8/1.3) * (128/8) = (128/1.3) = 98.46 characters

    How many people use a 98 character passphrase for you secret-key
    in PGP?  Below is 98 characters...


    1.3 comes from the fact that an arbitrary readable English sentence
    is usally going to consist of certian letters, thereby reducing it's
    entropy.  If any of the 26 letters in the Latin alphabet were equally
    possible and likely (which is seldom the case) the entropy increases.
    The so-called absolute rate would in this case, is:

      log(26) / log(2) = 4.7 bits

    In this case of increased entropy, a password with a truly random
    sequence of English characters will only need to be:

      (8/4.7) * (128/8) = (128/4.7) = 27.23 characters

       4 -- [The PRNG] -- 4

    PGP employs 2 PRNG's to generate and manipulate (psuedo) random data.
    The ANSI X9.17 generator and a function which measures the entropy
    from the latency in a user's keystrokes.  The random pool (which is
    the randseed.bin file) is used to seed the ANSI X9.17 PRNG (which uses
    IDEA, not 3DES).  Randseed.bin is initially generated from trueRand
    which is the keystroke timer.  The X9.17 generator is pre-washed with an
    MD5 hash of the plaintext and postwashed with some random data which is
    used to generate the next randseed.bin file.  The process is broken up
    and discussd below.

    -- ANSI X9.17 (cryptRand) --

    The ANSI X9.17 is the method of key generation PGP uses. It is
    oficially specified using 3DES, but was easily converted to IDEA.  It
    works as follows:

    E() = an IDEA encryption, with a reusable key used for key generation
    T = timestamp (data from randseed.bin used in place of timestamp)
    V = Initialization Vector, from randseed.bin
    R = random session key to be generated

    R = E[E(T) XOR V]

    the next V is generated thusly:

    V = E[E(T) XOR R]

    -- Latency Timer (trueRand) --

    The trueRand generator attempts to measure entropy from the latency
    of a user's keystrokes every time the user types on the keyboard.  It
    is used to generate the initial randseed.bin which is in turn used to
    seed to X9.17 generator.
    The quality of the output of trueRand is dependent upon it's input.
    If the input has a low amount of entropy, the output will not be as
    random as possible....

    -- X9.17 Prewash with MD5 --

    In most situations, the attacker does not know the content of the
    plaintext being encrypted by PGP.  So, in most cases, washing the
    X9.17 generator with an MD5 hash of the plaintext, simply adds to
    security.  This is based on the assumption that this added unknown
    information will add to the entropy of the generator.
    If, in the event that the attacker has some information about the
    plaintext (perhaps the attacker knows which file was encrypted, and
    wishes to prove this fact) the attacker may be able to execute a
    known-plaintext attack against X9.17.  However, it is not likely
    that, with all the other precautions taken, that this would weaken
    the generator.

       5 -- [Practical Attacks] -- 5

    Most of the attacks outlined above are either not possible or not
    fesaible by the average adversary.  So, what can the average cracker
    do to subvert the otherwise stalwart security of PGP?  As it turns,
    there are several "doable" attacks that can be launched by the typcial
    cracker.  They do not attack the cryptosystem protocols themselves,
    (which have shown to be secure) but rather system specific
    implementations of PGP.

    -- Passive Attacks (Snooping) --

    These attacks do not do need to do anything proactive and can easily
    go undetected.

    -- Keypress Snooping  --

    Still a very effective method of attack, keypress snooping can subvert
    the security of the strongest cryptosystem.  If an attacker can
    install a keylogger, and capture the passphrase of an unwary target,
    then no cryptanalysis whatsoever is necessary.  The attacker has the
    passphrase to unlock the RSA private key.  The system is completely
    The methods vary from system to system, but I would say DOS-based PGP
    would be the most vulnerable.  DOS is the easiest OS to subvert, and
    has the most key-press snooping tools that I am aware of.  All an
    attacker would have to do would be gain access to the machine for
    under 5 minutes on two seperate occasions and the attack would be
    complete.  The first time to install the snooping software, the second
    time, to remove it, and recover the goods. (If the machine is on a
    network, this can all be done *remotely* and the ease of the attack
    increases greatly.)  Even if the target boots clean, not loading any
    TSR's, a boot sector virus could still do the job, transparently.
    Keypress snooping under Unix is a bit more complicated, as root
    access is needed, unless the target is entering her passphrase from
    an X-Windows GUI.  There are numerous key loggers available to
    passively observe keypresses from an X-Windows session.

    -- Van Eck Snooping --

    The original invisible threat.  Below is a clip from a posting by
    noted information warfare guru Winn Schwartau describing a Van Eck

-------------------------------------------BEGIN INCLUDED TEXT---------------

Van Eck Radiation Helps Catch Spies

"Winn Schwartau" < >
Thu, 24 Feb 94 14:13:19 -0500

Van Eck in Action

Over the last several years, I have discussed in great detail how the
electromagnetic emissions from personal computers (and electronic gear in
general) can be remotely detected without a hard connection and the
information on the computers reconstructed.  Electromagnetic eavesdropping is
about insidious as you can get: the victim doesn't and can't know that anyone
is 'listening' to his computer.  To the eavesdropper, this provides an ideal
means of surveillance: he can place his eavesdropping equipment a fair
distance away to avoid detection and get a clear representation of what is
being processed on the computer in question.  (Please see previous issues of
Security Insider Report for complete technical descriptions of the

The problem, though, is that too many so called security experts, (some
prominent ones who really should know better) pooh-pooh the whole concept,
maintaining they've never seen it work.  Well, I'm sorry that none of them
came to my demonstrations over the years, but Van Eck radiation IS real and
does work.  In fact, the recent headline grabbing spy case illuminates the

Exploitation of Van Eck radiation appears to be responsible, at least in part,
for the arrest of senior CIA intelligence officer Aldrich Hazen Ames on
charges of being a Soviet/Russian mole.  According to the Affidavit in support
of Arrest Warrant, the FBI used "electronic surveillance of Ames' personal
computer and software within his residence," in their search for evidence
against him.  On October 9, 1993, the FBI "placed an electronic monitor in his
(Ames') computer," suggesting that a Van Eck receiver and transmitter was used
to gather information on a real-time basis.  Obviously, then, this is an ideal
tool for criminal investigation - one that apparently works quite well.  (From
the Affidavit and from David Johnston, "Tailed Cars and Tapped Telephones: How
US Drew Net on Spy Suspects," New York Times, February 24, 1994.)

>From what we can gather at this point, the FBI black-bagged Ames' house and

installed a number of surveillance devices.  We have a high confidence factor
that one of them was a small Van Eck detector which captured either CRT
signals or keyboard strokes or both.  The device would work like this:

A small receiver operating in the 22MHz range (pixel frequency) would detect
the video signals minus the horizontal and vertical sync signals.  Since the
device would be inside the computer itself, the signal strength would be more
than adequate to provide a quality source.  The little device would then
retransmit the collected data in real-time to a remote surveillance vehicle or
site where the video/keyboard data was stored on a video or digital storage

At a forensic laboratory, technicians would recreate the original screens and
data that Mr. Ames entered into his computer.  The technicians would add a
vertical sync signal of about 59.94 Hz, and a horizontal sync signal of about
27KHz.  This would stabilize the roll of the picture. In addition, the
captured data would be subject to "cleansing" - meaning that the spurious
noise in the signal would be stripped using Fast Fourier Transform techniques
in either hardware or software.  It is likely, though, that the FBI's device
contained within it an FFT chip designed by the NSA a couple of years ago to
make the laboratory process even easier.

I spoke to the FBI and US Attorney's Office about the technology used for
this, and none of them would confirm or deny the technology used "on an active

Of course it is possible that the FBI did not place a monitoring device within
the computer itself, but merely focused an external antenna at Mr. Ames'
residence to "listen" to his computer from afar, but this presents additional
complexities for law enforcement.

     1. The farther from the source the detection equipment sits means that
the detected information is "noisier" and requires additional forensic
analysis to derive usable information.

     2. Depending upon the electromagnetic sewage content of the immediate
area around Mr. Ames' neighborhood, the FBI surveillance team would be limited
as to what distances this technique would still be viable.  Distance squared
attenuation holds true.

     3. The closer the surveillance team sits to the target, the more likely
it is that their activities will be discovered.

In either case, the technology is real and was apparently used in this
investigation.  But now, a few questions arise.

     1.  Does a court surveillance order include the right to remotely
eavesdrop upon the unintentional emanations from a suspect's electronic
equipment?  Did the warrants specify this technique or were they shrouded
under a more general surveillance authorization?  Interesting question for the

     2. Is the information garnered in this manner admissible in court?  I
have read papers that claim defending against this method is illegal in the
United States, but I have been unable to substantiate that supposition.

     3. If this case goes to court, it would seem that the investigators would
have to admit HOW they intercepted signals, and a smart lawyer (contradictory
allegory :-) would attempt to pry out the relevant details.  This is important
because the techniques are generally classified within the intelligence
community even though they are well understood and explained in open source
materials.  How will the veil of national security be dropped here?

To the best of my knowledge, this is the first time that the Government had
admitted the use of Van Eck (Tempest Busting etc.)  in public.  If anyone
knows of any others, I would love to know about it.

---------------------------------------------END INCLUDED TEXT---------------

    The relevance to PGP is obvious, and the threat is real.  Snooping
    the passphrase from the keyboard, and even whole messages from
    the screen are viable attacks.  This attack, however exotic it may
    seem, is not beyond the capability of anyone with some technical
    know-how and the desire to read PGP encrypted files.

    -- Memory Space Snooping --

    In a multi-user system such as Unix, the physical memory of the
    machine can be examined by anyone with the proper privaleges (usally
    root).  In comparsion with factoring a huge composite number, opening
    up the virtual memory of the system (/dev/kmem) and directly reading
    a user's page is trivial.

    -- Disk Cache Snooping --

    In multitasking environments such as Windows, the OS has a nasty habit
    of paging the contents of memory to disk.  This is the last thing a
    PGP user wants...

    -- Packet Sniffing --

    -- Active Attacks --

    These attacks

    -- Trojan Horse --

    -- Reworked Code --

    Verify the checksum

       -- [Closing Comments] --

       -- [Thank You's] --

    PRZ, Paul Kocher, Bruce Schneier, Paul Rubin, Stephen McCluskey, Adam

 ----| Infinity / Route / daemon9 |--------|--------{ }--
--| Founding member: The 0x47 0x75 0x69 0x6C 0x64 | Finger for information |--
      Business wants to make money, Government wants to have control.
       Our privacy is at stake.  Use strong cryptography.
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