1993-08-15 - Summary: Denning’s report on SKIPJACK

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From: khijol!erc@apple.com (Ed Carp)
To: cypherpunks@toad.com
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From: khijol!erc@apple.com (Ed Carp)
Date: Sun, 15 Aug 93 02:11:53 PDT
To: cypherpunks@toad.com
Subject: Summary: Denning's report on SKIPJACK
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I hadn't seen this posted anywhere else, so I took the liberty of posting
it here.  Sorry if this creates unnecessary bandwidth, but flames can be sent
to /dev/null. :)

From: risks@CSL.SRI.COM (RISKS Forum)
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RISKS-LIST: RISKS-FORUM Digest  Wednesday 11 August 1993  Volume 14 : Issue 80

   ACM Committee on Computers and Public Policy, Peter G. Neumann, moderator


Date: Wed, 4 Aug 93 10:35:05 PDT
From: forags@nature.berkeley.edu (Al Stangenberger)
Subject: Article by Dorothy Denning on Clipper Chip

The July-August issue of American Scientist (Amer. Scientist 81:319-323) has a
column by Dorothy Denning describing the Clipper Encryption System.  It is
written from the Administration and law enforcement viewpoint and does not
discuss the serious privacy issues which have been raised in RISKS.  However,
it does present a clear discussion of the system and might be useful in
explaining the system to colleagues.

Al Stangenberger            Dept. of Env. Sci., Policy, & Mgt.
forags@nature.berkeley.edu  145 Mulford Hall, Univ. of Calif. Berkeley CA 94720


Date: Sun, 01 Aug 1993 21:16:56 -0400 (EDT)
From: Dorothy Denning <DENNING@guvax.acc.georgetown.edu>
Subject: SKIPJACK Review

                            SKIPJACK Review
                             Interim Report
                        The SKIPJACK Algorithm

           Ernest F. Brickell, Sandia National Laboratories
               Dorothy E. Denning, Georgetown University
            Stephen T. Kent, BBN Communications Corporation
                          David P. Maher, AT&T
                  Walter Tuchman, Amperif Corporation
                              July 28, 1993
                            (copyright 1993)

Executive Summary

The objective of the SKIPJACK review was to provide a mechanism whereby
persons outside the government could evaluate the strength of the
classified encryption algorithm used in the escrowed encryption devices
and publicly report their findings.  Because SKIPJACK is but one
component of a large, complex system, and because the security of
communications encrypted with SKIPJACK depends on the security of the
system as a whole, the review was extended to encompass other
components of the system.  The purpose of this Interim Report is to
report on our evaluation of the SKIPJACK algorithm.  A later Final
Report will address the broader system issues.

The results of our evaluation of the SKIPJACK algorithm are as

  1. Under an assumption that the cost of processing power is halved
     every eighteen months, it will be 36 years before the cost of
     breaking SKIPJACK by exhaustive search will be equal to the cost
     of breaking DES today.  Thus, there is no significant risk that
     SKIPJACK will be broken by exhaustive search in the next 30-40

  2. There is no significant risk that SKIPJACK can be broken through a
     shortcut method of attack.

  3. While the internal structure of SKIPJACK must be classified in
     order to protect law enforcement and national security objectives,
     the strength of SKIPJACK against a cryptanalytic attack does not
     depend on the secrecy of the algorithm.

1.  Background

On April 16, the President announced a new technology initiative aimed
at providing a high level of security for sensitive, unclassified
communications, while enabling lawfully authorized intercepts of
telecommunications by law enforcement officials for criminal
investigations.  The initiative includes several components:

    A classified encryption/decryption algorithm called "SKIPJACK."

    Tamper-resistant cryptographic devices (e.g., electronic chips),
    each of which contains SKIPJACK, classified control software, a
    device identification number, a family key used by law enforcement,
    and a device unique key that unlocks the session key used to
    encrypt a particular communication.

    A secure facility for generating device unique keys and programming
    the devices with the classified algorithms, identifiers, and keys.

    Two escrow agents that each hold a component of every device unique
    key.  When combined, those two components form the device unique

    A law enforcement access field (LEAF), which enables an authorized
    law enforcement official to recover the session key.  The LEAF is
    created by a device at the start of an encrypted communication and
    contains the session key encrypted under the device unique key
    together with the device identifier, all encrypted under the family

    LEAF decoders that allow an authorized law enforcement official to
    extract the device identifier and encrypted session key from an
    intercepted LEAF.  The identifier is then sent to the escrow
    agents, who return the components of the corresponding device
    unique key.  Once obtained, the components are used to reconstruct
    the device unique key, which is then used to decrypt the session key.

This report reviews the security provided by the first component, namely the
SKIPJACK algorithm.  The review was performed pursuant to the President's
direction that "respected experts from outside the government will be offered
access to the confidential details of the algorithm to assess its capabilities
and publicly report their finding."  The Acting Director of the National
Institute of Standards and Technology (NIST) sent letters of invitation to
potential reviewers.  The authors of this report accepted that invitation.

We attended an initial meeting at the Institute for Defense Analyses
Supercomputing Research Center (SRC) from June 21-23.  At that meeting, the
designer of SKIPJACK provided a complete, detailed description of the
algorithm, the rationale for each feature, and the history of the design.  The
head of the NSA evaluation team described the evaluation process and its
results.  Other NSA staff briefed us on the LEAF structure and protocols for
use, generation of device keys, protection of the devices against reverse
engineering, and NSA's history in the design and evaluation of encryption
methods contained in SKIPJACK.  Additional NSA and NIST staff were present at
the meeting to answer our questions and provide assistance.  All staff members
were forthcoming in providing us with requested information.

At the June meeting, we agreed to integrate our individual evaluations into
this joint report.  We also agreed to reconvene at SRC from July 19-21 for
further discussions and to complete a draft of the report.  In the interim, we
undertook independent tasks according to our individual interests and
availability.  Ernest Brickell specified a suite of tests for evaluating
SKIPJACK.  Dorothy Denning worked at NSA on the refinement and execution of
these and other tests that took into account suggestions solicited from
Professor Martin Hellman at Stanford University.  NSA staff assisted with the
programming and execution of these tests.  Denning also analyzed the structure
of SKIPJACK and its susceptibility to differential cryptanalysis.  Stephen
Kent visited NSA to explore in more detail how SKIPJACK compared with NSA
encryption algorithms that he already knew and that were used to protect
classified data.  David Maher developed a risk assessment approach while
continuing his ongoing work on the use of the encryption chip in the AT&T
Telephone Security Device.  Walter Tuchman investigated the anti-reverse
engineering properties of the chips.

We investigated more than just SKIPJACK because the security of communications
encrypted with the escrowed encryption technology depends on the security
provided by all the components of the initiative, including protection of the
keys stored on the devices, protection of the key components stored with the
escrow agents, the security provided by the LEAF and LEAF decoder, protection
of keys after they have been transmitted to law enforcement under court order,
and the resistance of the devices to reverse engineering.  In addition, the
success of the technology initiative depends on factors besides security, for
example, performance of the chips.  Because some components of the escrowed
encryption system, particularly the key escrow system, are still under design,
we decided to issue this Interim Report on the security of the SKIPJACK
algorithm and to defer our Final Report until we could complete our evaluation
of the system as a whole.

2.  Overview of the SKIPJACK Algorithm

SKIPJACK is a 64-bit "electronic codebook" algorithm that transforms a 64-bit
input block into a 64-bit output block.  The transformation is parameterized
by an 80-bit key, and involves performing 32 steps or iterations of a complex,
nonlinear function.  The algorithm can be used in any one of the four
operating modes defined in FIPS 81 for use with the Data Encryption Standard

The SKIPJACK algorithm was developed by NSA and is classified SECRET.  It is
representative of a family of encryption algorithms developed in 1980 as part
of the NSA suite of "Type I" algorithms, suitable for protecting all levels of
classified data.  The specific algorithm, SKIPJACK, is intended to be used
with sensitive but unclassified information.

The strength of any encryption algorithm depends on its ability to withstand
an attack aimed at determining either the key or the unencrypted ("plaintext")
communications.  There are basically two types of attack, brute-force and

3.  Susceptibility to Brute Force Attack by Exhaustive Search

In a brute-force attack (also called "exhaustive search"), the adversary
essentially tries all possible keys until one is found that decrypts the
intercepted communications into a known or meaningful plaintext message.  The
resources required to perform an exhaustive search depend on the length of the
keys, since the number of possible keys is directly related to key length.  In
particular, a key of length N bits has 2^N possibilities.  SKIPJACK uses
80-bit keys, which means there are 2^80 (approximately 10^24) or more than 1
trillion trillion possible keys.

An implementation of SKIPJACK optimized for a single processor on the
8-processor Cray YMP performs about 89,000 encryptions per second.  At that
rate, it would take more than 400 billion years to try all keys.  Assuming the
use of all 8 processors and aggressive vectorization, the time would be
reduced to about a billion years.

A more speculative attack using a future, hypothetical, massively parallel
machine with 100,000 RISC processors, each of which was capable of 100,000
encryptions per second, would still take about 4 million years.  The cost of
such a machine might be on the order of $50 million.  In an even more
speculative attack, a special purpose machine might be built using 1.2 billion
$1 chips with a 1 GHz clock.  If the algorithm could be pipelined so that one
encryption step were performed per clock cycle, then the $1.2 billion machine
could exhaust the key space in 1 year.

Another way of looking at the problem is by comparing a brute force attack on
SKIPJACK with one on DES, which uses 56-bit keys.  Given that no one has
demonstrated a capability for breaking DES, DES offers a reasonable benchmark.
Since SKIPJACK keys are 24 bits longer than DES keys, there are 2^24 times
more possibilities.  Assuming that the cost of processing power is halved
every eighteen months, then it will not be for another 24 * 1.5 = 36 years
before the cost of breaking SKIPJACK is equal to the cost of breaking DES
today.  Given the lack of demonstrated capability for breaking DES, and the
expectation that the situation will continue for at least several more years,
one can reasonably expect that SKIPJACK will not be broken within the next
30-40 years.

Conclusion 1: Under an assumption that the cost of processing power is halved
every eighteen months, it will be 36 years before the cost of breaking
SKIPJACK by exhaustive search will be equal to the cost of breaking DES today.
Thus, there is no significant risk that SKIPJACK will be broken by exhaustive
search in the next 30-40 years.

4.  Susceptibility to Shortcut Attacks

In a shortcut attack, the adversary exploits some property of the encryption
algorithm that enables the key or plaintext to be determined in much less time
than by exhaustive search.  For example, the RSA public-key encryption method
is attacked by factoring a public value that is the product of two secret
primes into its primes.

Most shortcut attacks use probabilistic or statistical methods that exploit a
structural weakness, unintentional or intentional (i.e., a "trapdoor"), in the
encryption algorithm.  In order to determine whether such attacks are
possible, it is necessary to thoroughly examine the structure of the algorithm
and its statistical properties.  In the time available for this review, it was
not feasible to conduct an evaluation on the scale that NSA has conducted or
that has been conducted on the DES.  Such review would require many man-years
of effort over a considerable time interval.  Instead, we concentrated on
reviewing NSA's design and evaluation process.  In addition, we conducted
several of our own tests.

4.1  NSA's Design and Evaluation Process

SKIPJACK was designed using building blocks and techniques that date back more
than forty years.  Many of the techniques are related to work that was
evaluated by some of the world's most accomplished and famous experts in
combinatorics and abstract algebra.  SKIPJACK's more immediate heritage dates
to around 1980, and its initial design to 1987.

SKIPJACK was designed to be evaluatable, and the design and evaluation
approach was the same used with algorithms that protect the country's most
sensitive classified information.  The specific structures included in
SKIPJACK have a long evaluation history, and the cryptographic properties of
those structures had many prior years of intense study before the formal
process began in 1987.  Thus, an arsenal of tools and data was available.
This arsenal was used by dozens of adversarial evaluators whose job was to
break SKIPJACK.  Many spent at least a full year working on the algorithm.
Besides highly experienced evaluators, SKIPJACK was subjected to cryptanalysis
by less experienced evaluators who were untainted by past approaches.  All
known methods of attacks were explored, including differential cryptanalysis.
The goal was a design that did not allow a shortcut attack.

The design underwent a sequence of iterations based on feedback from the
evaluation process.  These iterations eliminated properties which, even though
they might not allow successful attack, were related to properties that could
be indicative of vulnerabilities.  The head of the NSA evaluation team
confidently concluded "I believe that SKIPJACK can only be broken by brute
force; there is no better way."

In summary, SKIPJACK is based on some of NSA's best technology.  Considerable
care went into its design and evaluation in accordance with the care given to
algorithms that protect classified data.

4.2  Independent Analysis and Testing

Our own analysis and testing increased our confidence in the strength
of SKIPJACK and its resistance to attack.

4.2.1  Randomness and Correlation Tests

A strong encryption algorithm will behave like a random function of the key
and plaintext so that it is impossible to determine any of the key bits or
plaintext bits from the ciphertext bits (except by exhaustive search).  We ran
two sets of tests aimed at determining whether SKIPJACK is a good pseudo
random number generator.  These tests were run on a Cray YMP at NSA.  The
results showed that SKIPJACK behaves like a random function and that
ciphertext bits are not correlated with either key bits or plaintext bits.
Appendix A gives more details.

4.2.2  Differential Cryptanalysis

Differential cryptanalysis is a powerful method of attack that exploits
structural properties in an encryption algorithm.  The method involves
analyzing the structure of the algorithm in order to determine the effect of
particular differences in plaintext pairs on the differences of their
corresponding ciphertext pairs, where the differences are represented by the
exclusive-or of the pair.  If it is possible to exploit these differential
effects in order to determine a key in less time than with exhaustive search,
an encryption algorithm is said to be susceptible to differential
cryptanalysis.  However, an actual attack using differential cryptanalysis may
require substantially more chosen plaintext than can be practically acquired.

We examined the internal structure of SKIPJACK to determine its susceptibility
to differential cryptanalysis.  We concluded it was not possible to perform an
attack based on differential cryptanalysis in less time than with exhaustive

4.2.3  Weak Key Test

Some algorithms have "weak keys" that might permit a shortcut solution.  DES
has a few weak keys, which follow from a pattern of symmetry in the algorithm.
We saw no pattern of symmetry in the SKIPJACK algorithm which could lead to
weak keys.  We also experimentally tested the all "0" key (all 80 bits are
"0") and the all "1" key to see if they were weak and found they were not.

4.2.4  Symmetry Under Complementation Test

The DES satisfies the property that for a given plaintext-ciphertext pair and
associated key, encryption of the one's complement of the plaintext with the
one's complement of the key yields the one's complement of the ciphertext.
This "complementation property" shortens an attack by exhaustive search by a
factor of two since half the keys can be tested by computing complements in
lieu of performing a more costly encryption.  We tested SKIPJACK for this
property and found that it did not hold.

4.2.5  Comparison with Classified Algorithms

We compared the structure of SKIPJACK to that of NSA Type I algorithms used in
current and near-future devices designed to protect classified data.  This
analysis was conducted with the close assistance of the cryptographer who
developed SKIPJACK and included an in-depth discussion of design rationale for
all of the algorithms involved.  Based on this comparative, structural
analysis of SKIPJACK against these other algorithms, and a detailed discussion
of the similarities and differences between these algorithms, our confidence
in the basic soundness of SKIPJACK was further increased.

Conclusion 2:  There is no significant risk that SKIPJACK can be broken
through a shortcut method of attack.

5.   Secrecy of the Algorithm

The SKIPJACK algorithm is sensitive for several reasons.  Disclosure of the
algorithm would permit the construction of devices that fail to properly
implement the LEAF, while still interoperating with legitimate SKIPJACK
devices.  Such devices would provide high quality cryptographic security
without preserving the law enforcement access capability that distinguishes
this cryptographic initiative.  Additionally, the SKIPJACK algorithm is
classified SECRET  NOT RELEASABLE TO FOREIGN NATIONALS.  This classification
reflects the high quality of the algorithm, i.e., it incorporates design
techniques that are representative of algorithms used to protect classified
information.  Disclosure of the algorithm would permit analysis that could
result in discovery of these classified design techniques, and this would be
detrimental to national security.

However, while full exposure of the internal details of SKIPJACK would
jeopardize law enforcement and national security objectives, it would not
jeopardize the security of encrypted communications.  This is because a
shortcut attack is not feasible even with full knowledge of the algorithm.
Indeed, our analysis of the susceptibility of SKIPJACK to a brute force or
shortcut attack was based on the assumption that the algorithm was known.

Conclusion 3: While the internal structure of SKIPJACK must be classified in
order to protect law enforcement and national security objectives, the
strength of SKIPJACK against a cryptanalytic attack does not depend on the
secrecy of the algorithm.

  [The appendix in LaTeX form is available from Dorothy.  PGN]

Ed Carp, N7EKG			erc@apple.com			510/659-9560
If you want magic, let go of your armor.  Magic is so much stronger than
steel!        -- Richard Bach, "The Bridge Across Forever"