AES
Noise Purity Tests Results
"
A signal that is Pure Noise is thermodynamically
indistinguishable from a perfectly encoded and compressed semantic message: they both look
like a varying signal in which you could not predict one bit of the signal based on the
previous ones
"
Matt LaMantia, Data Integrity Engineer, Noise Laboratories.
NOISE
PURITY TEST #1: NON-LINEAR DATA INPUT, CONSTANT ZERO KEY (NICK)
The table below contains results
of the First of our Noise Purity Tests performed on 128 bit versions of all 15 AES
candidates encryption algorithms.
Multiple randomness tests were
performed on non-linear data input after 1 to 8 rounds of encryption with a constant key
(NICK).
In this test the same 128 bit key consisting of all 0s was used for data encryption.
Input data consisted of all combinations of 4 bit 1 and 124 bit 0 out of 128 bit of the
data block, therefore giving 10,668,000 combinations or 170,688,000 byte of input data for
encryption and the following noise purity analysis.
Values separated by / refer to the results of encryption performed WITH and WITHOUT
pre- and post- data whitening such as bit permutation or XOR or ADD or any other more
complex operation if it's present. If algorithm does not include any pre or post-
whitening, only one result is displayed and used.
Processor cycles per round (CPR) refer to the fastest known implementations for Intel®
Pentium® II processor. Extra possible minor speed increases due to instruction pairing
between encryption rounds themselves and between data whitening and the first and the last
rounds of encryption were not taken into consideration.
NICK |
CAST |
Crypton |
DEAL |
DFC |
E2 |
Frog |
HPC |
Loki97 |
Magenta |
Mars |
RC6* |
Rijndael* |
Safer+* |
Serpent |
Twofish |
1
Round |
0 |
0 / 0 |
/ 0 |
0 |
0 / 0 |
0 |
/ |
0 |
0 |
/ 0 |
0 / 0 |
0* / 0* |
0 / 0 |
0 / 0 |
0 /
0 |
2
Rounds |
+ |
0 / 0 |
/ 0 |
0 |
0 / 0 |
|
/ |
0 |
0 |
/ 0 |
0 / 0 |
0* / 0* |
X / X |
0 / 0 |
+ /
+ |
3
Rounds |
+ |
+ / 0 |
+ / + |
+ |
X / 0 |
|
X / |
0 |
X |
/ 0 |
0 / 0 |
0* / 0* |
X / X |
X / |
X /
X |
4
Rounds |
X |
+ / X |
X / + |
+ |
X / + |
+ |
X / |
|
X |
X / 0 |
/ 0 |
X* / X* |
+ / + |
X / + |
X /
X |
5
Rounds |
X |
X / X |
X / X |
X |
X / + |
X |
X / X |
X |
X |
X / |
+ / |
X* / X* |
X / X |
X / X |
X /
X |
6
Rounds |
X |
X / X |
X / X |
X |
X / X |
X |
X / X |
X |
X |
X / + |
X / +* |
X* / X* |
+* / +* |
X / X |
X /
X |
7
Rounds |
X |
X / X |
X / X |
X |
X / X |
X |
X / X |
X |
X |
X / X |
X / +* |
X* / X* |
+* / +* |
X / X |
X /
X |
8
Rounds |
X |
X / X |
X / X |
X |
X / X |
X |
X / X |
X |
X |
X / X |
X / +* |
X* / X* |
+* / +* |
X / X |
X /
X |
Max
Rounds |
12 |
11 |
16 |
8 |
12 |
8 |
8 |
16 |
6 |
16 |
20 |
10 |
16 |
31 |
8 |
Cycles |
600 |
392 |
2368 |
304 |
356 |
2416 |
380 |
2144 |
6540 |
368 |
244 |
284 |
1712 |
960 |
264 |
CPR |
50 |
32 |
140 |
38 |
27 |
302 |
47 |
134 |
1090 |
15 |
12 |
28 |
106 |
30 |
32 |
Whitening |
0 |
40 |
128 |
0 |
32 |
0 |
4 |
0 |
0 |
128 |
4 |
4 |
16 |
30 |
8 |
Min
Rounds Passing |
4 |
5 / 4 |
4 / 5 |
5 |
3 / 6 |
5 |
3 / 5 |
4 |
3 |
4 / 7 |
6 / 17* |
4* / 4* |
2* / 2* |
3 / 5 |
3 /
3 |
Min
Cycles Passing |
200 |
200
128 |
688
700 |
190 |
113
162 |
1510 |
145
235 |
536 |
3270 |
188
105 |
76
204* |
116*
112* |
228*
212* |
120
150 |
104
96 |
NICK |
CAST |
Crypton |
DEAL |
DFC |
E2 |
Frog |
HPC |
Loki97 |
Magenta |
Mars |
RC6* |
Rijndael* |
Safer+* |
Serpent |
Twofish |
Comments:
0 |
Failed all
tests |
|
Failed
some tests |
+ |
Passed,
but results look suspicious, almost failed some tests |
X |
Passed all
tests |
* RC6: Noise Purity NICK Test
of RC6 without data pre- and post- whitening returns very suspicious
results up to the maximum tested 20 rounds, possible minor flaw in the cipher.
* Rijndael: Input data
whitening XOR does not make absolutely any difference. Also 6 and 7 rounds of encryption
produce exactly the same output (!?), possible flaw in the cipher.
* Safer+: Starting with 6 and up to the maximum 8 rounds of
encryption, returned test results look very suspicious, possible minor flaw in the cipher.
* Crypton1: Only key schedule generation was modified in Crypton1, so
it performed identically to Crypton in this test and therefore it's not
included in this table.
We expected Bruce Schneier's Twofish
to look good, but we didn't expect it to show such an outstanding performance and such a
remarkable stability of the results
We also expected RC6 to perform
better than it did, but
So far Twofish
indubitably leads the list of the world's best 128 bit block ciphers.
Yes, Bruce, one can judge the encryption algorithm
quality by the speed of its secure version, one just has to determine that
"secure" number of rounds correctly. And we believe that practical results say
much more than any theoretical speculations.
AS
ALWAYS, PRACTICE IS FAR AWAY FROM THEORY
This was the first of the battery of tests we
plan to perform on AES and other encryption algorithms. The table above is a subject to
constant modifications according to all collected new information. More tests on different
parts of the encryption algorithms will be performed in the near future and more results
are coming.
Details on the results from the table above are under construction. Please also note
that just passing these tests alone is not a proof of the cipher's security, but failing
them by a single bit is what must be taken seriously.
We do not and never will provide a theoretical basis for or an explanation of the
results of our tests. This is not a cryptoanalytic work. All tests are meant purely for
demonstration of the practical difference in behavior and performance of different
encryption algorithms hopefully finding and bringing to attention possible flaws in them.
Any feedback will be highly appreciated.
LINKS
TO AES CANDIDATES AND THEIR AUTHORS
AES Algorithm |
Designed / Submitted By |
CAST-256 |
Carlisle
Adams (e-mail), Entrust
Technologies, Inc. |
CRYPTON |
Chae Hoon Lim (e-mail), Future
Systems, Inc. |
DEAL |
Lars Knudsen ( e-mail) and
Richard Outerbridge |
DFC |
Serge Vaudenay (e-mail), CNRS
Ecole Normale Superieure |
E2 |
Kazumaro
Aoki, Masayuki Kanda, Tsutomu Matsumoto, Shiho Moriai, Kazuo Ohta, Miyako Ookubo, Youichi
Takashima and Hiroki Ueda, (e-mail) NTT Nippon Telegraph and Telephone Corporation |
FROG |
Dianelos
Georgoudis (e-mail), Damian Leroux and Billy
Simon Chaves, TecApro International S.A. (e-mail) |
HPC |
Rich Schroeppel (e-mail) |
LOKI97 |
Lawrie Brown (e-mail or e-mail), Josef Pieprzyk (e-mail or e-mail)
and Jennifer Seberry
(e-mail) |
MAGENTA |
M.J.
Jacobson (e-mail) and Dr. Klaus
Huber (e-mail), Deutsche Telekom AG |
MARS |
Nevenko
Zunic (e-mail), IBM |
RC6 |
Ron Rivest ( e-mail, or his
secretary Be Blackburn e-mail ), Matthew Robshaw , RSA Laboratories (e-mail) |
RIJNDAEL |
Joan Daemen (e-mail) and Vincent Rijmen (e-mail ) who doesn't like Internet Explorer ;-) |
SAFER+ |
James
L. Massey, Charles Williams, Cylink Corporation |
SERPENT |
Ross Anderson (e-mail), Eli Biham (e-mail) and Lars Knudsen (e-mail) |
TWOFISH |
Bruce Schneier (e-mail), John Kelsey, Doug Whiting, David Wagner (e-mail), Chris Hall and Niels Ferguson |
OTHER AES RELATED
RESOURCES
NIST Home of AES
exactly where it all has begun, updated regularly.
Well organized AES Algorithms
Efficiency page by Brian Gladman
(e-mail ), contains next to perfect C
sources of all AES algorithms, updated regularly.
One of the best AES Algorithm
Performance Comparison documents by the TWOFISH team, not updated.
The one and only AES Block Cypher Lounge
by Lars Knudsen (e-mail) contains names of the papers and links to the
best known attacks on AES algorithms, updated often.
The largest Cryptography
People List by David Wagner (e-mail), some links are outdated though.
A nice AES Ciphers Speed site maintained
by Helger Lipmaa (e-mail), updated regularly.
And a very informative Candidate
AES Analysis and Reviews site maintained by Franois Kouene (e-mail), UCL Crypto Group, updated often.
Revision History:
April
21, 1999 |
Started the first
test, Non-Linear Input & Constant Key (NICK) |
May 16, 1999 |
First Published |
July
24, 1999 |
Started the
second test, Non-Linear Key & Constant Input (NKCI) |
July
27, 1999 |
Minor Corrections |
October,
1999 |
Planned to start the
third test, Non-Linear KeyStream & Constant Input (NSCI) |
Copyright © 1999 by Pure Noise Ltd.
|