Security - Telenor

Lars R. Knudsen (38) is Professor
at the Institute of Informatics
at the University of Bergen. He
received his M.Sc. and Ph.D.
degrees in computer science
and mathematics from Aarhus
University, Denmark, in 1992,
respectively 1994. He has written
numerous scientific papers
in the area of cryptology and is
regarded a world expert in block
cipher encryption algorithms.
lars.knudsen@ii.uib.no
10
Advanced Encryption Standard (AES).
Encryption for our Grandchildren
LARS R. KNUDSEN
Introduction
Encryption used to be something which only the
secret services and military had a real interest in
and which private citizens only knew from
crosswords and puzzles in Sunday newspapers.
Today encryption is an important part of the
information society. Outside of the secret services
the interest in encryption started to blossom
at the end of the 1970s.
First, IBM (International Business Machines)
developed the cryptosystem Lucifer, which later
was adapted as a US Federal Information Processing
Standard, although slightly modified.
This standard was published in January 1977
as the DES (Data Encryption Standard) and is
today probably the most used encryption system
in the world (at least outside of the secret services).
The system is a so-called secret-key cryptosystem,
where the same information, or key,
is used to encipher (or encrypt) and decipher (or
decrypt) the messages.
Second, the researchers Whitfield Diffie and
Martin Hellman discovered (or re-discovered 1) )
so-called public-key cryptography, where the
secret key is split into two parts, a public part
and a secret part. The public part of the key is
made available to everyone; the secret part stays
secret with one party. The public key can be
used by everyone to encrypt a message, while
the secret key can be used to decrypt the ciphertext
and restore the message.
The differences between today’s secret-key and
public-key cryptosystems are many, but there is
a need for both of them. Even though the DES
has withstood almost 25 years of cryptanalytic
attempts to find shortcuts in the algorithm by
cryptanalysts from all over the world, time is
running out for the algorithm. The main problem
is that the DES was designed to accept keys of
only 56 bits, which means that there are 2 56 ≈
10 17 different keys. Even though this number
may seem huge, (as an example, 2 56 seconds are
about 2 billion years), it is small enough to
enable the design of special-purpose built hardware,
which can run through all possible values
of the key in a very short time. In 1998 it was
estimated that an attacker who is willing to
invest one million US dollars, could try all values
of the key, one by one, in just half an hour!
With a few encrypted messages on hand, one
can simply decrypt these under all possible values
of the key. The value of the key which yields
some meaningful messages is with a high probability
the correct one, and the system is broken.
Technical Detail
In a cryptosystem the message is always first
converted to a number. This number is then
encrypted by applying some mathematical or
non-mathematical operations to it, and the
resulting number is then transformed back to
cipher-text. The numbers are represented in the
binary number system, that is, a number is either
a zero or a one. As an example, the number 17
in the decimal number system (the one we use
normally) is 10001 in the binary number system.
The symbols in the binary number system are
called bits.
AES – Advanced Encryption
Standard
In 1997 the American National Institute for
Standards and Technology (NIST) decided that
it was time to find a substitute for the DES. Surprisingly
(at least to this author) NIST invited
parties from all over the world to participate in
this process and announced a call-for-candidates
for the Advanced Encryption Standard (AES).
The conditions for the competition were many
and included a whole range of documentation
requirements and test results.
The most important requirements for the system
are that there must not be any trapdoors (shortcuts),
and that the best attack against the system
is the trivial one of trying all keys one by one. A
more specific requirement is that the secret keys
must be of length of at least 128 bits. This means
that there will be at least 2 128 different keys,
which is about 10 39 . The above mentioned special-purpose
built machines to try all keys one
by one will not have a chance of being applicable
in practice before 2030 – 2040, or probably
even later.
NIST also invited the world’s cryptanalysts to
participate in the process. The goal of NIST is
that the whole process be as open as it can be,
and that all aspects of the design and analysis
are made public.
1) The English intelligence service claims that they invented the public-key techniques around the
same time.
Telektronikk 3.2000