Cryptography Reference
In-Depth Information
It is mentioned in the section "Cryptology" in pri-
vate and commercial life that the 40-bit key cipher
systems approved for use in the 1990s were eventually
made insecure. There are 2
40
40-bit keys possible—very
close to 10
12
—which is the work function of these sys-
tems. Most personal computers (PCs) at the end of the
20th century could execute roughly 1,000 MIPS (mil-
lions of instructions per second) or 3.6 × 10
12
per hour.
Testing a key might involve many instructions, but even
so a single PC at that time could search a 2
40
-key space
in a matter of hours. Alternatively, partitioning the key
space and using multiple machines to carry out the
search would have made it possible to produce a solu-
tion with PCs of that era in minutes or even seconds.
Clearly, by the year 2000, 40-bit keys were not secure
by any standard, a situation that brought on the shift to
the current 128-bit key.
Because of its reliance on “hard” mathematical prob-
lems as a basis for cryptoalgorithms and because one
of the keys is publicly exposed, two-key cryptography
has led to a new type of cryptanalysis that is virtually
indistinguishable from research in any other area of com-
putational mathematics. Unlike the ciphertext attacks or
ciphertext/plaintext pair attacks in single-key cryptosys-
tems, this sort of cryptanalysis is aimed at breaking the
cryptosystem by analysis that can be carried out based
only on a knowledge of the system itself. Obviously there
is no counterpart to this kind of cryptanalytic attack in
single-key systems.
Similarly, the RSA cryptoalgorithm (described in the
section "RSA Encryption") is susceptible to a break-
through in factoring techniques. In 1970 the world record
in factoring was 39 digits. In 2009 the record was a 768-
digit RSA challenge. That achievement explains why
