Information Technology Reference
In-Depth Information
coding scheme is straightforward, fast (at least when machines do
the computation), and public. On the other hand, under certain cir
cumstances, the computation of
d
may be expected to require so
much time that data will remain secure for a long time.
4
With these formula encryption systems, there is always the possi
bility that a new discovery or insight will suddenly allow
d
to be com
puted easily and quickly from
m
and
e
, but this is beyond the capabili
ties of current knowledge. Thus, this approach currently is viewed as
reasonably secure, at least if
m
and
e
are chosen carefully. When you
use publickey encryption to store data or to send messages, therefore,
you can have some confidence that your material will be secure for
that storage or transmission. However, before the encryption (before
storage or transmission) or after decoding (when you retrieve your
data from the file or when the message is received), the data still will
be vulnerable, and this can threaten the security of your information.
Unfortunately, even limiting access to accounts and files by
passwords or encryption does not guarantee that data on multiuser
machines will be safe. At least three other types of risks should be
considered:
Programs accessing data may make unintended copies of the
material. An offending program could copy data to another
user's account as it was doing its work for an authorized user.
An intruder then could obtain information by just waiting for
an authorized user to access it. Alternatively, the offending
program could use an Internet connection to transmit your
data to another location. Often, you might expect such of
4 In one popular version of a public key system, developed by Rivest, Shamir, and Adleman,
m
,
e
,
and
d
are obtained as follows: One starts with two large prime numbers,
p
and
q
. Then let
m
pq
and let
L
lcm
(p 1,
q
1), the least common multiple of
p
1 and
q
1. Then
d
and
e
may be computed by taking any solutions to the equation
de
1 mod
L
. Although such computa
tions are easy once
p
and
q
are known, the discovery of
p
and
q
is difficult given only
n
, because the
factoring of very large integers can require a large amount of time and energy. Although further mo
tivation for such work and the reasons this works are beyond the scope of this topic, details may be
found in Davies'
Tutorial
, already cited, or in the original paper, R. L. Rivest, A. Shamir, and L.
Adleman, “A Method for Obtaining Digital Signatures and PublicKey Cryptosystems,”
Communications of the ACM
, Volume 21, Number 2, February 1978, pp. 120-126.
