RSA ENCRYPTION METHODOLOGY
The RSA (named after its inventors R.Rivest, A. Shamir and L.Adelman) is
generally
used in communication applications where the communication
channel is generally
unsafe. For such applications, RSA is more efficient
than DES in two respects:
1) Like DES, network users don't have to share a common key.
2) Dynamic generation of keys for each communication session is not
required. Hence
RSA is more time and computation efficient.
System Formulation:
RSA cryptosystem is characterized by generation of two “very large” prime
numbers p
and q (which have typically 512 bits each ) which are known
only to the user A .Then
mathematically the encryption system can be
defined as:
Here, the input signal M is supposed to be a series of decimal numbers
where m(i) and i
is the position of a particular number in the input series.
The output signal is PA(M)
(known as Public Key) which is also a series of
decimal numbers having same length as
that of input message.
For this system, we define following things:
M1 +M2 ={m1(i)+m2(i)}
{Defined and meaningful if and only if length of the two strings being
added is the
same}
and
cM ={cm(i)} for cbelongs to R
Then the properties of the RSA encrypting algorithm can be discussed as
follows:
Stability of RSA system shall be discussed in terms of whether a series of
bounded
decimal numbers gives bounded series of decimal numbers as
output. From the relation
describing the system, it can be noted that for finite
mi and e , the corresponding
output e mod
mi n is finite .
Hence RSA algorithm is stable system.
3) Memory:
The system is necessarily memoryless as any number in the output string
depends only on the corresponding position in the input.
4) Causality:
The system equation indicates that as long as input mi does not become
nonzero the output can not become nonzero. Hence the RSA cryptosystem is
causal.
Note that here; causality is with respect to position of the number in
the input string,
which is the independent variable in this case.
Now we come back to the point of
non-breakability of the Vernam Cipher.
As explained above, to break into Vernam
encrypting, one must find the
sequence
RSA DECRYPTION METHODOLOGY
RSA Decryption algorithm is classified as asymmetric cryptosystem because
the
encryption algorithm and decryption algorithm are not same.
System Formulation:
The Decryption algorithm uses same two prime numbers p and q but varies
in system
equation as follows:
The properties of the both encryption and decryption systems are same as
the relations
between input and output signals are of the same nature.
Cascading of these systems
as shown forms the complete “secure
communication system”:
SA(PA(M)) =M
References
1) Secure Communication Systems
Design, Analysis , and Implementation
Michael R.A. Huth
2) Making,Breaking Codes
An Introduction To Cryptology
Paul Garret
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