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