Question

Explain how encryption and decryption are done in the RSA cryptosystem.

Short answer

How encryption and decryption are done in the RSA cryptosystem is explained below.

Step-by-step solution

RSA cryptosystem

Ronald Rivest, Adi Shamir, and Leonard Adleman, three researchers at the Massachusetts Institute of Technology, gave the world to the public key cryptosystem known as the RSA system in 1976. The RSA system had been discovered some years previously in covert government research in the United Kingdom, as is typical with cryptographic innovations.

Explaining how encryption is done in the RSA cryptosystem

Given the encryption key:$(n,e)$

Step 1: Translate each plaintext letter into a two-digit number by shift chipper translation as,

$$\begin{gathered} A=0,B=1,C=2,D=3,E=4,F=5,G=6,H=7,I=8,J=9,K=10, \\ L=11,M=12,N=13,O=14,P=15,Q=16,R=17,S=18, \\ T=19,U=20,V=21,W=22,X=23,Y=24,Z=25 \end{gathered}$$

Step 2: If$25<n\le 2525...25$ with$2525...25$ having 2N digits, then we write the translated message into N digits.

Step 3: Encrypt each block of N digit by using the following function:

$C=M^{e}modn$

Then the encrypted message consists of these encrypted blocks.

Explaining how decryption is done in the RSA cryptosystem

Given the encryption key:$(n,e)$

Corresponding decryption key is d.

Step 1: Decrypt each block by using following function:

$M=C^{d}modn$

Step 2: Translate each two-digit number into a plaintext letter by shift chipper translation as,

$$\begin{gathered} A=0,B=1,C=2,D=3,E=4,F=5,G=6,H=7,I=8,J=9,K=10, \\ L=11,M=12,N=13,O=14,P=15,Q=16,R=17,S=18, \\ T=19,U=20,V=21,W=22,X=23,Y=24,Z=25 \end{gathered}$$

Then the letters which is found is form of the message.