Cryptography with Python Tutorial
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- Hacking RSA Cipher
- RSA Cipher Decryption
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- Understanding RSA Algorithm
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- Understanding Vignere Cipher
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- Decryption of Simple Substitution Cipher
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Understanding RSA Algorithm
Understanding RSA Algorithm
RSA algorithm is a pubpc key encryption technique and is considered as the most secure way of encryption. It was invented by Rivest, Shamir and Adleman in year 1978 and hence name RSA algorithm.
Algorithm
The RSA algorithm holds the following features −
RSA algorithm is a popular exponentiation in a finite field over integers including prime numbers.
The integers used by this method are sufficiently large making it difficult to solve.
There are two sets of keys in this algorithm: private key and pubpc key.
You will have to go through the following steps to work on RSA algorithm −
Step 1: Generate the RSA modulus
The initial procedure begins with selection of two prime numbers namely p and q, and then calculating their product N, as shown −
N=p*q
Here, let N be the specified large number.
Step 2: Derived Number (e)
Consider number e as a derived number which should be greater than 1 and less than (p-1) and (q-1). The primary condition will be that there should be no common factor of (p-1) and (q-1) except 1
Step 3: Pubpc key
The specified pair of numbers n and e forms the RSA pubpc key and it is made pubpc.
Step 4: Private Key
Private Key d is calculated from the numbers p, q and e. The mathematical relationship between the numbers is as follows −
ed = 1 mod (p-1) (q-1)
The above formula is the basic formula for Extended Eucpdean Algorithm, which takes p and q as the input parameters.
Encryption Formula
Consider a sender who sends the plain text message to someone whose pubpc key is (n,e). To encrypt the plain text message in the given scenario, use the following syntax −
C = Pe mod n
Decryption Formula
The decryption process is very straightforward and includes analytics for calculation in a systematic approach. Considering receiver C has the private key d, the result modulus will be calculated as −
Plaintext = Cd mod nAdvertisements