Secure_Client_N_Server

FTP: File Transfer Protocol

This project include secured server and secured client

Secure features achieved by RSA & Repeat Square algorithm

RSA (Rivest-Shamir-Adleman) Asymmetric Cryptographic Algorithm

1. Key Generation:
   • Choose 2 distinct prime numbers p and q
   • Computer their product, n = p X q which becomes the modulus for both the public and private keys
   • Compute the totient of n denoted as φ(n) where φ(n) = (p - 1) * (q - 1)
   • Choose an integer e such that 1 < e < φ(n) and e is coprime with φ(n) where e is the public exponent
   • Compute the modular multiplicative inverse of e modulo φ(n), denoted as d, where d * e ≡ 1 (mod φ(n)) where d is the private exponent
   • The public key consists of (n, e), and the private key consists of (n, d)
2. Encryption:
   • To encrypt a message M, the sender uses the recipients public key *(n, e)`*
   • Convert the message M into an integer m such that 0 ≤ m < n
   • Compute the ciphertext C using the formula C ≡ m^e (mod n)
   • Send the ciphertext C to the recipient
3. Decryption:
   • To decrypt the ciphertext C, the recipient uses their private key (n, d)
   • Compute the plaintext M using the formula M ≡ C^d (mod n)
   • Convert the integer M back into the original message

Repeat Square

The repeat square algorithm, also known as the square-and-multiply algorithm or binary exponentiation, is a method for efficiently computing the exponentiation of a number to a large power, especially in modular arithmetic contexts.

The basic idea behind the repeat square algorithm is to reduce the number of multiplications needed to compute the result compared to a straightforward approach.

Here's how the repeat square algorithm works:

Start with the base number b. Represent the exponent e in binary form. Scan the binary representation of the exponent from left to right. For each bit: If the bit is 0, square the current result. If the bit is 1, square the current result and multiply it by the base. After processing all the bits, the final result is obtained. Let`s illustrate this with an example:

Suppose we want to compute b^e using the repeat square algorithm.

Let b = 3 and e = 13. The binary representation of e is 1101. Now, applying the algorithm:

Start with b = 3. Since the rightmost bit of e is 1, multiply the result by b giving 3 X 3 = 9. The next bit is 0, so square the result, giving 9 X 9 = 81. The next bit is 1, so multiply the result by b, giving 81 X 3 = 243. The leftmost bit is 1, so multiply the result by b, giving 243 X 3 = 729. So, 3^13 = 729.

This algorithm significantly reduces the number of multiplications needed compared to a straightforward approach that directly computes b^e by multiplying b by itself e times. In cryptography, where large exponentiation operations are common, this efficiency is crucial for performance.

Encryption & Decryption Implementation

Client Site:

Using a big array of integer as hash table: give an index then return a different number of integer:

Repeat Square algorithm implementation:

Encrypring process, using a for-loop to iterate through the input buffer:

• Get ascii value of the char
• Applying the binary XOR value to the ascii value and pre-assigned temp_XOR value, use the result as the position number for hash table
• Get hashed value
• Update the temp_XOR value for the next char encryption
• Use RSA algorithm to get encrypted value and send to the server

Server Site:

Make required values for decryption:

The Greatest Common Divisor, big prime number and other associative attributes generation functions:

Decrypting process:

• Use RSA algorithm again for decrypting the first layer
• Substitute the value into hash table to get de-hashed value
• Apply de-hashed value to temp_XOR with binary XOR operation to get the original ascii value
• Convert ascii value to char to get the actual message
• Update the temp_XOR value for the next char decryption