namespace ra :: RSA

Aim:

To create a working RSA code, Using namespace ra::random_prime_engine, Here the link GitHub repo!

What is RSA?

The Rivest-Shamir-Adleman (RSA) is an asymmetric encryption algorithm. Asymmetric Encryption is when a box(data) can be locked by one key and unlocked by other. locking key cannot unlock the box and vice-versa. The locking key is the public key and the unlocking key is the private key, Public key is called so because we publicly distribute it, so anyone/everyone would send the user an encrypted msg, and the user can unlock it in private with the private key. By keeping private to the user-self, no hacker can get a method of unlocking it.

How RSA Works?

https://ra101.hashnode.dev/rsa-encryption-algorithm

Code:

• Private Members:

• private_key

• public_key

• create_key(long seed)

• Public Members:

• Constructor & Constructor(seed)

• std::size_t decrypt(std::size_t);

• std::size_t decrypt_with_padding(std::string);

• Key Getters

• std::size_t sign(Message message)

• Other Function within namespace but Outside class (All the functions utilizing public key):

• std::size_t encrypt(std::size_t digest, public_key);

• std::string encrypt_with_padding(std::size_t digest, public_key);

• bool verify(Message message, size_t digest, public_key)

• string padding(string)

Constructors:

The seed in the constructor is used in random prime engine and the logic of the seed argument is as follow,

# pseudo code implemented in python
def constructor(seed=None):
    if not seed:
        seed = timestamp()
    else:
        seed = hash(seed)
   return create_key(seed)

// Usage

ra::rsa_key_pair k1, k2("127.0.0.1");

create_key(seed) function,

I will not get into the mathematics of it all, but in the end, using 2 primary numbers we get

• public key: (n, e)
• private key: (n, d)

(n, e, d) all are integers.

To concatenate these two numbers (n, e/d) let us define a big number BIG_NO, such that

• n = key / BIG_NO
• e = public_key % BIG_NO
• d = private_key % BIG_NO

#define BIG_NO 100000000000

public_key = n * BIG_NO + e;
private_key = n * BIG_NO + d;

encrypt(digest, key) function,

return (digest ** e) % n

decrypt(encrypted_data) function,

return (encrypted_data ** d) % n

padding(string str) function,

#define PAD_SIZE 10

// 12345 -> 0000012345
while (str.length() < PAD_SIZE)
{
    str = '0' + str; // add 0 in front of no.
}
return str;

encrypt_with_padding(digest, key) function,

# encrypt each digit
for each_digit in digest:
    output = padding(encrypt(each_digit)) + output
return output

decrypt_with_padding(encrypted_data) function,

# cut the input string in chunks of length PAD_SIZE
# decrypt each chunk to digit and then form a output
for i_chunk in len(encrypted_data)/PAD_SIZE:
    i = i_chunk * PAD_SIZE
    digit = decrypt(int(encrypted_data[i: i + PAD_SIZE]))
    output = digit + output * 10
return output

sign(Message message) function,

return decrypt(hash(message))

verify(Message message, digest, others_public_key) function,

return ( hash(message) == encrypt(digest, others_public_key) )