Cryptography

1. AES(Advance Encryption Standard)

This app is about Cryptography using AES(Advanced Encryption Standard) algorithm, build in Microsoft Visual Studio 2022.
The Key, IV(Initialization Vector) and Ciphertext in Base64 number system.
The key lengths or key size is 128 bit(AES-128), 192 bit(AES-192) and 256 bit(AES-256).
Using lib : --> using System.Security.Cryptography;

using System.Security.Cryptography;
aes.GenerateKey();
aes.GenerateIV();

2. Nix Hashing(use SHA256, SHA512, MD5 algorithm)

This app to hashing text and file, as the result we got hashing text. Build in Microsoft Visual Studio 2022
-SHA256 is 256 bits(32 bytes) with hexadecimal characters is 64.
-SHA512 is string with 128 hexadecimal character.
-MD5 got 32 hexadecimal char.
Using lib : --> using System.Security.Cryptography;

using System.Security.Cryptography;

3. RSA Pascal

Implementation of RSA algorithm using Pascal (text base/terminal).

4. Nix Cryptography(RSA)

Implementation of RSA algorithm using Lazarus 4.8 FPC 3.2.2.

RSA :

On the RSA as asymmetric cryptography uses two different keys, e as public key/encrypt key(not secret) & d as private key/decrypt key(secret).

Formula:

p . q = n ;

p, q is prime number

$\phi(n)=(p-1)(q-1)$

$d=\frac{1+k\ \phi(n)}{e}$

k:integer

Encryption:

$m^e\ mod\ n$

m:integer

Decryption:

$c^d\ mod\ n$

c:integer
The public keys is (n,e)
The private key represent as (n,d) and p, q is secret also.

SLIMMING BRUTE FORCE :

The idea is to find p first as one of the prime factors, then get q using q=n/p.
The method as follows :

• On this app, the lower boundary required a minimum 3 digits decimal.
• Check n, Eliminate if last digit n is 2 or 5(because there is no composite number as a product of multiply two prime numbers.
• On a 3 digit or higher of prime number, the last digit must be 1 or 3 or 7 or 9 and so with p.
• First find a length digits of n(e.g 11 digits).
• Find digit p using: ceil(digit n/2), e.g, ceil(11/2)=6 digits.
• This method is called the "Slimming Brute Force", where it covers all possibilities to find p.
• After length digits of p or q found, we find all prime numbers(or candidates p) on [a,b], where a= 10^(m-1), b=(10^m)-1, where m is length digit of p. Example m=3, so p on the [100,999] with assume p & q got the same length digit.
• If two factors have different length digit then we use the 2nd scenario where we decrease a as the left boundary to find candidates of p where a becomes a= 10^(m-1-g), g start from 1. Now a=10(2 digit), [a,b] becomes [10,99],and so on.
• We can use the Sieve of Atkin algorithm to find all prime numbers on a given interval.
• We try the first scenario with assume p, q got the same length digit(it's usually used, because if one of the factor got shorter digit, easier to break), and try others scenarios till found p(automatically found q also). We got all candidates for p.
• Check the right candidate use: if (n mod p)=0 then p found & find q using q=n/p.
• We already have e, p, q.
• d=(1+k phi(n))/e ; we loop k as integer till satisfied the equation(start with k=1).
• Finally we got d as our private key.