ALU (Arithmetic Logic Unit)

An arithmetic logic unit (ALU) is a digital circuit used to perform arithmetic and logic operations. It represents the fundamental building block of the central processing unit (CPU) of a computer. Modern CPUs contain very powerful and complex ALUs. In addition to ALUs, modern CPUs contain a control unit (CU).

One or more ALUs load data from input registers to accomplish the majority of a CPU's operations. A register is a little piece of storage that comes with a CPU. The ALU is told what operation to do on the data by the control unit, and the result is stored in an output register by the ALU. The data is moved between these registers, the ALU, and memory by the control unit[10].

Factorial prime

The mathematical issue of prime factorization (or integer factorization) is frequently employed to secure public-key encryption systems. The use of very big semi-primes (the result of multiplying two prime integers) as the number ensuring the encryption is a widespread practice. They'd have to find the prime factorization of the huge semi-prime number — that is, two or more prime numbers multiplied together yield the original number – in order to break it.

First, a refresher in elementary math. What is the definition of a prime number? Any number that is evenly divided only by 1 and itself is called a prime number. 2, 3, 5, 7, 11, 13, 17, and so on are prime numbers. There exists an infinite number of prime numbers (numbers that are never divisible by something). Furthermore, every number has exactly one prime factorization — that is, any number may be obtained by multiplying a set of prime numbers.

It's relatively simple to generate a huge prime number in terms of computation. You start with a large number and then work backwards to see if it's divisible by anything. As a result, we can combine our two prime numbers. Then we multiply them all together - that's all. For a short illustration, consider the following primes: 19 x 31 = 589

Okay, the result of multiplying these two primes together is 589. Multiplying two integers is, after all, a mathematically simple task that scales nicely when dealing with larger numbers. Factoring numbers, on the other hand, is a computationally tough issue. When dealing with smaller numbers, it's simple, but when dealing with enormous numbers, it can take computers days, months, years, or even centuries to solve. Factoring numbers is a trial-and-error procedure with no fast shortcuts. You'd have to attempt all of the prime numbers that are smaller than 589 until you discovered which prime numbers add up to 589 when multiplied together. This works for smaller numbers, but when dealing with really large numbers, the number of possible numbers to compare gets so large that even current computers are unable to do so in a reasonable length of time[9].

Diffie Hellman

Diffie-Hellman is a method of generating a shared secret between two persons that cannot be seen by watching their communication. It's vital to note that throughout the key exchange, you're not sharing information; instead, you're working together to create a key.

This is especially handy since you can use it to build an encryption key with someone and then use that key to encrypt your communication. Even if the data is logged and studied afterward, there's no way to find out what the key was, even if the exchanges that generated it were visible. This is how absolute forward secrecy is achieved. Nobody can break in later by studying the traffic because the key was never kept, sent, or made accessible anywhere.

It works in a rather straightforward manner. In that a trapdoor function is employed, most of the math is similar to that seen in public-key cryptography. While the discrete logarithm problem (the x^y mod p business) is generally utilized, the general procedure can be adjusted to use elliptic curve cryptography instead.

However, even though it is based on the same principles as public-key cryptography, it is not asymmetric cryptography because no data is encrypted or decrypted during the exchange. It is, nevertheless, an important building piece that served as the foundation for asymmetric cryptography[1][7][8].

Diffie Hellman key exchange

The simplest and the original implementation of the protocol uses the multiplicative group of integers modulo p, where p is prime, and g is a primitive root modulo p. These two values are chosen in this way to ensure that the resulting shared secret can take on any value from 1 to p–1. Here is an example of the protocol, with non-secret values in blue, and secret values in red[1][7][8].

1. Alice and Bob publicly agree to use a modulus p = 23 and base g = 5 (which is a primitive root modulo 23).
2. Alice chooses a secret integer a = 4, then sends Bob A = g^a mod p
   • A = 5⁴ mod 23 = 4
3. Bob chooses a secret integer b = 3, then sends Alice B = g^b mod p
   • B = 5³ mod 23 = 10
4. Alice computes s = B^a mod p
   • s = 10⁴ mod 23 = 18
5. Bob computes s = A^b mod p
   • s = 4³ mod 23 = 18
6. Alice and Bob now share a secret (the number 18).

AES

The Advanced Encryption Standard (AES) is the most popular and commonly used symmetric encryption algorithm available today (AES). It is at least six times faster than triple DES in terms of discovery.

Because the key size of DES was too small, a replacement was required. It was thought to be vulnerable to an exhaustive key search assault as processing power increased. Triple DES was created to address this flaw, however it was proven to be sluggish[3][5][6].

AES Operation

Rather than being a Feistel cipher, AES is an iterative cipher. It is built based on a ‘substitution–permutation network.' It consists of a sequence of connected processes, some of which require substituting specified outputs for inputs (substitutions) and others involving shuffling bits around (permutations).

Surprisingly, AES uses bytes rather than bits for all of its calculations. As a result, AES considers a plaintext block's 128 bits as 16 bytes. For matrix processing, these 16 bytes are organized into four columns and four rows.

In contrast to DES, the number of rounds in AES is configurable and dependent on the key length. For 128-bit keys, AES employs 10 rounds, 12 rounds for 192-bit keys, and 14 rounds for 256-bit keys. Each of these rounds uses a unique 128-bit round key derived from the original AES key[3][5][6].

Triple Data Encryption Algorithm (3DES)

What is 3DES

Although the Triple Data Encryption Algorithm (3DEA) is the formal name, it is most generally referred to as 3DES. This is because the 3DES technique encrypts data three times with the Data Encryption Standard (DES) cipher.

DES is a Feistel network-based symmetric-key technique. It's an asymmetric key cipher, which means it uses the same key for encryption and decryption. The Feistel network renders each of these processes nearly identical, resulting in a more efficient technique to implement.

Although DES has a 64-bit block and key size, the key only provides 56-bits of security in practice. Because of DES's short key length, 3DES was created as a more secure alternative. The DES algorithm is executed three times with three different keys in 3DES, however, it is only considered secure if three different keys are utilized.

How does 3DES Work

Before employing 3DES, users must first generate and share a 3DES key K, which is made up of three DES keys: K₁, K₂, and K₃. This means that the true 3DES key is 356 bits or 168 bits.

The encryption-decryption process works in the following steps:[2]

• Encrypt the plaintext blocks using single DES with key K₁.
• Now decrypt the output of step 1 using single DES with key K₂.
• Finally, encrypt the output of step 2 using single DES with key K₃.
• The output of step 3 is the ciphertext.
• Decryption of a ciphertext is a reverse process. User first decrypt using K₃, then encrypt with K₂, and finally decrypt with K₁.

Because Triple-DES is designed as an encrypt–decrypt–encrypt procedure, a 3DES (hardware) implementation for a single DES can be used by setting K₁, K₂, and K₃ to the same value. This ensures that DES compatibility is maintained.

K₃ is substituted by K₁ in the second variant of Triple DES (2DES), which is identical to 3DES. To put it another way, the user encrypts plaintext blocks with key K₁, decrypts with key K₂, and then encrypts with K₁. As a result, the key length of 2DES is 112 bits.

Triple DES systems are much more secure than single DES, but they are unquestionably slower than single DES encryption.

References

1. Wikipedia contributors. (2021, October 31). Diffie–Hellman key exchange. Wikipedia. Retrieved November 1, 2021, from https://en.wikipedia.org/wiki/Diffie-Hellman_key_exchange
2. Triple DES. (n.d.). Tutorialspoint. Retrieved November 10, 2021, from https://www.tutorialspoint.com/cryptography
3. Secure your data with AES-256 encryption. (2019, September 26). Atpinc. Retrieved November 10, 2021, from https://www.atpinc.com/blog/what-is-aes-256-encryption
4. Wikipedia contributors. (2022, January 12). Block cipher mode of operation. Wikipedia. Retrieved January 14, 2022, from https://en.wikipedia.org/wiki/Block_cipher_mode_of_operation
5. Rimkienė, R. (2021, September 28). What is AES encryption and how does it work? CyberNews. Retrieved January 10, 2022, from https://cybernews.com/resources/what-is-aes-encryption/
6. Lake, J. (2020, February 17). What is AES encryption and how does it work? Comparitech. Retrieved January 12, 2022, from https://www.comparitech.com/blog/information-security/what-is-aes-encryption/
7. Wikipedia contributors. (2022c, January 18). Diffie–Hellman key exchange. Wikipedia. Retrieved January 11, 2022, from https://en.wikipedia.org/wiki/Diffie%E2%80%93Hellman_key_exchange
8. Lake, J. (2021, March 23). What is the Diffie–Hellman key exchange and how does it work? Comparitech. Retrieved January 11, 2022, from https://www.comparitech.com/blog/information-security/diffie-hellman-key-exchange/
9. Wikipedia contributors. (2022b, January 12). Factorial prime. Wikipedia. Retrieved January 12, 2022, from https://en.wikipedia.org/wiki/Factorial_prime
10. Wikipedia contributors. (2021b, November 21). Arithmetic logic unit. Wikipedia. Retrieved January 11, 2022, from https://en.wikipedia.org/wiki/Arithmetic_logic_unit