Random numbers are the numbers which play an essential role for various network security applications. There are some approaches that are used to generating random numbers including pseudorandom number generator and linear congruent generator also cryptographically generated random numbers etc.The main objective of the Chinese Reminder Theorem is to generating Random numbers. In essence, CRT says it is applicable to reconstruct integers in a certain range from their residues modulo a set of pair wise relatively prime modulo.CRT is one of the main theorems of mathematics. This can be utilized in the area of cryptography. It is a perfect set ... Read More

Fermat's little theorem is a fundamental theorem in elementary number theory, which provides compute powers of integers modulo prime numbers. It is a specific case of Euler's theorem, and is essential in applications of elementary number theory, such as primality testing and public-key cryptography. This is referred to as Fermat’s little theorem.Fermat’s theorem is also called a Fermat’s little theorem defines that is P is prime and ‘a’ is a positive integer not divisible by P then −aP−1 ≡ 1 mod PSecond condition says that if P is a prime and a is an integer then aP ≡ 1 mod ... Read More

AES encryption defines the phase of hiding electronic information using an approved 128-bit, 192-bit, or 256-bit symmetric encryption algorithm from the Advanced Encryption Standard (AES), also called a FIPS 197.In the 1990s, the US Government required to standardize a cryptographic algorithm which was to be used globally by them. It is known as the Advance Encryption Standard (AES).Several proposols were submitted and after multiple debate, an algorithm known as Rijndael was accepted. Rijandael was invented by Joan Daemen and Vincent Rijmen. The need for appearing up with a new algorithm was actually because of recognized weakness in DES.The 56-bit keys ... Read More

Modular arithmetic is a structure of arithmetic for integers, where numbers "wrap around" upon reaching a specific value. Modular arithmetic enables us to simply make groups, rings and fields which are the basic constructing piece of most modern public-key cryptosystems.For instance, Diffie-Hellman need the multiplicative group of integers modulo a prime pp. There are different groups which can work. Modular or clock arithmetic is arithmetic on a circle rather than a number line modulo N, it can use only the twelve entire numbers from 0 through N-1.Modular arithmetic is very well understood in method of algorithms for several basic operations. ... Read More

Groups, rings, and fields are the important elements of a branch of mathematics called as abstract algebra, or modern algebra. In abstract algebra, it is concerned with sets on whose elements and it can operate algebraically; that is, it can combine two elements of the set, perhaps in multiple ways, and it can obtain a third element of the set.GroupA group (G) is indicated by {G, ∙}. It is a group of elements with a binary operation ′ ∙ ′ that satisfies four properties. The properties of Group are as follows −Closure − If a and b are elements of ... Read More

There are various component of DES which are as follows −Key Transformation − An initial 64-bit key is changed into a 56-bit key by discarding each 8th bit of the initial key. Therefore for each round, a 56 bit key is applicable. From this 56-bit key, there are several 48-bit subkey is produced during every round utilizing a procedure is known as key transformation. The 56-bit key is breaked into two halves, each 28 bits.Round12345678910111213141516Number of key bits shifted1122222212222221No of key bits shifted per roundIn key transformation procedure, it includes permutation and selection of a 48-bit key from original 56-bit ... Read More

EncryptionData encryption is a method of translating information from plaintext (unencrypted) to ciphertext (encrypted). Users can access encrypted information with an encryption key and decrypted information with a decryption key.There are large amounts of sensitive information handled and stored online in the cloud or on combined servers. Encryption needs cybersecurity to protect against brute-force and cyber-attacks, such as malware and ransomware.Data encryption operates by protecting transmitted digital information on the cloud and computer systems. There are two types of digital information, transmitted information or in-flight information and stored digital information or data at rest.The main objective of data encryption is ... Read More

There are various techniques of Monoalphabetic cipher which are as follows −Additive Cipher − Additive cipher is one method of changing a permutation of the letters of the alphabet. Each letter in the alphabet is cyclically changed by the equivalent amount and the relative order of the letters is kept the similar.The number of position the letter has been transformed is known as key. For example if it can use a key value of 5, ‘a’ is changed 5 positions right in the alphabet to ‘F’, ‘b’, to ‘G’ and so on.The letter ‘u’ is changed to ‘Z’ and thus ... Read More

The substitution cipher is the oldest forms of encryption algorithms according to creates each character of a plaintext message and require a substitution process to restore it with a new character in the ciphertext.This substitution method is deterministic and reversible, enabling the intended message recipients to reverse-substitute ciphertext characters to retrieve the plaintext.The specific form of substitution cipher is the Monoalphabetic Substitution Cipher, is known as “Simple Substitution Cipher”. Monoalphabetic Substitution Ciphers based on an individual key mapping function K, which consistently replaces a specific character α with a character from the mapping K (α).A mono-alphabetic substitution cipher is a ... Read More

A poly-alphabetic cipher is any cipher based on substitution, using several substitution alphabets. In polyalphabetic substitution ciphers, the plaintext letters are enciphered differently based upon their installation in the text. Rather than being a one-to-one correspondence, there is a one-to-many relationship between each letter and its substitutes.For example, ‘a’ can be enciphered as ‘d’ in the starting of the text, but as ‘n’ at the middle. The polyalphabetic ciphers have the benefit of hiding the letter frequency of the basic language. Therefore attacker cannot use individual letter frequency static to divide the ciphertext.The first Polyalphabetic cipher was the Alberti Cipher ... Read More