# Cryptography ,Diffie Hellman and RSA Algorithm

Cryptography can reformat and transform our data, making it safer on its trip between computers. The technology is based on the essentials of secret codes, augmented by modern mathematics that protects our data in powerful ways.

• Computer Security – generic name for the collection of tools designed to protect data and to thwart hackers

• Network Security – measures to protect data during their transmission

• Internet Security – measures to protect data during their transmission over a collection of interconnected networks.

Security Attacks, Services and Mechanisms: To assess the security needs of an organization effectively, the manager responsible for security needs some systematic way of defining the requirements for security and characterization of approaches to satisfy those requirements. One approach is to consider three aspects of information security:

• Security attack – Any action that compromises the security of information owned by an organization.
• Security mechanism – A mechanism that is designed to detect, prevent or recover from a security attack.
• Security service – A service that enhances the security of the data processing systems and the information transfers of an organization. The services are intended to counter security attacks and they make use of one or more security mechanisms to provide the service.

Basic Concepts:

Cryptography:The art or science encompassing the principles and methods of transforming an intelligible message into one that is unintelligible, and then retransforming that message back to its original form

Plaintext The original intelligible message

Cipher text The transformed message

Cipher An algorithm for transforming an intelligible message into one that is unintelligible by transposition and/or substitution methods

Key Some critical information used by the cipher, known only to the sender& receiver

Encipher (encode) The process of converting plaintext to cipher text using a cipher and a key

Decipher (decode) the process of converting cipher text back into plaintext using a cipher and a key

Cryptanalysis The study of principles and methods of transforming an unintelligible message back into an intelligible message without knowledge of the key. Also called code breaking.Cryptanalysis uses mathematical formulas to search for algorithm vulnerabilities and break into cryptography or information security systems.

Cryptanalysis attack types include:

• Known-Plaintext Analysis (KPA): Attacker decrypt ciphertexts with known partial plaintext.
• Chosen-Plaintext Analysis (CPA): Attacker uses ciphertext that matches arbitrarily selected plaintext via the same algorithm technique.
• Ciphertext-Only Analysis (COA): Attacker uses known ciphertext collections.
• Man-in-the-Middle (MITM) Attack: Attack occurs when two parties use message or key sharing for communication via a channel that appears secure but is actually compromised. Attacker employs this attack for the interception of messages that pass through the communications channel. Hash functions prevent MITM attacks.
• Adaptive Chosen-Plaintext Attack (ACPA): Similar to a CPA, this attack uses chosen plaintext and ciphertext based on data learned from past encryptions.

Cryptology Both cryptography and cryptanalysis

Code An algorithm for transforming an intelligible message into an unintelligible one using a code-book

Cryptography:

Cryptographic systems are generally classified along 3 independent dimensions:

Type of operations used for transforming plain text to cipher text All the encryption algorithms are based on two general principles: substitution, in which each element in the plaintext is mapped into another element, and transposition, in which elements in the plaintext are rearranged.

The number of keys used If the sender and receiver uses same key then it is said to be symmetric key (or) single key (or) conventional encryption. If the sender and receiver use different keys then it is said to be public key encryption.

The way in which the plain text is processed A block cipher processes the input and block of elements at a time, producing output block for each input block. A stream cipher processes the input elements continuously, producing output element one at a time, as it goes along.

Cryptanalysis:

The process of attempting to discover X or K or both is known as cryptanalysis. The strategy used by the cryptanalysis depends on the nature of the encryption scheme and the information available to the cryptanalyst.

There are various types of cryptanalytic attacks based on the amount of information known to the cryptanalyst.

• Cipher text only – A copy of cipher text alone is known to the cryptanalyst. Known plaintext – The cryptanalyst has a copy of the cipher text and the corresponding plaintext.
• Chosen plaintext – The cryptanalysts gains temporary access to the encryption machine. They cannot open it to find the key, however; they can encrypt a large number of suitably chosen plaintexts and try to use the resulting cipher texts to deduce the key.
• Chosen cipher text – The cryptanalyst obtains temporary access to the decryption machine, uses it to decrypt several string of symbols, and tries to use the results to deduce the key.

### Diffie-Hellman:

• a method of exchanging cryptographic keys
• establishes a shared secret that can be used for secret communications
• vulnerable to Man-in-the-middle attack
• Key identity: (gens1)s2 = (gens2)s1 = shared secret   (mod prime)
• Where:
• gen is an integer whose powers generate all integer in [1, prime)   (mod prime)
• s1 and s2 are the individuals’ “secrets”, only used to generate the symmetric key

RSA is used to come up with a public/private key pair for asymmetric (“public-key”) encryption:

Working: (based upon the above paint example)

• alice and bob produces a mix based upon their secret colour
• exchange the mix between them
• finalize a common secret

### RSA:

• Used to perform “true” public-key cryptography
• an encryption algorithm
• very slow for bulk data encryption
• Key identity: (me)d = m   (mod n)   (lets you recover the encrypted message)
• Where:
• n = prime1 × prime2    (n is publicly used for encryption)
• φ = (prime1 – 1) × (prime2 – 1)   (Euler’s totient function)
• e is such that 1 < e < φ, and (e, φ) are coprime    (e is publicly used for encryption)
• d × e = 1   (mod φ)    (the modular inverse d is privately used for decryption)

Working:

• sender encrypts the data to be transferred using using the public key of the recipient
• receiver decrypts the encrypted data using his private key