Basics of Cryptography
 Mithun Ashok
 May 29, 2019
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Cryptography
(derived from Ancient Greek: κρυπτός, romanized: kryptós "hidden, secret"; and γράφειν graphein, "to write", or λογία logia, "study", respectively) is the practice and study of techniques for secure communication in the presence of third parties called adversaries. More generally, cryptography is about constructing and analyzing protocols that prevent third parties or the public from reading private messages; various aspects in information security such as data confidentiality, data integrity, authentication, and nonrepudiation are central to modern cryptography. Modern cryptography exists at the intersection of the disciplines of mathematics, computer science, electrical engineering, communication science, and physics. Applications of cryptography include electronic commerce, chipbased payment cards, digital currencies, computer passwords, and military communications.
Cryptography prior to the modern age was effectively synonymous with encryption, the conversion of information from a readable state to apparent nonsense. The originator of an encrypted message shares the decoding technique only with intended recipients to preclude access from adversaries. The cryptography literature often uses the names Alice ("A") for the sender, Bob ("B") for the intended recipient, and Eve ("eavesdropper") for the adversary. Since the development of rotor cipher machines in World War I and the advent of computers in World War II, the methods used to carry out cryptology have become increasingly complex and its application more widespread.
Modern cryptography is heavily based on mathematical theory and computer science practice; cryptographic algorithms are designed around computational hardness assumptions, making such algorithms hard to break in practice by any adversary. It is theoretically possible to break such a system, but it is infeasible to do so by any known practical means. These schemes are therefore termed computationally secure; theoretical advances, e.g., improvements in integer factorization algorithms, and faster computing technology require these solutions to be continually adapted. There exist informationtheoretically secure schemes that probably cannot be broken even with unlimited computing power—an example is a onetime pad—but these schemes are more difficult to use in practice than the best theoretically breakable but computationally secure mechanisms.
(Above Definition is from Wiki: https://en.wikipedia.org/wiki/Cryptography)
In cryptography, encryption is the process of encoding a message or information in such a way that only authorized parties can access it and those who are not authorized cannot. Encryption does not itself prevent interference but denies the intelligible content to a wouldbe interceptor.
Encryption is the process of converting messages, information, or data into a form unreadable by anyone except the intended recipient. As shown in the figure below, Encrypted data must be deciphered, or decrypted, before it can be read by the recipient.
The root of the word encryption—crypt—comes from the Greek word kryptos, meaning hidden or secret.
History of Cryptography
1900 BC: A scribe in Egypt uses a derivation of the standard hieroglyphics
ABCDEFGHIJKLMNOPQRSTUVWXYZ
ZYXWVUTSRQPONMLKJIHGFEDCBA
ATBASH Cipher
10044 BC: Julius Caesar uses a simple substitution with the normal alphabet in government communications.
ABCDEFGHIJKLMNOPQRSTUVWXYZ
DEFGHIJKLMNOPQRSTUVWXYZABC
Caesar Cypher
In 1518 Johannes Trithemius wrote the first printed book on cryptology. It was also known as changing key cipher.
ABCDEFGHIJKLMNOPQRSTUVWXYZ Plaintext
FGUQHXSZACNDMRTVWEJBLIKPYO T00
OFGUQHXSZACNDMRTVWEJBLIKPY T01
YOFGUQHXSZACNDMRTVWEJBLIKP T02
PYOFGUQHXSZACNDMRTVWEJBLIK T03
...
GUQHXSZACNDMRTVWEJBLIKPYOF T25
Changing Key Cypher
1790: Thomas Jefferson invented the wheel cipher
GJTXUVWCHYIZKLNMARBFDOESQP
W1
IKMNQLPBYFCWEDXGZAJHURSTOV
W2
HJLIKNXWCGBDSRVUEOFYPAMQZT
W3
...
BDFONGHJIKLSTVUWMYEPRQXZAC
Wn
A Wheel Cypher
Modern Encryption Algorithms
Private Key Encryption
Private Key encryption algorithms use a single key for both encryption and decryption. In order to communicate using this class of ciphers, the key must be known to both the sender and receiver of the message.
Public Key Encryption
Public key methods require two unique keys per user; one called the public key, and the other called the private key.
Quantum Cryptography
Public key methods require two unique keys per user; one called the public key, and the other called the private key.
The private key is mathematically linked to the public key. While public keys are published, private keys are never exchanged and always kept secret.
Mathematical Basis of Public Key Algorithms
Factoring of large integers  RSA Algorithm
Discrete Log Problem  DSA Algorithm
Quantum Cryptography
 Method of a secure key exchange over an insecure channel based on the nature of photons
 Polarized photons are transmitted between sender and receiver to create a random a string of numbers, the quantum cryptographic key
 Perfect encryption for the 21st century
 Experimental stages
 Very secure
Modern Encryption Methods and Authentication Devices
 Cryptographic Accelerators
 Authentication Tokens
 Biometric/Recognition Methods
Type  Cryptographic Accelerator  Authentication Token  Biometric/ Recognition 
Definition  Coprocessor that calculates and handles the Random Number Generation  External device that interfaces with the device to grant access. 2 types: contact and NonContact  External device that measures human body factors to allow access 
Examples  PCI coprocessor
 Credit Card, RSA SecurID
 Fingerprint, Optical, Voice and Signature recognition

Image credits: Google Dictionary