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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 non-repudiation 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, chip-based 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 information-theoretically secure schemes that probably cannot be broken even with unlimited computing power—an example is a one-time 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 would-be 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

 

100-44 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 Cypherdiagram showing shift three alphabetic cypher D becomes A and E becomes B

 

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

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