Elliptical curve cryptography (ECC)

[seminar class]

PRESENTED BY,
Ayesha Farhin

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Cryptography considered as a branch of both mathematics and computer science.
Affiliated closely with information theory, computer security, and engineering.
Definitions:
 Cryptography comes from the Greek words Kryptos, meaning hidden, and Graphen, meaning to write.
 Thus Cryptography is the study of secret (crypto-) writing (-graphy)
 Cryptography deals with all aspects of secure messaging, authentication, digital signatures, electronic money, and other applications.
 The practitioner of Cryptography is called Cryptographer
Cryptography Through History
 Cryptography has a history of at least 4000 years.
 Ancient Egyptians enciphered some of their hieroglyphic writing on monuments.
 Ancient Hebrews enciphered certain words in the scriptures.
 2000 years ago Julius Caesar used a simple substitution cipher, now known as the Caesar cipher.
 Roger Bacon in the middle ages described several methods in 1200s.
 Geoffrey Chaucer included several ciphers in his works (e.g. Canterbury Tales).
 Leon Alberti devised a cipher wheel, and described the principles of frequency analysis in the 1460s.
 Blaise de Vigenère published a book on cryptology in 1585, & described the polyalphabetic substitution cipher.
 Increasing use, especially in diplomacy & war over centuries.
Areas of Study
Computer Security:
Cryptanalysis, Cryptology, Cryptography
Terminologies:
Encryption
Decryption
Plaintext
Cipher Text
Cryptanalaysis
 The study of principles and methods of transforming an unintelligible message back into an intelligible message without knowledge of the key is called Cryptanalysis.
 Also called “code breaking” sometimes.
 Practitioners of cryptanalysis are cryptanalysts.
Cryptology
 Cryptology is the branch of mathematics that studies the mathematical foundations of cryptographic methods.
 Cryptology is actually the study of codes and ciphers.
 Cryptology = both cryptography and cryptanalysis
Definitions:
 In cryptographic terminology, the message is called plaintext or cleartext.
 Encoding the contents of the message in such a way that hides its contents from outsiders is called encryption.
 A method of encryption and decryption is called a cipher - The name cipher originates from the Hebrew word "Saphar," meaning "to number.”
 The encrypted message is called the ciphertext.
 The process of retrieving the plaintext from the ciphertext is called decryption.
 Encryption and decryption usually make use of a key, and the coding method is such that decryption can be performed only by knowing the proper key.
The Key
 All modern algorithms use a key to control encryption and decryption; a message can be decrypted only if the key matches the encryption key.
 The key used for decryption can be different from the encryption key, but for most algorithms they are the same.