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ECC is a public key encryption technique based on elliptic curve theory. ECC can be used to create faster, smaller and more efficient cryptographic keys. It generates keys through the properties of the elliptic curve equation rather than the traditional method of generation, as the product of very large prime numbers. This technology can be used in conjunction with most of the public key encryption methods such as RSA and Diffie-Hellman.

ECC can yield a level of security with a 164-bit key compared with other systems that require a 1,024-bit key. Since ECC provides an equivalent security at a lower computing power and battery resource usage, it is widely used for mobile applications. ECC was developed by Certicom, a mobile e-business security provider and was recently licensed by Hifn, a manufacturer of integrated circuitry and network security products. Many manufacturers, including 3COM, Cylink, Motorola, Pitney Bowes, Siemens, TRW and VeriFone have incorporated support for ECC in their products .

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Elliptical Curve Cryptography

Abstract

Elliptical curve cryptography (ECC) is a public key encryption technique based on elliptic curve theory that can be used to create faster, smaller, and more efficient cryptographic keys. ECC generates keys through the properties of the elliptic curve equation instead of the traditional method of generation as the product of very large prime numbers. The technology can be used in conjunction with most public key encryption methods, such as RSA, and Diffie-Hellman. ECC can yield a level of security with a 164-bit key that other systems require a 1,024-bit key to achieve. Because ECC helps to establish equivalent security with lower computing power and battery resource usage, it is becoming widely used for mobile applications. ECC was developed by Certicom, a mobile e-business security provider, and was recently licensed by Hifn, a manufacturer of integrated circuitry and network security products. Many manufacturers, including 3COM, Cylink, Motorola, Pitney Bowes, Siemens, TRW, and VeriFone have included support for ECC in their products.

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Cryptography
CONTENTS

Secrecy

Ciphers

Secret Key Cryptography

Key Exchange

Public Key Cryptography

Digital Signatures

Internet applications

Secrecy
Scenario: Alice wants to send a message (plaintext p) to Bob. The communication channel is insecure and can be eavesdropped by Trudy. If Alice and Bob have previously agreed on an encryption scheme (cipher), the message can be sent encrypted (ciphertext c)

Issues:

What is a good cipher?

What is the complexity of encrypting/decrypting?

What is the size of the ciphertext, relative to the plaintext?

If Alice and Bob have never interacted before, how can they agree on a cipher?

Traditional Cryptography
Ciphers were already studied in ancient times

Caesar’s cipher:

replace a with d

replace b with e

...

replace z with c

A more general monoalphabetic substitution cipher maps each letter to some other letter.

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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.