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This innovative technology can produce smaller, faster and efficient cryptographic keys using the break through technique of elliptic curve equation rather than employing the traditional method of producing the key as the product of very large prime numbers. Although ECC can be used in collaboration with other public key encryption methods like the RSA, and Diffie-Hellman, it gains upper hand over the other encryption methods in the level of security it offers. A 164-bit ECC key can provide with an equivalent amount of security that a 1024-bit RSA key can give.
Apart from the smaller key size, which leads to faster processing along with the higher level of security, ECC consumes only less power, as well as saves on the memory and the bandwidth, that has today made ECC an attractive public-key cryptosystem for mobile/wireless environments. Developed by Certicom, a mobile e-business security provider and licensed by Hifn, a manufacturer of integrated circuitry and network security products today many manufacturers, including 3COM, Cylink, Motorola, Pitney Bowes, Siemens, TRW and VeriFone have today incorporated support for ECC in their products, welcoming the new era in public key encryption technique.
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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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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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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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[attachment=5941]
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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