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**1 - 2**of**2**### On the security of the KMOV public key cryptosystem

- Advances in Cryptology— CRYPTO ’97, Lecture Notes in Computer Science
, 1997

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### A Discussion on Elliptic Curve Cryptography and its Application

"... Abstract- Cryptography is an important part of preventing private data from being stolen. Even if an attacker were to break into your computer or intercept your messages they still will not be able to read the data if it is protected by cryptography or encrypted. In addition to concealing the meanin ..."

Abstract
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Abstract- Cryptography is an important part of preventing private data from being stolen. Even if an attacker were to break into your computer or intercept your messages they still will not be able to read the data if it is protected by cryptography or encrypted. In addition to concealing the meaning of data, cryptography performs other critical security requirements for data including authentication, repudiation, confidentiality, and integrity. Cryptography comes from Greek words meaning “hidden writing”. Cryptography converts readable data or clear text into encoded data called cipher text. By definition cryptography is the science of hiding information so that unauthorized users cannot read it. It involves Encryption and decryption of messages. Encryption is the process of converting a Plain text into cipher text and decryption is the process of getting back the original Message from the encrypted text. The Crux of cryptography lies in the key involved and the secrecy of the keys used to Encrypt or decrypt. Another important factor is the key strength, i.e. the size of the Key so that it is difficult to perform a brute force on the plain and cipher text and retrieve the key. There have been various cryptographic algorithms suggested. Elliptic curve cryptography (ECC) is a kind of public key cryptosystem like RSA. But it differs from RSA in its quicker evolving capacity and by providing attractive and alternative way to researchers of cryptographic algorithm. The security level which is given by RSA can be provided even by smaller keys of ECC (for example, a 160 bit ECC has roughly the same security strength as 1024 bit RSA). In this paper, we will present some ECC algorithms and also gives mathematical explanations on the working of these algorithms.