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Modern Cryptography does not depend on the secrecy of its algorithms, however cryptographic algorithms use keys to protect information. Thus, key management is an important issue and needs to be protected by access control mechanisms on computer systems. Public key cryptography based on elliptic curves is widely used because it presents higher security per key bit. Additionally, the Elliptic Curve Cryptosystems (ECCs) are systems of public key, which can be used in applications where the computation resources are limited such as smart cards and cellular telephones. The algorithms used for Elliptic Curve Cryptosystems can be divided hierarchically into three levels; arithmetic level, group operation level and encryption level.
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