Abstract

In Cryptography, there are two kinds of methods for encryption and decryption. They are symmetric cryptography and asymmetric cryptography. In symmetric cryptography, it uses a single key for encryption and decryption. In asymmetric cryptography, it uses both public key and private key for encryption and decryption. In MANET (mobile ad-hoc network) every node usually moves and has limited energy, so network link is not stable and has low bandwidth. Therefore it is very carefully to choose the cryptography for ad-hoc network or MANET. If the transaction is very important, for example online banking, can use an asymmetric algorithm. So Elliptic Curve Cryptography is right choice. For data and control traffic, the symmetric cryptography can be the good selection, especially stream ciphers are very comfortable. We use Elliptic Curve Cryptography (ECC) with its arithmetic operations on finite fields to build public - key cryptographic schemes consisting of: i) signature schemes; ii) encryption schemes; and iii) key agreement schemes. In key management, public key cryptography is used to distribute the secret keys used in other cryptographic algorithms (for example DES). For digital signatures, public key cryptography is used to authenticate the origin of data and protect the integrity of that data. Early public key systems are secure based on difficulty of factoring a large integer composed by two or more large prime integers. With Elliptic Curve based protocol, its security is based on assuming that is difficult to find the discrete logarithm of a random point on Elliptic Curve with respect to a publicly known base point. The size of EC determines the level of difficulty of the problem. If comparing to RSA, with the same level of security, RSA has to use larger public key, for example ECC of 256 bits public key is with the same level of security as 3072 bits public key RSA. To use RSA or Diffie-Hellman to protect 128-bit AES keys one should use 3072-bit parameters: three times the size in use throughout the Internet today. The equivalent key size for elliptic curves is only 256 bits.

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