TAILIEUCHUNG - Public key cryptography applications algorithms and mathematical explanations

The paper discusses some public key algorithms such as DH, RSA, DSA, ECDH and ECDSA and also gives mathematical explanations on the working of these algorithms. The paper also gives a brief introduction to modular arithmetic, which is the core arithmetic of almost all public key algorithms. | Public Key Cryptography - Applications Algorithms and Mathematical Explanations Public Key Cryptography Applications Algorithms and Mathematical Explanations Anoop MS Tata Elxsi Ltd India anoopms@ Abstract The paper discusses public key cryptography and its use in applications such as Key Agreement Data Encryption and Digital Signature. The paper discusses some public key algorithms such as DH RSA DSA ECDH and ECDSA and also gives mathematical explanations on the working of these algorithms. The paper also gives a brief introduction to modular arithmetic which is the core arithmetic of almost all public key algorithms. 1. Introduction The data transferred from one system to another over public network can be protected by the method of encryption. On encryption the data is encrypted scrambled by any encryption algorithm using the key . Only the user having the access to the same key can decrypt de-scramble the encrypted data. This method is known as private key or symmetric key cryptography. There are several standard symmetric key algorithms defined. Examples are AES 3DES etc. These standard symmetric algorithms defined are proven to be highly secured and time tested. But the problem with these algorithms is the key exchange. The communicating parties require a shared secret key to be exchanged between them to have a secured communication. The security of the symmetric key algorithm depends on the secrecy of the key. Keys are typically hundreds of bits in length depending on the algorithm used. Since there may be number of intermediate points between the communicating parties through which the data passes these keys cannot exchanged online in a secured manner. In a large network where there are hundreds of system connected offline key exchange seems too difficult and even unrealistic. This is where public key cryptography comes to help. Using public key algorithm a shared secret can be established online between communicating parties with out the .

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