Implementasi aritmatik field prima dengan bahasa c

Abstract

Cryptography is the science of keeping message secure. Cryptography involves encryption and decryption of messages. Encryption is the process of converting a plaintext into chipertext and decryption is the process of getting back the encrypted message. Cryptographic systems can be divided into two kinds: symmetric-key cryptography and asymmetric-key cryptography (publickey cryptography). The major advantage of symmetric-key cryptography is high efficiency, but it has a number of drawbacks like key distribution and the provision of non-repudiation. Public-key cryptography provides solution to the problems in symmetric-key cryptography. Unfortunately, public-key operations are significantly slower than symmetric-key operation. It is caused by using a big number in its operations. The biggest problem of the big number is how to compute it in constrained machines like computer. A computer’s hardware can only perform operations on integers smaller than the machine word-size W. If bigger numbers are needed, the programmer has to provide routines for representation and manipulation of big number. In this research, big number is representated with base 2 W. This base is efficient in memory-space. Arithmetic of big number is constrained in prime-field. The big number that is used in this arithmetic is up to 1024 bit. Operations of this arithmetic are addition, subtraction, multiplication, division, and exponentiation. The result of this research shows that operations of big number can be executed fast in 32-bit computer