After a fine introduction to basic notions, he covers unique factorization, the Gaussian integers
, and Pell's equation, and moves on to algebraic number theory.
In later secondary years students may also study prime numbers as part of enrichment and extension of the curriculum in the area of number theory, or as a component of school-based assessment, for example exploration of Gaussian integers as part of work on complex numbers in advanced mathematics.
Clearly the natural numbers are Gaussian integers where a [member of] N and b = 0.
Mathematica includes an option for number theoretic functionality to apply for Gaussian integers, for example:
It describe the elgamal public-key cryptosystem and the diffehellman key exchange and the then extends these cryptosystem over the domain of gaussian integers.
In this paper, we extended the computational procedures behind the elgamal algorithm using arithmetics module gaussian integers.
p] and then we will modify these cryptosystems to the domain of gaussian integers.
The alogrithm here is similar to the algorithm in classical case but we choose the prime [beta] in this case from the domain of gaussian integers.
Next we give the algorithm of the extended elgamal public-key cryptosystem in the domain of gaussian integers.
El gamal public key cryptosystem in the domain of gaussian integers.
To be able to generate a common private key using Diffie-Hellman key exchange over the domain of gaussian integers, Ali and Basem must follow these steps:
2 ElGamal public-key cryptosystem in the domain of gaussian integers [i]