Cryptographic Schemes
In this section it is explained how the concepts above using traces of elements can be applied to cryptography. In general, XTR can be used in any cryptosystem that relies on the (subgroup) Discrete Logarithm problem. Two important applications of XTR are the Diffie-Hellman key agreement and the ElGamal encryption. We will start first with Diffie-Hellman.
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“Science is a dynamic undertaking directed to lowering the degree of the empiricism involved in solving problems; or, if you prefer, science is a process of fabricating a web of interconnected concepts and conceptual schemes arising from experiments and observations and fruitful of further experiments and observations.”
—James Conant (1893–1978)