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xtr

In cryptography, XTR is an algorithm for public-key encryption. XTR stands for 'ECSTR', which is an abbreviation for Efficient and Compact Subgroup Trace Representation. It is a method to represent elements of a subgroup of a multiplicative group of a finite field. To do so, it uses the trace over G F ( p 2 ) {\displaystyle GF(p^{2})} to represent elements of a subgroup of G F ( p 6 ) ∗ {\displaystyle GF(p^{6})^{*}} . From a security point of view, XTR relies on the difficulty of solving Discrete Logarithm related problems in the full multiplicative group of a finite field. Unlike many cryptographic protocols that are based on the generator of the full multiplicative group of a finite field, XTR uses the generator g {\displaystyle g} of a relatively small subgroup of some prime order q {\displaystyle q} of a subgroup of G F ( p 6 ) ∗ {\displaystyle GF(p^{6})^{*}} . With the right choice of q {\displaystyle q} , computing Discrete Logarithms in the group, generated by g {\displaystyle g} , is, in general, as hard as it is in G F ( p 6 ) ∗ {\displaystyle GF(p^{6})^{*}} and thus cryptographic applications of XTR use G F ( p 2 ) {\displaystyle GF(p^{2})} arithmetics while achieving full G F ( p 6 ) {\displaystyle GF(p^{6})} security leading to substantial savings both in communication and computational overhead without compromising security. Some other advantages of XTR are its fast key generation, small key sizes and speed.

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