Name

XTR

Description

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 GF(p^2) to represent elements of a subgroup of 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 of a relatively small subgroup of some prime order q of a subgroup of GF(p^6)^*. With the right choice of q, computing Discrete Logarithms in the group, generated by g, is, in general, as hard as it is in GF(p^6)^* and thus cryptographic applications of XTR use GF(p^2) arithmetics while achieving full GF(p^6) security leading to substan

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