##### Wiktionary

**xtr**

abbr. (context text messaging English) extra (any sense)

##### Wikipedia

**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*) to represent elements of a subgroup of *G**F*(*p*).

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 *G**F*(*p*). With the right choice of *q*, computing Discrete Logarithms in the group, generated by *g*, is, in general, as hard as it is in *G**F*(*p*) and thus cryptographic applications of XTR use *G**F*(*p*) arithmetics while achieving full *G**F*(*p*) 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.