Fundamentals of XTR
XTR uses a subgroup, commonly referred to as XTR subgroup or just XTR group, of a subgroup called XTR supergroup, of the multiplicative group of a finite field with elements. The XTR supergroup is of order, where p is a prime such that a sufficiently large prime q divides . The XTR subgroup has now order q and is, as a subgroup of, a cyclic group with generator g. The following three paragraphs will describe how elements of the XTR supergroup can be represented using an element of instead of an element of and how arithmetic operations take place in instead of in .
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