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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 novel method that makes use of traces to represent and calculate powers of elements of a subgroup of a finite field. It is based on the primitive underlying the very first public key cryptosystem, the Diffie-Hellman key agreement protocol.

From a security point of view, XTR is a traditional discrete logarithm system: For its security it relies on the difficulty of solving discrete logarithm related problems in the multiplicative group of a finite field. Some advantages of XTR are its fast key generation (much faster than RSA), small key sizes (much smaller than RSA, comparable with ECC for current security settings), and speed (overall comparable with ECC for current security settings).

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