Intex 18ft x 52in Ultra XTR Round Frame Above Ground Pool Set and Cleaning Kit

Above may refer to:

• Above (artist), Tavar Zawacki (born 1981), contemporary urban artist
• Above (magazine), an American environmental magazine 2009–2010
• Above (Mad Season album), 1995
• Above (Pillar album), 2000
• Above (Samael album), 2009
• "Above", a song by Finger Eleven from Tip

Cleaning is the process of removing unwanted substances, such as dirt, infectious agents, and other impurities, from an object or environment. Cleaning is often performed for aesthetic, hygienic, functional, safety, or environmental protection purposes. Cleaning occurs in many different contexts, and uses many different methods. Several occupations are devoted to cleaning.

A frame is often a structural system that supports other components of a physical construction and/or steel frame that limits the construction's extent.

Frame and FRAME may also refer to:

X, or x, is the twenty-fourth letter of the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is ex (pronounced ), plural exes.

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 ${\displaystyle GF(p^{2})}$ to represent elements of a subgroup of ${\displaystyle GF(p^{6})^{*}}$.

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