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Reference.org
Tate pairing
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<p>In mathematics, Tate pairing is any of several closely related <a href="/facts/Pairing-based_cryptography/vpk8ygca">bilinear pairings</a> involving <a href="/facts/Elliptic_curve/60jvaHSA">elliptic curves</a> or <a href="/facts/Abelian_varieties/dGSDVruG">abelian varieties</a>, usually over <a href="/facts/Local_field/vqIgPIX3">local</a> or <a href="/facts/Finite_field/UkMGJo3m">finite fields</a>, based on the <a href="/facts/Tate_duality/hQwrbFm1">Tate duality</a> pairings introduced by <a href="/facts/John_Tate_(mathematician)/nBntLCG0">Tate</a> (1958, 1963) and extended by Lichtenbaum (1969). Rück & Frey (1994) applied the Tate pairing over finite fields to cryptography. </p>