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Pairing-based cryptography is a relatively young§field revolving around a family of functions known as§pairings, or bilinear maps, whose remarkable§properties allow the creation of novel§cryptosystems that are otherwise difficult or§impossible to construct. This book begins§by giving abstract definitions of pairings and§related hardness problems, and showing how they are§used in cryptography. Later chapters discuss methods§for finding elliptic curves yielding suitable§pairings, along with algorithms for computing on§them. The final chapters describe vital§optimizations. Aside from low-level arithmetic, this§text quotes algorithms unlikely to be taught in a§basic course in abstract algebra, enabling a§mathematically inclined programmer to implement§pairings without referring to any other sources.
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