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212 IndexForm class group . . . . . . . . . 146Form class semigroup . . . . . . . 146Picard group . . . . . see Class groupProper class semigroup . . . . 144, 169Class numberClass number . . . 104, 126, 144, 146Kronecker class number . 104, 126, 144,146Proper class number . . . . . . . 144Class polynomial . . . . . . . . . . 153, 154Hilbert class polynomial . . . . . 148Igusa class polynomial . . . . 182, 184CM abelian variety . . . . . . . . . 174, 175a-multiplication . . . . . . . . . . 178a-transform . . . . . . . . . . . . 178Classification up to isomorphism . 178Dual . . . . . . . . . . . . . . . . 176Polarization . . . . . . . . . . . . 177Principal . . . . . . . . . . . . 174, 179Simple . . . . . . . . . . . . . . . 174Type . . . . . . . . . . . . . . 174, 175CM algebra . . . . . . . . . . . . . . . 172CM field . . . . . . . . . . . . . . . . . 172CM method . . . . . . . . . . . . . 154, 156CM type . . . . . . . . . . . . . . . . 173Equivalence . . . . . . . . . . . . 173Primitive . . . . . . . . . . . . 173, 174Simple . . . . . . . . . . see PrimitiveType norm . . . . . . . . . . . . . 173Type trace . . . . . . . . . . . . . 173Type transfer . . . . . . . . . . . 180Complementary lattice . . . see Trace dualComplex Lie group . . . . . . . . . 142, 161Exponential map . . . . . . . . . 161Complex torus . . . . . . . . 140, 161, 175Dual torus . . . . . . . . . . . . . 165Eisenstein series . . . . . . . . . . 142Riemann conditions . . . . . . . . 163Weierstraß ℘-function . . . . . . . 142Computation of the Hilbert class polynomialComplex analytic method . . . . 152CRT method . . . . . . . . . . . . 153p-adic method . . . . . . . . . . . 152Computation of the Igusa class polynomialsComplex analytic method . . . . 184CRT method . . . . . . . . . . . . 184p-adic method . . . . . . . . . . . 184Cryptographic property of Boolean functions8Algebraic degree . . . . . . . . . 10, 97Algebraic immunity . . . . . . . . . 10Balancedness . . . . . . . . . . . . . . 9Bentness . . . . . . see Bent functionHyper-bentnesssee Hyper-bent functionNonlinearity . . . . . . . . . . . . . 11Resiliency . . . . . . . . . . . . 9, 10Semi-bentness see Semi-bent functionCyclotomic character . . . . . . . . . . 180Cyclotomic class . . . . . . . . . . . 22, 88Coset leader . . see Cyclotomic leaderCyclotomic leader . . . . . 88, 97, 117Equivalence . . . . . . . . . . . . . 22Cyclotomic coset . . . see Cyclotomic classCyclotomic polynomial . . . . . . . . . 156DDedekind η function . . . . . . . . . . 153Dedekind ring . . . . . . . . . . . . 143, 168Dickson polynomial . . . . . . . . 99, 113Dillon criterion . . . . . . . . . . . . . 110using elliptic curves . . . . . . . . 114Discriminant . . . . . . . . . . . . . . 156of a binary quadratic form . . . . 146of a number field . . . . . . . . . 145of a Weierstraß equation . . . 100, 140of an order . . . . . . . . . . . 104, 105Divisibility of Kloosterman sumsClassical approach . . . . . . . . . 119using elliptic curves . . . . . . . . 120Divisor . . . . . . . . . . . . . . . . . 134Algebraic equivalence . . . . . . . 164Ample . . . . . . . . . . . . . . . 164Degree . . . . . . . . . . . . . . . 134Group of . . . . . . . . . . . . . . 134Linear equivalence . . . . . . . 134, 164of a function . . . . . . . . . . . . 134Principal . . . . . . . . . . . . . . 134Support . . . . . . . . . . . . . . 134Double η quotient . . . . . . . . . . . 153EElliptic curve . . . . . . . . . . 99, 114, 161Addition law . . . . . . . . . . . . 100Bad reduction . . . . . . . . . 139, 149Canonical lift . . . . . . . . . . . 107Chord-and-tangent lawsee Addition lawCM curve . . . . . . . . . . . . . 154Discriminant . . . . . . . . . . 100, 140