Patent Document ID: 20120027206
Application ID: 13258165
Patent Flag: 0

Claim One:
1 : An information generation apparatus comprising: a random number generator adapted to generate a random number σ Y εZ q and a random number σ Yj εZ q corresponding to each element jεw(Y) of a set w(Y); a main information generator adapted to use the generated random number σ Y to calculate main information k Y that satisfies k Yj =σ Yj Σ iε{1,. .. , N-1}w(Y) Y i b i *+b N *; and a derivation information generator adapted to use the generated random number σ Yj to calculate derivation information k Yj that satisfies k Yj Σ iε{1,. .. , N-1}w(Y) Y i b i *+b j * for each element jεw(Y) of the set w(Y); where e is a non-degenerate, bilinear function that outputs one element of a cyclic group G T in response to inputs of N elements γ L (L=1,. .. , N) (N≧2) of a cyclic group G 1 and N elements γ L * (L=1,. .. , N) of a cyclic group G 2 ; b i εG 1 N (i=1,. .. , N) is an N-dimensional basis vector having N elements of the cyclic group G 1 as elements; b j *εG 2 N (j=1,. .. , N) is an N-dimensional basis vector having N elements of the cyclic group G 2 as elements; a function value obtained when each element of the basis vector b i εG 1 N (i=1,. .. , N) and each element of the basis vector b j *εG 2 N (j=1,. .. , N) are put into the bilinear function e is represented by g T τ·δ(i,j) εG T , using a Kronecker's delta function in which δ(i, j)=1 F when i=j and δ(i, j)=0 F when i≠j; 0 F is an additive unit element of a finite field F q ; 1 F is a multiplicative unit element of the finite field F q ; τ is an element of the finite field F q , other than 0 F ; and g T is a generator of the cyclic group G T ; and * indicates an indeterminate character, an index Y is Y=(Y 1 ,. .. , Y N-1 )εI=(F q ∪{*}) N-1 , the set w(Y) corresponds to the index Y, and w(Y)={i|Y i =*}.