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US 8,619,980 B2Granted
Information generation apparatus, method, program, and recording medium for deriving a decryption key from another decryption key
AssigneeNippon Telegraph and Telephone Corporation
InventorsKoutarou Suzuki, Ryo Nishimaki
Life of this patent
Estimating the term…
Abstract
Hierarchical cryptography expressed in a general semiordered structure other than a tree structure is implemented. In information generation, random numbers σv and (σvj)jεw(v)εZq are generated; main information kv=σvΣiε{1, . . . , N-1}\w(v)vibi*+bN* is calculated; and derivation information kvj=σvjΣiε{1, . . . , N-1}\w(v)vibi*+bj* is calculated for each jεw(v). In information derivation, random numbers σu and (σuj)jεw(u)εZq are generated; main information ku=σuΣiεw(v)\w(u)uikvi+kv is calculated; and derivation information kuj=σujΣiεw(v)\w(u)uikvi+kvj is calculated for each jεw(v).
Claims13
An information generation apparatus comprising:
- a processor;
- a random number generator, implemented by the processor, adapted to generate a random number σYεZq and a random number σYjεZq corresponding to each element jεw(Y) of a set w(Y);
- a main information generator, implemented by the processor, adapted to use the generated random number σY to calculate main information kY that satisfies kY=σYΣiε{1, . . . , N-1}\w(Y)Yibi*+bN*;
- and
- a derivation information generator, implemented by the processor, adapted to use the generated random number σYj to calculate derivation information kYj that satisfies kYj=σYjΣiε{1, . . . , N-1}\w(Y)Yibi*+bj* 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 GT in response to inputs of N elements γL (L=1, . . . , N) (N≧2) of a cyclic group G1 and N elements γL* (L=1, . . . , N) of a cyclic group G2;
- biεG1N (i=1, . . . , N) is an N-dimensional basis vector having N elements of the cyclic group G1 as elements;
- bj*εG2N (j=1, . . . , N) is an N-dimensional basis vector having N elements of the cyclic group G2 as elements;
- a function value obtained when each element of the basis vector biεG1N (i=1, . . . , N) and each element of the basis vector bj*εG2N (j=1, . . . , N) are put into the bilinear function e is represented by gTτ·δ(i,j)εGT, using a Kronecker's delta function in which δ(i, j)=1F when i=j and δ(i, j)=0F when i≠j;
- 0F is an additive unit element of a finite field Fq;
- 1F is a multiplicative unit element of the finite field Fq;
- τ is an element of the finite field Fq, other than 0F;
- and gT is a generator of the cyclic group GT;
- and
- * indicates an indeterminate character, an index Y is Y=(Y1, . . . , YN-1)εI=(Fq∪{*})N-1, the set w(Y) corresponds to the index Y, and w(Y)={i|Yi=*}.
12 more elements
An information generation apparatus comprising:
- a storage device adapted to store main information kv serving as main information kY or corresponding to an index v, derived from the main information kY and derivation information kYj, and derivation information kvj serving as the derivation information kYj or corresponding to the index v, derived from the derivation information kYj;
- a processor;
- a random number generator, implemented by the processor, adapted to generate a random number σuεZq;
- and
- a main information deriving unit, implemented by the processor, adapted to use the main information kv and derivation information kvi, both of which are read from the storage unit, and the generated random number σu to calculate main information ku corresponding to an index u, which satisfies ku=σuΣiεw(v)\w(u)uikvi+kv;
- where e is a non-degenerate, bilinear function that outputs one element of a cyclic group GT in response to inputs of N elements γL (L=1, . . . , N) (N≧2) of a cyclic group G1 and N elements γL* (L=1, . . . , N) of a cyclic group G2;
- biεG1N (i=1, . . . , N) is an N-dimensional basis vector having N elements of the cyclic group G1 as elements;
- bj*εG2N (j=1, . . . , N) is an N-dimensional basis vector having N elements of the cyclic group G2 as elements;
- a function value obtained when each element of the basis vector biεG1N (i=1, . . . , N) and each element of the basis vector bj*εG2N (j=1, . . . , N) are put into the bilinear function e is represented by gTτ·δ(i,j)εGT, using a Kronecker's delta function in which δ(i, j)=1F when i=j and δ(i, j)=0F when i≠j;
- 0F is an additive unit element of a finite field Fq;
- 1F is a multiplicative unit element of the finite field Fq;
- τ is an element of the finite field Fq, other than 0F;
- and gT is a generator of the cyclic group GT;
- and
- * indicates an indeterminate character;
- an index Y is Y=(Y1, . . . , YN-1)εI=(Fq∪{*})N-1;
- a set w(Y) corresponding to the index Y is w(Y)={i|Yi=*};
- σYεZq is a random number;
- σYiεZq is a random number corresponding to each element jεw(Y) of the set w(Y);
- the main information kY corresponds to the index Y and satisfies kY=σYΣiε{1, . . . , N-1}\w(Y)Yibi*+bN*;
- and the derivation information kYi corresponds to the index Y and satisfies kYj=σYjΣiε{1, . . . , N-1}\w(Y)Yibi*bj*;
- * indicates an indeterminate character;
- the index v is v=(v1, . . . , vN-1)εI=(Fq∪{*})N-1;
- the index u is u=(u1, . . . , uN-1)εI=(Fq∪{*})N-1;
- w(v) is a set corresponding to the index v and w(v)={i|vi=*};
- w(u) is a set corresponding to the index u and w(u)={i|ui=*};
- w(u)⊂w(v);
- and vi=ui(iε{1, . . . N−1}\w(v)).
25 more elements
An information generation apparatus comprising:
- a processor;
- a random number generator, implemented by the processor, adapted to generate a random number rYεZq;
- a first main information generator, implemented by the processor, adapted to use the generated random number rY to calculate first main information kY that satisfies kY=g2a(g3Πiε{1, . . . , N−1}\w(Y)hiYi)rY;
- a second main information generator, implemented by the processor, adapted to use the generated random number rY to calculate second main information grY;
- and
- a derivation information generator, implemented by the processor, adapted to use the generated random number rY to calculate derivation information kYj that satisfies kYj=hjrY for each element jεw(Y) of a set w(Y);
- where G and GT are cyclic groups having a prime number order q;
- g is a generator of the cyclic group G;
- the cyclic group G has a pairing function e:
- G×G→GT, which makes gT=e(g, g) a generator of the cyclic group GT;
- a is a random number selected at random from Zp;
- and g, g1=gaεG, and g2, g3, h1, . . . , hN-1εG randomly selected from the cyclic group G are made publicly available as public keys;
- and
- * indicates an indeterminate character;
- an index Y is Y=(Y1, . . . , YN-1)εI=(Fq∪{*})N-1;
- the set w(Y) corresponds to the index Y;
- and w(Y)={i|Yi=*}.
14 more elements
An information generation apparatus comprising:
- a processor;
- a random number generator, implemented by the processor, adapted to generate a random number ruεZq;
- a storage device adapted to store main information kv serving as main information KY or corresponding to an index v, derived from first main information kY and derivation information kYj, and derivation information kvj serving as derivation information kYj or corresponding to the index v, derived from the derivation information kYj;
- a first main information deriving unit, implemented by the processor, adapted to use the first main information kv and derivation information kvi, both of which are read from the storage device, to calculate first main information ku corresponding to an index u, which satisfies ku=kv(Πiεw(v)\w(u)kviui)(g3Πiε{1, . . . , N-1}\w(v)hiviΠiεw(v)\w(u)hiui)ru;
- and
- a second main information deriving unit, implemented by the processor, adapted to use the generated random number ru to calculate second main information gru;
- where G and GT are cyclic groups having a prime number order q;
- g is a generator of the cyclic group G;
- the cyclic group G has a pairing function e:
- G×G→GT, which makes gT=e(g, g) a generator of the cyclic group GT;
- a is a random number selected at random from Zp;
- and g, g1=gaεG, and g2, g3, h1, . . . , hN-1εG randomly selected from the cyclic group G are made publicly available as public keys;
- * indicates an indeterminate character;
- an index Y is Y=(Y1, . . . , YN-1)εI=(Fq∪{*})N-1;
- and a set w(Y) corresponding to the index Y is w(Y)={i|Y1=*};
- rYεZq is a random number;
- the first main information kY corresponds to the index Y and satisfies kY=g2a(g3(Πiε{1, . . . , N-1}\w(v)hiYi)rY;
- grY is second main information corresponding to the index Y;
- and the derivation information kYj corresponds to the index Y and satisfies kYj=hjrY;
- and
- * indicates an indeterminate character;
- the index v is v=(v1, . . . , vN-1)εI=(Fq∪{*})N-1;
- w(v) is a set corresponding to the index v and w(v)={i|vi=*};
- the index u is u=(u1, . . . , uN-1)ε=I(Fq∪{*})N-1;
- w(u) is a set corresponding to the index u and w(u)={i|ui=*};
- set w(u)⊂set w(v);
- and vi=ui(iε{1, . . . , N−1}\w(v)).
24 more elements
An information generation method, implemented by an information generation apparatus having a processor, comprising:
- generating, in a random number generator, a random number σYεZq and a random number σYjεZq corresponding to each element jεw(Y) of a set w(Y);
- using, in a main information generator, the generated random number σY to calculate main information kY that satisfies kY=σYΣiε{1, . . . , N-1}\w(Y)Yibi*+bN*;
- and
- using, in a derivation information generator, the generated random number σYj to calculate derivation information kYj that satisfies kYj=σYjΣiε{1, . . . , N-1}\w(Y)Yibi*+bj* 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 GT in response to inputs of N elements γL (L=1, . . . , N) (N≧2) of a cyclic group G1 and N elements γL* (L=1, . . . , N) of a cyclic group G2;
- biεG1N (i=1, . . . , N) is an N-dimensional basis vector having N elements of the cyclic group G1 as elements;
- bj*εG2N (j=1, . . . , N) is an N-dimensional basis vector having N elements of the cyclic group G2 as elements;
- a function value obtained when each element of the basis vector biεG1N (i=1, . . . , N) and each element of the basis vector bj*εG2N (j=1, . . . , N) are put into the bilinear function e is represented by gTτ·δ(i,j)εGT, using a Kronecker's delta function in which δ(i, j)=1F when i=j and δ(i, j)=0F when i≠j;
- 0F is an additive unit element of a finite field Fq;
- 1F is a multiplicative unit element of the finite field Fq;
- τ is an element of the finite field Fq, other than 0F;
- and gT is a generator of the cyclic group GT;
- and
- * indicates an indeterminate character, an index Y is Y=(Y1, . . . , YN-1)εI=(Fq∪{*})N-1, and the set w(Y) corresponds to the index Y and w(Y)={i|Yi=*}.
11 more elements
An information generation method, implemented by an information generation apparatus having a processor, comprising:
- generating, in a random number generator, a random number rYεZq;
- using, in a first main information generator, the generated random number rY to calculate first main information kY that satisfies kY=g2a(g3Πiε{1, . . . , N-1}\w(Y)hiYi)rY;
- using, in a second main information generator, the generated random number rY to calculate second main information grY;
- and
- using, in a derivation information generator, the generated random number rY to calculate derivation information kYj that satisfies kYj=hjrY for each element jεw(Y) of a set w(Y);
- where G and GT are cyclic groups having a prime number order q;
- g is a generator of the cyclic group G;
- the cyclic group G has a pairing function e:
- G×G→GT, which makes gT=e(g, g) a generator of the cyclic group GT;
- a is a random number selected at random from Zp;
- and g, g1=gaεG, and g2, g3, h1, . . . , hN-1εG randomly selected from the cyclic group G are made publicly available as public keys;
- and
- * indicates an indeterminate character;
- an index Y is Y=(Y1, . . . , YN-1)εI=(Fq∪{*})N-1;
- and the set w(Y) corresponds to the index Y and w(Y)={i|Yi=*}.
12 more elements
Dependencies are inferred from the claim text.