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Boneh–Franklin scheme
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Boneh–Franklin scheme : ウィキペディア英語版
Boneh–Franklin scheme
The Boneh–Franklin scheme is an identity-based encryption system proposed by Dan Boneh and Matthew K. Franklin in 2001.〔Dan Boneh, Matthew K. Franklin, "Identity-Based Encryption from the Weil Pairing", ''Advances in Cryptology - Proceedings of CRYPTO 2001'' (2001)〕 This article refers to the protocol version called BasicIdent. It is an application of pairings (Weil pairing) over elliptic curves and finite fields.
==Groups and parameters==
As the scheme bases upon pairings, all computations are performed in two groups, \textstyle G_1 and \textstyle G_2:
For \textstyle G_1, let \textstyle p be prime, \textstyle p \equiv 2 \mod 3 and consider the elliptic curve \textstyle E: y^2 = x^3 + 1 over \textstyle \mathbb/p\mathbb. Note that this curve is not singular as \textstyle 4a^3+27b^2 = 27 = 3^3 only equals \textstyle 0 for the case \textstyle p = 3 which is excluded by the additional constraint.
Let \textstyle q > 3 be a prime factor of \textstyle p + 1 (which is the order of \textstyle E) and find a point \textstyle P \in E of order \textstyle q. \textstyle G_1 is the set of points generated by \textstyle P: \textstyle \left\
\textstyle G_2 is the subgroup of order \textstyle q of \textstyle GF\left(p^2\right)^
*. We do not need to construct this group explicitly (this is done by the pairing) and thus don't have to find a generator.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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