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Cryptographic protocols depend on the hardness of some computational
problems for their security. Joux briefly summarized known relations
between assumptions related bilinear map in a sense that if one
problem can be solved easily, then another problem can be solved
within a polynomial time [6].
In this paper, we investigate additional relations between them.
Firstly, we show that the computational Diffie-Hellman assumption
implies the bilinear Diffie-Hellman assumption or the general
inversion assumption. Secondly, we show that a cryptographic useful
self-bilinear map does not exist. If a self-bilinear map exists, it
might be used as a building block for several cryptographic
applications such as a multilinear map. As a corollary, we show that
a fixed inversion of a bilinear map with homomorphic property is
impossible. Finally, we remark that a self-bilinear map proposed in
[7] is not essentially self-bilinear.
목차
등록된 정보가 없습니다.
참고문헌 (11)
참고문헌 신청
A. Joux / 2000 / A one round protocol for tripartite Diffie-Hellman / Algorithmic number theory (Leiden, 2000) : 385 ~ 393
A. Joux / 2002 / The Weil and Tate pairings as building blocks for public key cryptosystems / number theory (Sydney, 2002) : 20 ~ 32
A. Menezes / 1993 / Reducing elliptic curve logarithms to logarithms in a finite field / IEEE Trans. Inform. Theory 39 (5) : 1639 ~ 1646
D. Boneh / 2001 / Identity-based encryption from the Weil pairing / Advances in cryptology?CRYPTO 2001 (Santa Barbara, CA) : 213 ~ 229
D. Boneh / 2001 / Short signatures from the Weil pairing / Advances in cryptology?ASIACRYPT 2001 (Gold Coast) : 514 ~ 532
A. Joux / 2002 / The Weil and Tate pairings as building blocks for public key cryptosystems / number theory (Sydney, 2002) : 20 ~ 32
A. Menezes / 1993 / Reducing elliptic curve logarithms to logarithms in a finite field / IEEE Trans. Inform. Theory 39 (5) : 1639 ~ 1646
D. Boneh / 2001 / Identity-based encryption from the Weil pairing / Advances in cryptology?CRYPTO 2001 (Santa Barbara, CA) : 213 ~ 229
D. Boneh / 2001 / Short signatures from the Weil pairing / Advances in cryptology?ASIACRYPT 2001 (Gold Coast) : 514 ~ 532
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