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Let G be an additive group generated by an element G of prime order r. The discrete logarithm problem with auxiliary input (DLPwAI) is a problem to find α on inputs G, αG, αdG ∈ G for a positive integer d dividing r-1. The infeasibility of DLPwAI ensures the security of some pairing-based cryptographic schemes. In 2006, Cheon proposed an algorithm for solving DLPwAI which works better than conventional algorithms. In this paper, we report our experimental results of Cheon's algorithm on a pairing-friendly elliptic curve defined over GF(3 127). Moreover, based on our experimental results, we estimate the required cost of Cheon's algorithm to solve DLPwAI on some pairing-friendly elliptic curves over a finite field of characteristic 3. Our estimation implies that DLPwAI on a part of pairing-friendly curves can be solved at reasonable cost when the optimal parameter d is chosen.
Let G be an additive group generated by an element G of prime order r. The discrete logarithm problem with auxiliary input (DLPwAI) is a problem to find α on inputs G, αG, αdG ∈ G for a positive integer d dividing r-1. The infeasibility of DLPwAI ensures the security of some pairing-based cryptographic schemes. In 2006, Cheon proposed an algorithm for solving DLPwAI which works better than conventional algorithms. In this paper, we report our experimental results of Cheon's algorithm on a pairing-friendly elliptic curve defined over GF(3 127). Moreover, based on our experimental results, we estimate the required cost of Cheon's algorithm to solve DLPwAI on some pairing-friendly elliptic curves over a finite field of characteristic 3. Our estimation implies that DLPwAI on a part of pairing-friendly curves can be solved at reasonable cost when the optimal parameter d is chosen.
収録刊行物
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- 情報処理学会論文誌
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情報処理学会論文誌 52 (9), 2652-2661, 2011-09-15
東京 : 情報処理学会
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詳細情報 詳細情報について
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- CRID
- 1050564287854094720
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- NII論文ID
- 110008608828
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- NII書誌ID
- AN00116647
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- ISSN
- 18827764
- 18827837
- 03875806
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- NDL書誌ID
- 024140236
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- 本文言語コード
- en
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- 資料種別
- journal article
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- データソース種別
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- IRDB
- NDL
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