基于新型秘密共享方法的高效RSA門(mén)限簽名方案
A New RSA Threshold Group Signature Scheme Based on Modified Shamirs Secret Sharing Solution
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摘要: 針對(duì)傳統(tǒng)的門(mén)限RSA簽名體制中需對(duì)剩余環(huán)Z(N)中元素求逆(而環(huán)中元素未必有逆)的問(wèn)題，該文首先提出一種改進(jìn)的Shamir秘密共享方法。 該方法通過(guò)在整數(shù)矩陣中的一系列運(yùn)算來(lái)恢復(fù)共享密鑰。由于其中涉及的參數(shù)均為整數(shù)，因此避免了傳統(tǒng)方案中由Lagrange插值公式產(chǎn)生的分?jǐn)?shù)而引起的環(huán)Z(N)中的求逆運(yùn)算。然后基于該改進(jìn)的秘密共享方法給出了一個(gè)新型的門(mén)限RSA Rivest Shanair Atleman簽名方案。由于該方案無(wú)須在任何代數(shù)結(jié)構(gòu)(比如Z(N))中對(duì)任何元素求逆，也無(wú)須進(jìn)行代數(shù)擴(kuò)張，因此在實(shí)際應(yīng)用中更為方便、有效。
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關(guān)鍵詞:
- 秘密共享;門(mén)限群簽名;RSA;子密鑰(密鑰影子);可信任中心
Abstract: In order to avoid computing elements inverses in the ring Z(N) since they may not exit, a new RSA threshold group signature scheme based on modified Shamirs secret sharing solution is proposed. Differing from the old schemes based on Lagrange interpolation solution in which fraction arithmetic operations leading to the computation of elements inverses in Z(N) should be handled, this new scheme reconstructs its group secret key through series of integer arithmetic operations in integral matrixes, by which it can efficiently avoid the computation of any elements inverse in any algebraic structure (such as Z(N)), and can further avoid algebraic extensions. Therefore, this new scheme is more efficient and convenient than the old ones. -
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