本文選題：秘密共享 + 多秘密�。� 參考：《長(zhǎng)沙理工大學(xué)》2014年碩士論文

【摘要】：秘密共享是一種用于分發(fā)、保存和恢復(fù)秘密信息的方法。秘密共享體制的提出為解決密鑰管理問題提供了非常有效的途徑,已成為了現(xiàn)代密碼學(xué)和信息安全研究領(lǐng)域的一個(gè)重要分支�？沈�(yàn)證秘密共享方案是一種能檢測(cè)出秘密分發(fā)者和參與者之間的欺騙行為的秘密共享方案�？晒_驗(yàn)證秘密共享是對(duì)可驗(yàn)證秘密共享的改進(jìn),方案中任何驗(yàn)證者都能公開地檢驗(yàn)秘密份額的正確性�？沈�(yàn)證多秘密共享方案不但能檢測(cè)分發(fā)者和參與者的欺騙,而且能同時(shí)共享多個(gè)秘密。本文主要從秘密份額的可公開驗(yàn)證和定期更新這兩個(gè)方面對(duì)可驗(yàn)證多秘密共享進(jìn)行了深入研究,研究成果如下：研究了基于雙線性對(duì)的秘密共享方案的可公開驗(yàn)證性問題,并結(jié)合Hermite插值多項(xiàng)式構(gòu)造了一個(gè)雙線性對(duì)上的可公開驗(yàn)證多秘密共享方案。該方案由Hermite插值法重構(gòu)秘密多項(xiàng)式,突破了傳統(tǒng)公開可驗(yàn)證秘密共享方案由拉格朗日插值多項(xiàng)式或中國(guó)剩余定理來構(gòu)造的局限性,而且在一次秘密共享過程中多個(gè)秘密可以同時(shí)被重構(gòu)。方案的安全性是基于橢圓曲線離散對(duì)數(shù)問題和雙線性Diffie-Hellman困難問題。針對(duì)現(xiàn)有多秘密共享方案不能夠同時(shí)滿足秘密份額的公開驗(yàn)證和定期更新的問題,提出了一種秘密份額可更新的可公開驗(yàn)證多秘密共享方案。該方案利用單向散列鏈的安全特性構(gòu)造更新多項(xiàng)式,從而實(shí)現(xiàn)秘密份額的定期更新。同時(shí),在秘密分發(fā)和更新階段公開一些驗(yàn)證信息,驗(yàn)證者能夠根據(jù)這些公開信息來驗(yàn)證秘密份額和更新份額的有效性,以便于及時(shí)檢測(cè)出某個(gè)或某些成員的惡意欺騙行為。本文對(duì)以上兩個(gè)方案的正確性、安全性和性能均給出了詳細(xì)的分析與對(duì)比。分析結(jié)果表明,本文提出的方案是正確可行的,并且具有較好的安全性和實(shí)用性。
[Abstract]:Secret sharing is a method for distributing, preserving, and restoring secret information. The secret sharing system provides a very effective way to solve the problem of key management and has become an important branch of modern cryptography and information security research field. Verifiable secret sharing scheme is a secret sharing scheme which can detect the cheating behavior between secret distributors and participants. Publicly verifiable secret sharing is an improvement on verifiable secret sharing. Any verifier in the scheme can openly verify the correctness of secret share. The verifiable multi-secret sharing scheme not only detects the spoofing of distributors and participants, but also shares multiple secrets at the same time. In this paper, we mainly study the verifiable multi-secret sharing from the aspects of publicly verifiable secret share and periodic update. The research results are as follows: the open verifiability of secret sharing scheme based on bilinear pairings is studied. A publicly verifiable multi-secret sharing scheme over bilinear pairs is constructed by using Hermite interpolation polynomials. In this scheme, the secret polynomial is reconstructed by Hermite interpolation method, which breaks through the limitation of the traditional publicly verifiable secret sharing scheme constructed by Lagrange interpolation polynomial or Chinese remainder theorem. Moreover, in a secret sharing process, multiple secrets can be reconstructed at the same time. The security of the scheme is based on the elliptic curve discrete logarithm problem and bilinear Diffie-Hellman problem. In order to solve the problem that the existing multi-secret sharing schemes can not satisfy both the public verification and periodic updating of secret share, a publicly verifiable multi-secret sharing scheme with updatable secret share is proposed. The scheme uses the security characteristics of the one-way hash chain to construct update polynomials, so that the secret share can be updated periodically. At the same time, some verification information is disclosed in the secret distribution and update stage, according to which the verifier can verify the validity of secret share and update share, so as to detect the malicious cheating of one or some members in time. In this paper, the correctness, security and performance of the two schemes are analyzed and compared in detail. The results show that the proposed scheme is correct and feasible, and has good safety and practicability.
【學(xué)位授予單位】：長(zhǎng)沙理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：TN918.4
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本文編號(hào)：1929560