Tighter Reduction for Lattice-Based Multisignature
Tighter Reduction for Lattice-Based Multisignature
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DOI：
10.1587/transfun.2020eap1131
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Masayuki Fukumitsu;Shingo Hasegawa
中科院分区：
文献类型：
--
作者：
Masayuki Fukumitsu;Shingo Hasegawa
摘要多重签名使多个用户能够交互地对消息进行签名。许多多重签名的实例被提出，然而，他们中的大多数是量子不安全的，因为这些都是基于整数分解假设或离散对数假设。虽然存在一些基于格问题的构造，它们被认为是量子安全的，但它们的安全性约简是松散的.本文将ElBansarkhani和Sturm提出的多重签名方案与Abdalla，Fouque，Lyubashevsky和Tibouchi提出的基于格的签名方案相结合，改进了基于格的多重签名方案的安全性约简，并将其与Ring-LWE的安全性约简相结合（RingLearningwithErrors）假设，我们的结果表明标准签名方案的证明技术可以应用于多签名方案，第二个结果是针对Damgård，Orlandi，Takahashi和Tibouchi提出的基于格的多重签名方案的安全性证明问题，我们采用一种新的密码学方法--拒绝环LWE假设，来完成安全性证明。
SUMMARY Multisignaturesenablemultipleuserstosignamessagein-teractively. Many instantiations are proposed for multisignatures, however, most of them are quantum-insecure, because these are based on the integer factoring assumption or the discrete logarithm assumption. Although there existsomeconstructionsbasedonthelatticeproblems,whicharebelievedtobequantum-secure,theirsecurityreductionsareloose.Inthispaper,weaim toimprovethesecurityreductionoflattice-basedmultisignatureschemesconcerningtightness.Ourbasicstrategyiscombiningthemultisignature schemeproposedbyElBansarkhaniandSturmwiththelattice-basedsig-natureschemebyAbdalla,Fouque,Lyubashevsky,andTibouchiwhichhas atightsecurityreductionfromtheRing-LWE(RingLearningwithErrors)assumption.Ourresultshowsthatprooftechniquesforstandardsignature schemescanbeappliedtomultisignatureschemes,thenwecanimprovethepolynomiallossfactorconcerningtheRing-LWEassumption.Oursecond resultistoaddresstheproblemofsecurityproofsofexistinglattice-basedmultisignatureschemespointedoutbyDamgård,Orlandi,Takahashi,and Tibouchi.WeemployanewcryptographicassumptioncalledtheRejected-Ring-LWEassumption,tocompletethesecurityproof.