{"title":"Overfull: Too Large Aggregate Signatures Based on Lattices","authors":"Katharina Boudgoust, Adeline Roux-Langlois","doi":"10.1093/comjnl/bxad013","DOIUrl":null,"url":null,"abstract":"Abstract The Fiat-Shamir with Aborts paradigm of Lyubashevsky has given rise to efficient lattice-based signature schemes. One popular implementation is Dilithium, which has been selected for standardization by the US National Institute of Standards and Technology (NIST). Informally, it can be seen as a lattice analog of the well-known discrete-logarithm-based Schnorr signature. An interesting research question is whether it is possible to combine several unrelated signatures, issued from different signing parties on different messages, into one single aggregated signature. Of course, its size should be significantly smaller than the trivial concatenation of all signatures. Ideally, the aggregation can be done offline by a third party, called public aggregation. Previous works have shown that it is possible to half-aggregate Schnorr signatures, but it was left open if the underlying techniques can be adapted to the lattice setting. In this work, we show that, indeed, we can use similar strategies to obtain a signature scheme allowing for public aggregation whose hardness is proven assuming the intractability of well-studied problems on module lattices. Unfortunately, our scheme produces aggregated signatures that are larger than the trivial solution of concatenating. This is due to peculiarities that seem inherent to lattice-based cryptography. Its motivation is thus mainly pedagogical.","PeriodicalId":50641,"journal":{"name":"Computer Journal","volume":null,"pages":null},"PeriodicalIF":1.5000,"publicationDate":"2023-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computer Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1093/comjnl/bxad013","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, HARDWARE & ARCHITECTURE","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract The Fiat-Shamir with Aborts paradigm of Lyubashevsky has given rise to efficient lattice-based signature schemes. One popular implementation is Dilithium, which has been selected for standardization by the US National Institute of Standards and Technology (NIST). Informally, it can be seen as a lattice analog of the well-known discrete-logarithm-based Schnorr signature. An interesting research question is whether it is possible to combine several unrelated signatures, issued from different signing parties on different messages, into one single aggregated signature. Of course, its size should be significantly smaller than the trivial concatenation of all signatures. Ideally, the aggregation can be done offline by a third party, called public aggregation. Previous works have shown that it is possible to half-aggregate Schnorr signatures, but it was left open if the underlying techniques can be adapted to the lattice setting. In this work, we show that, indeed, we can use similar strategies to obtain a signature scheme allowing for public aggregation whose hardness is proven assuming the intractability of well-studied problems on module lattices. Unfortunately, our scheme produces aggregated signatures that are larger than the trivial solution of concatenating. This is due to peculiarities that seem inherent to lattice-based cryptography. Its motivation is thus mainly pedagogical.
Lyubashevsky的Fiat-Shamir with Aborts范式提出了高效的基于格的签名方案。一种流行的实现是二锂,它已被美国国家标准与技术研究所(NIST)选择用于标准化。非正式地,它可以被看作是众所周知的基于离散对数的Schnorr签名的晶格模拟。一个有趣的研究问题是,是否有可能将不同签名方在不同消息上发布的几个不相关的签名合并为一个聚合签名。当然,它的大小应该明显小于所有签名的简单连接。理想情况下,聚合可以由第三方离线完成,称为公共聚合。先前的研究已经表明,Schnorr特征有可能半聚合,但如果基础技术可以适应晶格设置,那么它仍然是开放的。在这项工作中,我们表明,我们确实可以使用类似的策略来获得一个允许公共聚合的签名方案,其硬度被证明是假设在模格上研究得很好的问题的难解性。不幸的是,我们的方案产生的聚合签名比简单的连接解决方案要大。这是由于基于格的密码学所固有的特性。因此,其动机主要是教学性的。
期刊介绍:
The Computer Journal is one of the longest-established journals serving all branches of the academic computer science community. It is currently published in four sections.