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Modular lattice signatures, revisited

机译:模块化格子签名,重新审视

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In this paper we revisit the modular lattice signature scheme and its efficient instantiation known as pqNTRUSign. First, we show that a modular lattice signature scheme can be based on a standard lattice problem. The fundamental problem that needs to be solved by the signer or a potential forger is recovering a lattice vector with a restricted norm, given the least significant bits. We show that this problem is equivalent to the short integer solution (SIS) problem over the corresponding lattice. In addition, we show that by replacing the uniform sampling in pqNTRUSign with a bimodal Gaussian sampling, we can further reduce the size of a signature. An important new contribution, enabled by this Gaussian sampling version of pqNTRUSign, is that we can now perform batch verification of messages signed by the same public key, which allows the verifier to check approximately 24 signatures in a single verification process.
机译:在本文中,我们将回顾模块化的格架签名方案及其有效的实例化,称为pqNTRUSign。首先,我们证明了模块化的格子签名方案可以基于标准格子问题。给定最低有效位,签名者或潜在伪造者需要解决的基本问题是恢复具有受限范数的晶格向量。我们表明,该问题等效于相应晶格上的短整数解决方案(SIS)问题。另外,我们显示出通过用双峰高斯采样替换pqNTRUSign中的均匀采样,我们可以进一步减小签名的大小。由pqNTRUSign的高斯采样版本实现的一项重要的新贡献是,我们现在可以对由同一公钥签名的消息执行批量验证,这使验证者可以在单个验证过程中检查大约24个签名。

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