基于误差受限的身份认证方案的码基签名新途径
A New Path to Code-based Signatures via Identification Schemes with Restricted Errors
摘要：
在本文中，我们介绍了一个变种的综合征解码问题（SDP），我们称之为限制SDP（R-SDP），其中搜索向量的条目定义在一个子集的基础有限域。我们证明了NP-完全的R-SDP，通过减少从经典的SDP，并描述算法，解决这样的新问题。我们研究了在这种新的解码角度下的随机码的性质，在传统的编码理论的结果的时尚，并评估解决一个随机R-SDP实例的复杂性。作为一个具体的应用，我们描述了如何零知识识别（ZK-ID）计划的基础上SDP可以调整到依赖于R-SDP，并表明，这导致紧凑的公钥以及显着降低通信成本。因此，这些方案提供了一个改进的基础上建设的代码为基础的数字签名计划来自识别计划，通过著名的Fiat-Shamir变换。
英文摘要：
In this paper we introduce a variant of the Syndrome Decoding Problem (SDP), that we call Restricted SDP (R-SDP), in which the entries of the searched vector are defined over a subset of the underlying finite field. We prove the NP-completeness of R-SDP, via a reduction from the classical SDP, and describe algorithms which solve such new problem. We study the properties of random codes under this new decoding perspective, in the fashion of traditional coding theory results, and assess the complexity of solving a random R-SDP instance. As a concrete application, we describe how Zero-Knowledge Identification (ZK-ID) schemes based on SDP can be tweaked to rely on R-SDP, and show that this leads to compact public keys as well as significantly reduced communication costs. Thus, these schemes offer an improved basis for the construction of code-based digital signature schemes derived from identification schemes through the well-know Fiat-Shamir transformation.
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