We propose a novel digital signature cryptosystem that exploits the concept of the brute-force problem. To ensure the security of the cryptosystem, we employed several mechanisms: sharing a common secret for factorable permutations, associating permutations with the message being signed, and confirming knowledge of the shared secret using a zero-knowledge proof. We developed a secret-sharing theory based on homomorphic matrix transformations for factorized permutations. The inverse matrix transformation for computing the shared secret is determined by secret parameters, which results in incompletely defined functionality and gives rise to a brute-force cryptanalysis problem. Randomization of session keys using a message hash and random parameters guarantees the uniqueness of each signature, even for identical messages. We employed a zero-knowledge authentication protocol to confirm knowledge of the shared secret, thereby protecting the verifier against unauthorized signature imposition. The LINEture cryptosystem is built on linear matrix algebra and does not rely on a computationally hard problem. High security is achieved through the appropriate selection of matrix transformation dimensions. Matrix computations potentially offer low operational costs for signature generation and verification.

翻译：我们提出了一种新颖的数字签名密码系统，该系统利用了暴力破解问题的概念。为确保密码系统的安全性，我们采用了多种机制：为可分解置换共享一个公共秘密、将置换与待签名消息相关联，以及使用零知识证明来确认对共享秘密的知晓。我们为分解置换开发了一种基于同态矩阵变换的秘密共享理论。用于计算共享秘密的逆矩阵变换由秘密参数决定，这导致了功能的不完全定义，并由此产生了一个暴力密码分析问题。利用消息哈希和随机参数对会话密钥进行随机化，保证了每个签名的唯一性，即使对于相同的消息也是如此。我们采用了一种零知识认证协议来确认对共享秘密的知晓，从而保护验证者免受未经授权的签名强加。LINEture密码系统建立在线性矩阵代数基础之上，不依赖于计算困难问题。通过适当选择矩阵变换的维度可以实现高安全性。矩阵计算可能为签名生成和验证提供较低的操作成本。