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A New Analysis of the McEliece Cryptosystem Based on QC-LDPC Codes

机译：基于QC-LDPC码的McEliece密码系统的新分析

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摘要

We improve our proposal of a new variant of the McEliece cryptosystem based on QC-LDPC codes. The original McEliece cryptosystem, based on Goppa codes, is still unbroken up to now, but has two major drawbacks: long key and low transmission rate. Our variant is based on QC-LDPC codes and is able to overcome such drawbacks, while avoiding the known attacks. Recently, however, a new attack has been discovered that can recover the private key with limited complexity. We show that such attack can be avoided by changing the form of some constituent matrices, without altering the remaining system parameters. We also propose another variant that exhibits an overall increased security level. We analyze the complexity of the encryption and decryption stages by adopting efficient algorithms for processing large circulant matrices. The Toom-Cook algorithm and the short Winograd convolution are considered, that give a significant speed-up in the cryptosystem operations.
机译：我们改进了基于QC-LDPC码的McEliece密码系统新变体的建议。最初的基于Goppa码的McEliece密码系统至今仍未中断，但有两个主要缺点：长密钥和低传输速率。我们的变体基于QC-LDPC码，能够克服此类缺陷，同时避免已知攻击。但是，最近发现了一种新攻击，可以以有限的复杂度恢复私钥。我们表明，可以通过更改某些组成矩阵的形式来避免这种攻击，而无需更改其余系统参数。我们还提出了另一个变体，该变体具有总体上提高的安全级别。我们通过采用有效的算法来处理大型循环矩阵来分析加密和解密阶段的复杂性。考虑了Toom-Cook算法和简短的Winograd卷积，这大大提高了密码系统的运算速度。

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