QC-LDPC
A new analysis of the McEliece cryptosystem based on QC-LDPC codes 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.
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References in zbMATH (referenced in 10 articles , 1 standard article )
Showing results 1 to 10 of 10.
Sorted by year (- Amirzade, F.; Alishahi, M.; Rafsanjani-Sadeghi, M. R.: A reduction in the search space of QC-LDPC codes with girth 8 (2020)
- Amirzade, Farzane; Sadeghi, Mohammad-Reza; Panario, Daniel: QC-LDPC construction free of small size elementary trapping sets based on multiplicative subgroups of a finite field (2020)
- Singh, Jasvinder; Gupta, Manish; Bhullar, Jaskarn Singh: On the search of smallest QC-LDPC code with girth six and eight (2020)
- Ivanov, F. I.: A special class of quasi-cyclic low-density parity-check codes based on repetition codes and permutation matrices (2017)
- Ivanov, F. I.; Zyablov, V. V.: Low-density parity-check codes based on Steiner systems and permutation matrices (2013)
- Baldi, Marco; Bodrato, Marco; Chiaraluce, Franco: A new analysis of the McEliece cryptosystem based on QC-LDPC codes (2008)
- Huang, Wei; Zhang, Jianqiu: Block Gauss elimination approach to construction of the generator matrices of quasi-cycle LDPC codes (2008)
- Sun, Shuqi; Zhou, Wuyang: Construction of quasi-cyclic LDPC codes based on compressing (2008)
- Zhang, Wei; Zhu, Guangxi; Peng, Li; Shen, Qiongxia: Design of LDPC codes using iterative-filled method (2008)
- Zhan, Wei; Zhu, Guangxi; Peng, Li: Design of QC-LDPC codes using Fibonacci sequence (2008)