A weighted group shuffled decoding for low-density parity-check codes

In this paper, we have developed several concepts such as the tree concept, the short cycle concept and the group shuffling concept of a propagation cycle to decrypt low-density parity-check (LDPC) codes. Thus, we proposed an algorithm based on group shuffling propagation where the probability of occurrence takes exponential form exponential factor appearance probability belief propagation-group shuffled belief propagation (EFAP-GSBP). This algorithm is used for wireless communication applications by providing improved decryption performance with low latency. To demonstrate the effectiveness of our suggested technique EFAP-GSBP, we ran numerous simulations that demonstrated that our algorithm is superior to the traditional BP/GSBP algorithm for decrypting LPDC codes in both regular and non-regular forms

Development of Niederriter crypto-code design models on LDPC-codes

The development of mobile technologies and computing resources has expanded the range of digital services and practically outstripped the development of computer technologies. This approach ensures the use of mobile and wireless networks in almost all areas of smart technologies, provides a further synthesis of cyberspace and the mobile Internet. However, the absence of security service protocols: confidentiality and integrity, initially when they are formed in the structure of LTE technologies, provides cyber attackers with the opportunity to use mobile Internet channels to implement targeted (APT) attacks. The development and emergence of a full-scale quantum computer with Shor and Grover algorithms can lead to a sharp decrease in the level of security of cryptosystems based on symmetric and asymmetric cryptography (including cryptography on elliptic curves). In addition, modern cyber threats have signs of synergy and hybridity, and their integration with social engineering methods practically does not allow providing the required level of preventive measures (protection). The article proposes post-quantum cryptosystems based on the Niederreiter crypto-code construction on low-density parity-check codes (LDPC-codes). This approach makes it easy to integrate into wireless networks based on IEEE 802.16 and IEEE 802.15.4 standards, as well as LTE mobile technologies. At the same time, the required level of resistance to modern threats ensured.

A digital signature scheme $\mathrm{mCFS}^{\mathrm{QC{-}LDPC}}$ based on $\mathrm{QC}$-$\mathrm{LDPC}$ codes

Предлагается заменить коды Гоппы кодами $\mathrm{QC}$-$\mathrm{LDPC}$ в схеме электронной подписи $\mathrm{mCFS}$. Это дает значительное (в среднем в $50$ раз) сокращение размеров открытых ключей без потери стойкости. Используется такая же теоретическая модель, как для схемы $\mathrm{mCFS}$. Обсуждаются возможности использования ряда известных методов для атаки на хэш-функцию и на процедуру выработки открытого/закрытого ключей. Предложены наборы параметров для нескольких уровней стойкости, например $80$-битовый уровень стойкости достижим с открытым ключом размера $\approx 1.82$ KB, $128$-битовый уровень стойкости - с ключом $\approx 3.87$ KB и $256$-битовый уровень стойкости - с ключом $\approx 13.88$ KB.

An illegal user model of communication channel with error correction codeс

The situation when an illegal user intercepts data from the communication channel of two legal users is considered. The data in the legal channel is protected from distortion by error correction codes. It is assumed that the intercept channel may be noisier than the legal channel. And, consequently, the interceptor receives low-quality data. The possibility of using a special type of error-correction code decoders by an illegal user to restore damaged data is discussed. The interceptor model is constructed. The model includes a receiving block of the intercept channel, as well as several auxiliary blocks, such as a memory device, a block for determining the quality of communication in the legal channel, databases with possible decoders and their parameters. Examples are given that show the potential capabilities of the interceptor. The examples demonstrate the difference in decoding quality between different decoders for LDPC codes and Reed-Muller codes. These examples show that an illegal user with the various decoders described in the open press can receive information with satisfactory quality even at a weak signal level in the intercept channel. The constructed model can be useful in the tasks of developing methods of protection against intruders who organize illegitimate data interception channels.