Abstract This paper investigates blind identification methods for linear scramblers under non‐cooperative conditions, which are essential for the inverse analysis of communication protocols using scramblers. In this paper, a blind identification scheme for feedback polynomials of synchronous scramblers is proposed. A variable is first proposed that measures the correctness of the test polynomial by using the soft information of the received sequence, then the mean and variance of the variable in different cases are obtained, and finally the optimal threshold value to determine whether the test primitive polynomial is correct or not is obtained. That is, the blind identification problem is transformed into a hypothesis testing problem. The simulations verify that the proposed scheme requires a much smaller scrambled sequence length than existing blind identification schemes. Furthermore, the proposed scheme is more fault tolerant than existing schemes and has a signal‐to‐noise ratio (SNR) gain of at least 3 dB when the intercepted scrambled sequences are of the same length and high identification accuracy is achieved.

Abstract This paper studies the blind recognition method of the sparse parity‐check matrices of low‐density parity‐check codes in noncooperative communication, which is critical to the reverse analysis of communication protocols using LDPC codes. In this paper, two improvements are made to the algorithm of Liu Qian et al. (2021) for this problem. Firstly, a Gaussian elimination method based on random column exchange and soft information is proposed to enhance the fault tolerance of the elimination process. Secondly, according to the sparse property of the parity‐check matrices of LDPC codes, a random extraction method is proposed to further improve the fault tolerance of the algorithm, and it is verified theoretically. Finally, simulations verify the superior performance of the algorithm proposed in this paper.

Abstract The inverse analysis of the intercepted signals to reconstruct the communication scheme used by the transmitter is a key problem in the non‐cooperative context. In this paper, the problem of blind reconstruction of cyclic codes and self‐synchronous scramblers is considered. There is no existing solution to this problem. To solve this problem, a joint blind reconstruction method for cyclic codes and self‐synchronous scramblers is proposed in this paper. A lemma is proposed and proved theoretically that the maximum common factor of the inverse polynomial of the polynomial form of the dual vectors of the self‐synchronous scrambled bit matrix is the product of the parity polynomial of the cyclic code and the feedback polynomial of the self‐synchronous scrambler. Using this lemma, the joint blind reconstruction of the cyclic code and the self‐synchronous scrambler is completed. Finally, a Gaussian elimination based on random column exchange and soft information (GERCESI) method is proposed, which can apply the proposed method to a noisy environment. Simulations prove that the fault‐tolerance performance of the GERCESI method proposed in this paper is at least 0.5 dB higher than that of the GJETP method.

Reverse analysis of the intercepted signal to reconstruct the communication scheme used by the transmitter is a key problem in the non-cooperative context. In this paper, we propose a new algorithm for the joint blind reconstruction of the cyclic codes and self-synchronous scramblers directly using soft-decision sequences. First, we derive the conclusion that if the parity polynomial of the factor of the generator polynomial of the cyclic code and the feedback polynomial of the self-synchronous scrambler are multiplied, then the vector corresponding to the inverse polynomial of this product forms a parity-check relation with the row vector of the self-synchronously scrambled cyclic code bit matrix, which is constructed by the sequence of self-synchronously scrambled cyclic codes. To detect this parity-check relation, the concept of average parity-check probability (APCP) is defined, which uses the intercepted soft-decision sequence to measure the reliability of the parity-check relation. An optimal threshold based on the minimum error criterion is then derived. When the APCP is greater than this optimal threshold, the parity-check relation is considered to be detected, i.e., the corresponding irreducible polynomial is a factor of the generator polynomial of the cyclic code and the corresponding candidate feedback polynomial is the feedback polynomial of the self-synchronous scrambler. Therefore, the blind reconstruction problem in this paper is exactly equivalent to the hypothesis-testing problem. Simulation results show that the algorithm is more fault-tolerant than existing algorithms in noisy environments.

Abstract As one of the key technologies of modern communication, a linear scrambler is a technique to randomize the data to be transmitted at the bit layer to improve the timing recovery and confidentiality of the transmitted data. Therefore, the reconstruction of scramblers under non‐cooperative communication conditions has attracted extensive research interest. Existing efficient reconstruction methods are implemented by traversing the primitive polynomial of all orders, leading to extremely high computational complexity. Here, a fast reconstruction method for feedback polynomials of synchronous scramblers is proposed. The order of the feedback polynomial is first estimated by a hypothesis testing method, and then the primitive polynomial of the corresponding order is traversed to reduce the traversal range of the primitive polynomial, which greatly reduces the computational complexity of the reconstruction method. The simulation results verify the performance of the scheme.