It is known that a naive implementation of the decryption algorithm in the McEliece cryptosystem allows an attacker to recover the secret matrix P by measuring the power consumption. We demonstrate that a similar threat is present in the QC-LDPC variant of the McEliece cryptosystem. We consider a naive implementation of the decryption algorithm in the QC-LDPC McEliece cryptosystem. We demonstrate that this implementation leaks information about positions of ones in the secret matrix Q. We argue that this leakage allows an attacker to completely recover the matrix Q. In addition, we note that the quasi-cyclic nature of the matrix Q allows to accelerate the attack significantly.
In this paper we study equivalence classes of binary vectors with regards to their rotation by using an algebraic approach based on the theory of linear feedback shift registers. We state the necessary and sufficient condition for existence of an equivalence class with given cardinality and provide two formulas. The first represents the sharp distribution of cardinalities for given length and Hamming weight of binary vectors and the second enables us to determine the number of different classes with the same cardinality.
A prefix code, a P-code, is a code where no codeword is a prefix of another codeword. In this paper, a symmetric cipher based on prefix codes is proposed. The simplicity of the design makes this cipher usable for Internet of Things applications. Our goal is to investigate the security of this cipher. A detailed analysis of the fundamental properties of P-codes shows that the keyspace of the cipher is too large to mount a brute-force attack. Specifically, in this regard we will find bounds on the number of minimal P-codes containing a binary word given in advance. Furthermore, the statistical attack is difficult to mount on such cryptosystem due to the attacker’s lack of information about the actual words used in the substitution mapping. The results of a statistical analysis of possible keys are also presented. It turns out that the distribution of the number of minimal P-codes over all binary words of a fixed length is Gaussian.
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