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.

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.

A prefix code minimal with respect to a bitstring x is a prefix code where x is a concatenation of its codewords and it is minimal with respect to this property. What is the maximum size M(n) among all minimal codes over all bitstrings of length n ? In this paper we determine the value of M(n) for all natural numbers n , discuss its computational complexity, relation to the Lambert function, provide tight upper bounds, and describe how the value of M(n) enables one to construct efficiently a Huffman code in the case of uniform probability distribution of the codewords.

PQC migration represents multiple challenges in education. We will need to educate our future cryptography researchers and engineers on new topics, introduce new challenges, and explain new cryptographic primitives. In the paper, we present our view on education challenges associated with the transition to post-quantum cryptography.