Biblio

The paradigm of quantum computation has led to the development of new algorithms as well variations on existing algorithms. In particular, novel cryptographic techniques based upon quantum computation are of great interest. Many classical encryption techniques naturally translate into the quantum paradigm because of their well-structured factorizations and the fact that they can be phased in the form of unitary operators. In this work, we demonstrate a quantum approach to data encryption and decryption based upon the McEliece cryptosystem using Reed-Muller codes. This example is of particular interest given that post-quantum analyses have highlighted this system as being robust against quantum attacks. Finally, in anticipation of quantum computation operating over binary fields, we discuss alternative operator factorizations for the proposed cryptosystem.

Grassmannian frames in composite dimensions D are constructed as a collection of orthogonal bases where each is the element-wise product of a mask sequence with a generalized Hadamard matrix. The set of mask sequences is obtained by exponentiation of a q-root of unity by different quadratic forms with m variables, where q and m are the product of the unique primes and total number of primes, respectively, in the prime decomposition of D. This method is a generalization of a well-known construction of mutually unbiased bases, as well as second-order Reed-Muller Grassmannian frames for power-of-two dimension D = 2m, and allows to derive highly symmetric nested families of frames with finite alphabet. Explicit sets of symmetric matrices defining quadratic forms leading to constructions in non-prime-power dimension with good distance properties are identified.

Nowadays, physical tampering and counterfeiting of electronic devices are still an important security problem and have a great impact on large-scale and distributed applications, such as Internet-of-Things. Physical Unclonable Functions (PUFs) have the potential to be a fundamental means to guarantee intrinsic hardware security, since they promise immunity against most of known attack models. However, inner nature of PUF circuits hinders a wider adoption since responses turn out to be noisy and not stable during time. To overcome this issue, most of PUF implementations require a fuzzy extraction scheme, able to recover responses stability by exploiting error correction codes (ECCs). In this paper, we propose a Reed-Muller (RM) ECC design, meant to be embedded into a fuzzy extractor, that can be efficiently configured in terms of area/delay constraints in order to get reliable responses from PUFs. We provide implementation details and experimental evidences of area/delay efficiency through syntheses on medium-range FPGA device.