Section: New Results
Solving Systems in Finite Fields, Applications in Cryptology and Algebraic Number Theory.
Algebraic Cryptanalysis of a Quantum Money Scheme – The Noisy Case.
At STOC 2012, Aaronson and Christiano proposed a noisy and a noiseless version
of the first public-key quantum money scheme endowed with a security proof.
[5] addresses the so-called noisy hidden subspaces
problem, on which the noisy version of their scheme is based. The first
contribution of this work is a non-quantum cryptanalysis of the
above-mentioned noisy quantum money scheme extended to prime fields
On the Complexity of MQ in the Quantum Setting.
In August 2015 the cryptographic world was shaken by a sudden and surprising
announcement by the US National Security Agency NSA concerning plans to
transition to post-quantum algorithms. Since this announcement post-quantum
cryptography has become a topic of primary interest for several
standardization bodies. The transition from the currently deployed public-key
algorithms to post-quantum algorithms has been found to be challenging in many
aspects. In particular the problem of evaluating the quantum-bit security of
such post-quantum cryptosystems remains vastly open. Of course this question
is of primarily concern in the process of standardizing the post-quantum
cryptosystems. In [21] we consider the quantum security
of the problem of solving a system of
MQsoft .
In 2017, NIST shook the cryptographic world by starting a process for
standardizing post-quantum cryptography. Sixty-four submissions have been
considered for the first round of the on-going NIST Post-Quantum Cryptography
(PQC) process. Multivariate cryptography is a classical post-quantum candidate
that turns to be the most represented in the signature category. At this stage
of the process, it is of primary importance to investigate efficient
implementations of the candidates. [17] presents MQsoft , an efficient library which permits to implement HFE -based
multivariate schemes submitted to the NIST PQC process such as GeMSS, Gui and DualModeMS. The library is implemented in
C targeting Intel 64-bit processors and using avx2 set
instructions. We present performance results for our library and its
application to GeMSS, Gui and DualModeMS. In
particular, we optimize several crucial parts for these schemes. These include
root finding for HFE polynomials and evaluation of multivariate
quadratic systems in