No abstract

In this paper, we address the weighted linear matroid intersection problem from the computation of the degree of the determinants of a symbolic matrix. We show that a generic algorithm computing the degree of noncommutative determinants, proposed by the second author, becomes an O(mn 3 log n) time algorithm for the weighted linear matroid intersection problem, where two matroids are given by column vectors n × m matrices A, B. We reveal that our algorithm is viewed as a "nonstandard" implementation of Frank's weight splitting algorithm for linear matroids. This gives a linear algebraic reasoning to Frank's algorithm. Although our algorithm is slower than existing algorithms in the worst case estimate, it has a notable feature: Contrary to existing algorithms, our algorithm works on different matroids represented by another "sparse" matrices A 0 , B 0 , which skips unnecessary Gaussian eliminations for constructing residual graphs.

At PKC 2018, Chen et al. proposed SOFIA, the first MQ-based digital signature scheme having tight security in the quantum random oracle model (QROM). SOFIA is constructed by applying an extended version of the Unruh transform (EUROCRYPT 2015) to the MQ-based 5-pass identification scheme (IDS) proposed by Sakumoto et al. (CRYPTO 2011). In this paper, we propose an MQ-based 3-pass IDS with impersonation probability of 1 2 and apply the original version of the Unruh transform to it to obtain a more efficient MQ-based digital signature scheme tightly secure in the QROM. The signature size of our digital signature scheme decreases by about 35% compared with SOFIA in the level I of NIST PQC security category, and is supposed to be the shortest among that of MQ-based signatures tightly secure in the QROM.

No abstract