In [Sa], it was proved that the Selberg zeta function for SL 2 (Z) is expressed in terms of the fundamental units and the class numbers of the primitive indefinite binary quadratic forms. The aim of this paper is to obtain similar arithmetic expressions of the logarithmic derivatives of the Selberg zeta functions for congruence subgroups of SL 2 (Z). As… (More)
General fault attacks on multivariate public key cryptosystems
It is well known that the problem to solve a set of randomly chosen multivariate quadratic equations over a finite field is NP-hard. However, when the number of variables is much larger than the number of equations, it is not necessarily difficult to solve equations. In fact, when n ≥ m(m+1) (n, m are the numbers of variables and equations respectively) and… (More)
The aim of the present paper is to study the distributions of the length multi-plicities for negatively curved locally symmetric Riemannian manifolds. In Theorem 2.1, we give upper bounds of the length multiplicities and the square sums of them for general (not necessarily compact) cases. Furthermore in Theorem 2.3, we obtain more precise estimates of the… (More)
We study splitting densities of primitive elements of a discrete subgroup˜Γ of a connected non-compact semisimple Lie group G of real rank one with finite center in another larger such Γ. When the corresponding cover of such locally symmetric negative curved spaces is regular, the densities can be easily obtained from the results of [Sa] or [Su]. Our main… (More)
The unbalanced oil and vinegar signature scheme (UOV) is one of signature schemes whose public key is a set of multivariate quadratic forms. Recently, a new variant of UOV called Cubic UOV was proposed at Inscrypt 2015. It was claimed that the cubic UOV was more efficient than the original UOV and its security was enough. However, an equivalent secret key… (More)
Sarnak gave an expressions of Selberg's zeta function for the modular group in terms of the class numbers and the fundamental units of the indefinite binary quadratic forms. The main result of the present paper is the extension of his expression to the congruence subgroups of the modular groups in SL 2 (R) and SL 2 (C).