Lattice-based cryptography has recently emerged as a prime candidate for efficient and secure post-quantum cryptography. The two main hard problems underlying its security are the shortest vector problem (SVP) and the closest vector problem (CVP). Various algorithms have been studied for solving these problems, and for SVP, lattice sieving currently dominates in terms of the asymptotic time com...

We obtain a 2 O(n==) time algorithm to approximate the length of the shortest vector in an n-dimensional lattice to within a factor of n 3+. In this note we consider the complexity of approximating the shortest lattice vector length (called SVP-Length) when the approximation factor is poly(n). An obvious candidate for producing polynomial approximations to SVP-Length | Schnorr's improvement of ...

This paper shows the closest vector in a lattice to be NPhard to approximate to within any factor up to 2(logn)1 where = (log logn) c for any constant c < 12 . Introduction A lattice L = L(v1; ::; vn), for vectors v1; ::; vn 2 Rn is the set of all integer linear combinations of v1; ::; vn, that is, L = fP aivi j ai 2 Zg. Given a lattice L and an arbitrary vector y, the Closest Vector Problem (C...

In this paper, we propose approximate lattice algorithms for solving the shortest vector problem (SVP) and the closest vector problem (CVP) on an n-dimensional Euclidean integral lattice L. Our algorithms run in polynomial time of the dimension and determinant of lattices and improve on the LLL algorithm when the determinant of a lattice is less than 2 2/4. More precisely, our approximate SVP a...

Most short vegetative phase (SVP)-group MADS-box genes control meristem identity and flowering time. Among the three SVP-group genes in rice, OsMADS47 has been reported as a negative regulator of brassinosteroid (BR) responses. Here, we investigated the functional roles of two close homologs, OsMADS22 and OsMADS55, by generating single, double and triple RNAi lines and overexpression lines. Ana...

Register allocation is one of the biggest challenges in compiler design. The allocation scheme implemented by the compiler impacts directly on the processor’s performance. The SVP model, implemented in processors supporting micro-threads, provides an alternative solution for programming the next generation of many-core chip multiprocessors. This model is captured in a new language called μTC (a...

The structural protein VP2 of infectious bursal disease virus (IBDV) spontaneously forms a dodecahedral T=1 subviral particle (SVP), and is a primary immunogen of the virus. In this study, the structure of IBDV SVP was determined in a cubic crystal and refined to 2.6A resolution. It contains 20 independent VP2 subunits in a crystallographic asymmetric unit. Each subunit is folded mainly into a ...

Combining the efficient cross-polytope locality-sensitive hash family of Terasawa and Tanaka with the heuristic lattice sieve algorithm of Micciancio and Voulgaris, we show how to obtain heuristic and practical speedups for solving the shortest vector problem (SVP) on both arbitrary and ideal lattices. In both cases, the asymptotic time complexity for solving SVP in dimension n is 2. For any la...

Sonic layer depth (SLD) plays an important role in antisubmarine warfare in terms of identifying the shadow zones for submarine safe parking. SLD is estimated from sound velocity profiles (SVP) which is inturn is obtained from temperature and salinity (T/S) profiles. Given the limited availability of salinity data in comparison to temperature, SVPs need to be obtained from alternate methods. In...