15 research outputs found
Modular Inversion Hidden Number Problem- A Lattice Approach
The Modular Inversion Hidden Number Problem (MIHNP) was introduced by
Boneh, Halevi and Howgrave-Graham in Asiacrypt 2001 (BHH’01). They provided
two heuristics - in Method I, two-third of the output bits are required to solve the
problem, whereas the more efficient heuristic (Method II) requires only one-third of
the bits of the output. After more than a decade, here Sarkar in [28] identified that
the claim in Method II is actually not correct and a detailed calculation justified that
this method too requires two-third of the bits of the output, contrary to the claim in
BHH’01. He reconstructed the lattice and give a bound which heuristically solve with
half of the output bits. Although J.Xu et al in [29] solved it with only one-third of the
output bits asymptotically but that technique is difficult to understand and implement.
Here we essentially use similar idea of [28] but in a clever way such that it is a better
bound although we solve the problem heuristically with only half of the output bits in
asymptotic sense. This is lot easier to understand and implement.
Also experimental results support the claim corresponding to our heuristics. In the last
section we actually talk about a variant of this which seems to be hard to solve under
lattice attack
Deterministic Identity Testing Paradigms for Bounded Top-Fanin Depth-4 Circuits
Polynomial Identity Testing (PIT) is a fundamental computational problem. The famous depth-4 reduction (Agrawal & Vinay, FOCS\u2708) has made PIT for depth-4 circuits, an enticing pursuit. The largely open special-cases of sum-product-of-sum-of-univariates (?^[k] ? ? ?) and sum-product-of-constant-degree-polynomials (?^[k] ? ? ?^[?]), for constants k, ?, have been a source of many great ideas in the last two decades. For eg. depth-3 ideas (Dvir & Shpilka, STOC\u2705; Kayal & Saxena, CCC\u2706; Saxena & Seshadhri, FOCS\u2710, STOC\u2711); depth-4 ideas (Beecken, Mittmann & Saxena, ICALP\u2711; Saha,Saxena & Saptharishi, Comput.Compl.\u2713; Forbes, FOCS\u2715; Kumar & Saraf, CCC\u2716); geometric Sylvester-Gallai ideas (Kayal & Saraf, FOCS\u2709; Shpilka, STOC\u2719; Peleg & Shpilka, CCC\u2720, STOC\u2721). We solve two of the basic underlying open problems in this work.
We give the first polynomial-time PIT for ?^[k] ? ? ?. Further, we give the first quasipolynomial time blackbox PIT for both ?^[k] ? ? ? and ?^[k] ? ? ?^[?]. No subexponential time algorithm was known prior to this work (even if k = ? = 3). A key technical ingredient in all the three algorithms is how the logarithmic derivative, and its power-series, modify the top ?-gate to ?
Electric Vehicle Battery Supply Chain and Critical Materials: A Brief Survey of State of the Art
Electric vehicles (EVs) have been garnering wide attention over conventional fossil fuel-based vehicles due to the serious concerns of environmental pollution and crude oil depletion. In this article, we have conducted a systematic literature survey to explore the battery raw material supply chain, material processing, and the economy behind the commodity price appreciation. We present significant areas of concern, including resource reserves, supply, demand, geographical distribution, battery reuse, and recycling industries. Furthermore, details of the battery supply chain and its associated steps are illustrated. The authors believe the presented study will be an information cornerstone in boosting manufacturing and understanding the key components and materials required to facilitate EV battery production. Further, this study discusses the major industries, and their policies and global market share in each material category