human: Given a hyperedge-centered hypergraph: <hypergraph>, where the center hyperedge is induced by one source paper and its member nodes are the cited papers.

Details of the hypergraph:
Center hyperedge (induced by source paper "solving multivariate polynomial systems and an invariant from commutative algebra"):
  Abstract: The security of several post-quantum cryptosystems is based on the assumption that solving a system of multivariate (quadratic) polynomial equations $p_1=\dots=p_r=0$ over a finite field is hard. Such a system can be solved by computing a lexicographic Gr\"obner basis of the ideal $(p_1,\dots,p_r)$. The most efficient algorithms for computing Gr\"obner bases transform the problem into several instances of Gaussian elimination. The computational complexity of these algorithms is not completely understood, especially when the polynomials $p_1,\dots,p_r$ are not homogeneous. In this paper, we prove that this complexity is controlled by the Castelnuovo-Mumford regularity of the ideal $(p_1^h,\dots,p_r^h)$ obtained by homogenizing the input polynomials. This allows us to bound the complexity of solving a system of polynomial equations when the associated ideal is zero-dimensional, a common situation in cryptography. In combination with some theorems in commutative algebra, our results also allow us to bound the complexity of the ABC and cubic simple matrix schemes, as well as some instances of the MinRank Problem.

Includes members:
  Member "index calculus in the trace zero variety":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "an optimal representation for the trace zero subgroup")
  Member "on the complexity of the generalized minrank problem":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "the complexity of minrank")

Question: Please tell me which class the source paper belongs to. The 40 classes are: cs.NA(Numerical Analysis), cs.MM(Multimedia), cs.LO(Logic in Computer Science), cs.CY(Computers and Society), cs.CR(Cryptography and Security), cs.DC(Distributed, Parallel, and Cluster Computing), cs.HC(Human-Computer Interaction), cs.CE(Computational Engineering, Finance, and Science), cs.NI(Networking and Internet Architecture), cs.CC(Computational Complexity), cs.AI(Artificial Intelligence), cs.MA(Multiagent Systems), cs.GL(General Literature), cs.NE(Neural and Evolutionary Computing), cs.SC(Symbolic Computation), cs.AR(Hardware Architecture), cs.CV(Computer Vision and Pattern Recognition), cs.GR(Graphics), cs.ET(Emerging Technologies), cs.SY(Systems and Control), cs.CG(Computational Geometry), cs.OH(Other Computer Science), cs.PL(Programming Languages), cs.SE(Software Engineering), cs.LG(Machine Learning), cs.SD(Sound), cs.SI(Social and Information Networks), cs.RO(Robotics), cs.IT(Information Theory), cs.PF(Performance), cs.CL(Computation and Language), cs.IR(Information Retrieval), cs.MS(Mathematical Software), cs.FL(Formal Languages and Automata Theory), cs.DS(Data Structures and Algorithms), cs.OS(Operating Systems), cs.GT(Computer Science and Game Theory), cs.DB(Databases), cs.DL(Digital Libraries), cs.DM(Discrete Mathematics). Directly output the class name.

gpt: cs.CR(Cryptography and Security)