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 "folding alternant and goppa codes with non trivial automorphism groups"):
  Abstract: The main practical limitation of the McEliece public-key encryption scheme is probably the size of its key. A famous trend to overcome this issue is to focus on subclasses of alternant/Goppa codes with a non trivial automorphism group. Such codes display then symmetries allowing compact parity-check or generator matrices. For instance, a key-reduction is obtained by taking quasi-cyclic (QC) or quasi-dyadic (QD) alternant/Goppa codes. We show that the use of such symmetric alternant/Goppa codes in cryptography introduces a fundamental weakness. It is indeed possible to reduce the key-recovery on the original symmetric public-code to the key-recovery on a (much) smaller code that has not anymore symmetries. This result is obtained thanks to a new operation on codes called folding that exploits the knowledge of the automorphism group. This operation consists in adding the coordinates of codewords which belong to the same orbit under the action of the automorphism group. The advantage is twofold: the reduction factor can be as large as the size of the orbits, and it preserves a fundamental property: folding the dual of an alternant (resp. Goppa) code provides the dual of an alternant (resp. Goppa) code. A key point is to show that all the existing constructions of alternant/Goppa codes with symmetries follow a common principal of taking codes whose support is globally invariant under the action of affine transformations (by building upon prior works of T. Berger and A. D{\"{u}}r). This enables not only to present a unified view but also to generalize the construction of QC, QD and even quasi-monoidic (QM) Goppa codes. All in all, our results can be harnessed to boost up any key-recovery attack on McEliece systems based on symmetric alternant or Goppa codes, and in particular algebraic attacks.

Includes members:
  Member "new algorithms for decoding in the rank metric and an attack on the lrpc cryptosystem":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "algebraic attacks for solving the rank decoding and minrank problems without gr obner basis")
  Member "polynomial time attack on wild mceliece over quadratic extensions":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "squares of matrix product codes")
  Member "key reduction of mceliece s cryptosystem using list decoding":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "structural properties of twisted reed solomon codes with applications to cryptography")
  Member "cryptanalysis of two mceliece cryptosystems based on quasi cyclic codes":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "protograph based decoding of ldpc codes with hamming weight amplifiers")

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.IT(Information Theory)