[go: up one dir, main page]

Narayanan et al., 2024 - Google Patents

Algorithms for matrix code and alternating trilinear form equivalences via new isomorphism invariants

Narayanan et al., 2024

View PDF
Document ID
16104910043892259196
Author
Narayanan A
Qiao Y
Tang G
Publication year
Publication venue
Annual International Conference on the Theory and Applications of Cryptographic Techniques

External Links

Snippet

We devise algorithms for finding equivalences of trilinear forms over finite fields modulo linear group actions. Our focus is on two problems under this umbrella, Matrix Code Equivalence (MCE) and Alternating Trilinear Form Equivalence (ATFE), since their hardness …
Continue reading at eprint.iacr.org (PDF) (other versions)

Classifications

    • GPHYSICS
    • G06COMPUTING; CALCULATING; COUNTING
    • G06FELECTRICAL DIGITAL DATA PROCESSING
    • G06F17/00Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/30Information retrieval; Database structures therefor; File system structures therefor
    • G06F17/3061Information retrieval; Database structures therefor; File system structures therefor of unstructured textual data
    • G06F17/30613Indexing
    • G06F17/30619Indexing indexing structures
    • GPHYSICS
    • G06COMPUTING; CALCULATING; COUNTING
    • G06FELECTRICAL DIGITAL DATA PROCESSING
    • G06F17/00Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/30Information retrieval; Database structures therefor; File system structures therefor
    • G06F17/30943Information retrieval; Database structures therefor; File system structures therefor details of database functions independent of the retrieved data type
    • G06F17/30946Information retrieval; Database structures therefor; File system structures therefor details of database functions independent of the retrieved data type indexing structures
    • GPHYSICS
    • G06COMPUTING; CALCULATING; COUNTING
    • G06FELECTRICAL DIGITAL DATA PROCESSING
    • G06F17/00Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/30Information retrieval; Database structures therefor; File system structures therefor
    • G06F17/30286Information retrieval; Database structures therefor; File system structures therefor in structured data stores
    • G06F17/30386Retrieval requests
    • G06F17/30424Query processing
    • G06F17/30533Other types of queries
    • GPHYSICS
    • G06COMPUTING; CALCULATING; COUNTING
    • G06FELECTRICAL DIGITAL DATA PROCESSING
    • G06F17/00Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10Complex mathematical operations
    • G06F17/11Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • GPHYSICS
    • G06COMPUTING; CALCULATING; COUNTING
    • G06FELECTRICAL DIGITAL DATA PROCESSING
    • G06F7/00Methods or arrangements for processing data by operating upon the order or content of the data handled
    • G06F7/60Methods or arrangements for performing computations using a digital non-denominational number representation, i.e. number representation without radix; Computing devices using combinations of denominational and non-denominational quantity representations, e.g. using difunction pulse trains, STEELE computers, phase computers
    • G06F7/72Methods or arrangements for performing computations using a digital non-denominational number representation, i.e. number representation without radix; Computing devices using combinations of denominational and non-denominational quantity representations, e.g. using difunction pulse trains, STEELE computers, phase computers using residue arithmetic
    • G06F7/724Finite field arithmetic
    • G06F7/726Inversion; Reciprocal calculation; Division of elements of a finite field
    • GPHYSICS
    • G06COMPUTING; CALCULATING; COUNTING
    • G06FELECTRICAL DIGITAL DATA PROCESSING
    • G06F9/00Arrangements for programme control, e.g. control unit
    • G06F9/06Arrangements for programme control, e.g. control unit using stored programme, i.e. using internal store of processing equipment to receive and retain programme
    • GPHYSICS
    • G06COMPUTING; CALCULATING; COUNTING
    • G06FELECTRICAL DIGITAL DATA PROCESSING
    • G06F19/00Digital computing or data processing equipment or methods, specially adapted for specific applications
    • G06F19/10Bioinformatics, i.e. methods or systems for genetic or protein-related data processing in computational molecular biology
    • G06F19/22Bioinformatics, i.e. methods or systems for genetic or protein-related data processing in computational molecular biology for sequence comparison involving nucleotides or amino acids, e.g. homology search, motif or SNP [Single-Nucleotide Polymorphism] discovery or sequence alignment
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00Cryptographic mechanisms or cryptographic arrangements for secret or secure communication
    • H04L9/32Cryptographic mechanisms or cryptographic arrangements for secret or secure communication including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials
    • H04L9/3247Cryptographic mechanisms or cryptographic arrangements for secret or secure communication including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving digital signatures
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00Cryptographic mechanisms or cryptographic arrangements for secret or secure communication
    • H04L9/08Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0816Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00Cryptographic mechanisms or cryptographic arrangements for secret or secure communication
    • H04L9/32Cryptographic mechanisms or cryptographic arrangements for secret or secure communication including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials
    • H04L9/3218Cryptographic mechanisms or cryptographic arrangements for secret or secure communication including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials using proof of knowledge, e.g. Fiat-Shamir, GQ, Schnorr, ornon-interactive zero-knowledge proofs
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00Cryptographic mechanisms or cryptographic arrangements for secret or secure communication
    • H04L9/30Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy
    • H04L9/3066Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy involving algebraic varieties, e.g. elliptic or hyper-elliptic curves
    • GPHYSICS
    • G06COMPUTING; CALCULATING; COUNTING
    • G06FELECTRICAL DIGITAL DATA PROCESSING
    • G06F2207/00Indexing scheme relating to methods or arrangements for processing data by operating upon the order or content of the data handled
    • GPHYSICS
    • G06COMPUTING; CALCULATING; COUNTING
    • G06FELECTRICAL DIGITAL DATA PROCESSING
    • G06F21/00Security arrangements for protecting computers, components thereof, programs or data against unauthorised activity
    • GPHYSICS
    • G06COMPUTING; CALCULATING; COUNTING
    • G06NCOMPUTER SYSTEMS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N99/00Subject matter not provided for in other groups of this subclass
    • GPHYSICS
    • G06COMPUTING; CALCULATING; COUNTING
    • G06FELECTRICAL DIGITAL DATA PROCESSING
    • G06F19/00Digital computing or data processing equipment or methods, specially adapted for specific applications
    • G06F19/70Chemoinformatics, i.e. data processing methods or systems for the retrieval, analysis, visualisation, or storage of physicochemical or structural data of chemical compounds
    • G06F19/708Chemoinformatics, i.e. data processing methods or systems for the retrieval, analysis, visualisation, or storage of physicochemical or structural data of chemical compounds for data visualisation, e.g. molecular structure representations, graphics generation, display of maps or networks or other visual representations

Similar Documents

Publication Publication Date Title
Albrecht et al. Estimating quantum speedups for lattice sieves
Aono et al. Improved progressive BKZ algorithms and their precise cost estimation by sharp simulator
Bootle et al. Arya: Nearly linear-time zero-knowledge proofs for correct program execution
Campanelli et al. Lunar: a toolbox for more efficient universal and updatable zkSNARKs and commit-and-prove extensions
Wu et al. {DIZK}: A distributed zero knowledge proof system
Ball et al. Proofs of useful work
Ducas et al. Hawk: Module LIP makes lattice signatures fast, compact and simple
Calabrese et al. Entanglement entropy of two disjoint intervals in conformal field theory: II
Göpfert et al. A hybrid lattice basis reduction and quantum search attack on LWE
Banegas et al. Low-communication parallel quantum multi-target preimage search
Narayanan et al. Algorithms for matrix code and alternating trilinear form equivalences via new isomorphism invariants
Kirshanova et al. Quantum algorithms for the approximate k-list problem and their application to lattice sieving
Bai et al. Improved combinatorial algorithms for the inhomogeneous short integer solution problem
Beullens Graph-theoretic algorithms for the alternating trilinear form equivalence problem
Guo et al. Coded-BKW with sieving
Ekerå On post-processing in the quantum algorithm for computing short discrete logarithms
Singh et al. Zero knowledge proofs towards verifiable decentralized ai pipelines
Bruno et al. Cryptographic smooth neighbors
van Baarsen et al. On time-lock cryptographic assumptions in abelian hidden-order groups
Di Giusto et al. Breaking the power-of-two barrier: noise estimation for BGV in NTT-friendly rings
Daruki et al. Streaming verification in data analysis
Zhao et al. Practical improvements on BKZ algorithm
Bindel et al. Quantum lattice enumeration in limited depth
Coladangelo et al. On black-box separations of quantum digital signatures from pseudorandom states
Géraud et al. Twisting lattice and graph techniques to compress transactional ledgers