Reducing elliptic curve logarithms to logarithms in a finite field

No abstract is available for this paper.

• Publication year

  1991

• Venue

  Symposium on the Theory of Computing

• Publication date

  1991-01-03

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.1145/103418.103434
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Discrete Logarithms in GF(P) Using the Number Field Sieve

  1993cited by this paper
• Rigorous, subexponential algorithms for discrete logarithms over finite fields

  1992cited by this paper
• Massively Parallel Computation of Discrete Logarithms

  1992cited by this paper
• The number field sieve

  1990cited by this paper
• The implementation of elliptic curve cryptosystems

  1990cited by this paper
• On the Implementation of Elliptic Curve Cryptosystems

  1989cited by this paper
• Elliptic curves and cryptography : a pseudorandom bit generator and the other tools

  1988cited by this paper
• Elliptic curve cryptosystems

  1987cited by this paper
• The multiple polynomial quadratic sieve

  1987cited by this paper
• Nonsingular plane cubic curves over finite fields

  1987cited by this paper
• Fast, Rigorous Factorization and Discrete Logarithm Algorithms

  1987cited by this paper
• A Pseudo-Random Bit Generator Based on Elliptic Logarithms

  1986cited by this paper
• The arithmetic of elliptic curves

  1986cited by this paper
• Elliptic Curves Over Finite Fields and the Computation of Square Roots mod p

  1985cited by this paper
• A subexponential-time algorithm for computing discrete logarithms over GF(p^2)

  1985cited by this paper
• Discrete Logarithms in Finite Fields and Their Cryptographic Significance

  1985cited by this paper
• Factorizations of b[n]±1, b=2, 3, 5, 6, 7, 10, 11, 12 up to high powers

  1985cited by this paper
• Use of Elliptic Curves in Cryptography

  1985cited by this paper
• Fast evaluation of logarithms in fields of characteristic two

  1984cited by this paper
• Fast Computation of Discrete Logarithms in GF(q)

  1982cited by this paper
• Probabilistic algorithms in finite fields

  1980cited by this paper
• On taking roots in finite fields

  1977cited by this paper
• Approximate formulas for some functions of prime numbers

  1962cited by this paper

• A Blockchain-Empowered Decentralized and Secure Spectrum Allocation for Wireless Vehicular Communications

  2026cites this paper
• Distortion maps for elliptic curves over finite fields

  2026cites this paper
• Toward practical quantum encryption in phase space: simulated QPSK and 16-QAM with dynamic displacement operators

  2026cites this paper
• Breaking the KAZ Suite: Practical Key Recovery Attacks on MySEAL 2.0's Post-Quantum Candidates

  2026cites this paper
• Cycles of supersingular elliptic curves for pairing-based proof systems

  2026cites this paper
• PEDA: Privacy-Enhancing Distance-Aware Aggregation of Graph Neural Networks

  2025cites this paper
• Quantum Encryption in Phase Space with Dynamic Displacement Operators and Quantum Permutation Pad

  2025cites this paper
• Fast Implementation of SM9 Digital Signature Algorithm Based on FPGA

  2025cites this paper
• Multisignature on Isogenies of Elliptic Curves with Participant Masking and Authentication

  2025cites this paper
• Simpler and Faster Pairings from the Montgomery Ladder

  2025cites this paper
• Quantum Permutation Pad for Quantum Secure Symmetric and Asymmetric Cryptography

  2025cites this paper
• Fault Attacks on ECC Signature Verification

  2025cites this paper
• An efficient practical alternative to ECC by Pell curve cryptography with a new vision

  2025cites this paper
• On the Existence and Construction of Very Strong Elliptic Curves

  2025cites this paper
• Aggregatable Subvector Commitment with Efficient Updates

  2025cites this paper
• Eccfrog512ck2: An Enhanced 512-bit Weierstrass Elliptic Curve

  2025cites this paper
• A Survey of Threshold Signatures: NIST Standards, Post-Quantum Cryptography, Exotic Techniques, and Real-World Applications

  2025cites this paper
• ECTester: Reverse-engineering side-channel countermeasures of ECC implementations

  2025cites this paper
• A Note on the Post-Quantum Security of Identity-Based Encryption on Isogenous Pairing Groups

  2025cites this paper
• A survey on isogeny-based cryptographic protocols

  2025cites this paper
• An Algebraic Point of View on the Generation of Pairing-Friendly Curves

  2025cites this paper
• Hashing-friendly elliptic curves

  2025cites this paper
• Hard Instances of Discrete Logarithm Problem and Cryptographic Applications

  2025cites this paper
• Lossy Cryptography from Code-Based Assumptions Dense-Sparse LPN: A New Subexponentially Hard LPN Variant in SZK

  2025cites this paper
• Accelerating pairings on BW10 and BW14 curves

  2025cites this paper
• An optimization method for the generalized simplified SWU algorithm

  2024cites this paper
• On cycles of pairing-friendly abelian varieties

  2024influential citation
• Short Programs for Functions on Curves: A STOC Rejection

  2024cites this paper
• QPP and HPPK: Unifying Non-Commutativity for Quantum-Secure Cryptography with Galois Permutation Group

  2024cites this paper
• Linearly Homomorphic Signature Scheme With High-Signature Efficiency and Its Application in IoT

  2024cites this paper
• Elliptic Curve Cryptography with Machine Learning

  2024cites this paper
• Agile Asymmetric Cryptography and the Case for Finite Fields

  2024cites this paper
• DKGAuth: Blockchain-Assisted Distributed Key Generation and Authentication for Cross-Domain Intelligent IoT

  2024cites this paper
• Attribute-Based Designated Combiner Transitive Signature Scheme

  2024cites this paper
• A structure-preserving linearly homomorphic signature scheme with designated combiner

  2024cites this paper
• Area-Time-Efficient Secure Comb Scalar Multiplication Architecture Based on Recoding

  2024cites this paper
• Solving modular cubic equations with Coppersmith's method

  2024cites this paper
• Simultaneously simple universal and indifferentiable hashing to elliptic curves

  2024cites this paper
• Research on Data Aggregation Scheme of Power Internet of Things in Cloud-Edge-End Environment

  2024cites this paper
• Publicly Verifiable and Secure SVM Classification for Cloud-Based Health Monitoring Services

  2024cites this paper
• Improved Polynomial Division in Cryptography

  2024cites this paper
• Unmasking: An Elliptic Curve Cryptography and AI Approach to Mitigate Deepfake Threats and Societal Impact

  2024cites this paper
• Covert Cryptography in Pixel Realms: Unveiling Nonlinear-Encrypted Generative Adversarial Networks for Stealthy Image Steganography

  2024cites this paper
• Efficient implementation of cancelable face recognition based on elliptic curve cryptography

  2023cites this paper
• Leopard: Sublinear Verifier Inner Product Argument Under Discrete Logarithm Assumption

  2023cites this paper
• Deep-Learning-Based Physical-Layer Lightweight Authentication in Frequency-Division Duplex Channel

  2023cites this paper
• Novel area-efficient and flexible architectures for optimal Ate pairing on FPGA

  2023cites this paper
• Achieving Privacy-Preserving and Verifiable Support Vector Machine Training in the Cloud

  2023influential citation
• Exp function for Edwards curves over local fields

  2023cites this paper
• Constructing CM Fields for NFS to Accelerate DL Computation in Non-Prime Finite Fields

  2023cites this paper
• Wireless Sensor Network with Blockchain Technology using Elliptic Curve Discrete Logarithm Problem and its Applications

  2023cites this paper
• ID-Based Digital Signatures with Security Enhanced Approach

  2023cites this paper
• Computationally Efficient Pairing-Friendly Curves for a 128bit Security Level

  2023cites this paper
• Elliptic curves over a finite ring

  2023cites this paper
• Cryptographically Strong Elliptic Curves of Prime Order

  2023cites this paper
• zk-Bench: A Toolset for Comparative Evaluation and Performance Benchmarking of SNARKs

  2023cites this paper
• A Comprehensive Survey of Threshold Digital Signatures: NIST Standards, Post-Quantum Cryptography, Exotic Techniques, and Real-World Applications

  2023cites this paper
• Secure and Efficient Encryption Scheme Based on Bilinear Mapping

  2023cites this paper
• Efficient Countermeasures against

  2023cites this paper
• Secure Registration Protocol for the Internet of Drones Using Blockchain and Physical Unclonable Function Technology

  2023cites this paper
• Explicit Riemann-Roch spaces in the Hilbert class field

  2023cites this paper
• IoT-friendly, pre-computed and outsourced attribute based encryption

  2023cites this paper
• Construction and Implementation of a Privacy-Preserving Identity-Based Encryption Architecture

  2023cites this paper
• Scalable, password-based and threshold authentication for smart homes

  2022cites this paper
• PVCLS-SI: Isogeny-based Certificateless Signature Scheme

  2022cites this paper
• T-HIBE: A Novel Key Establishment Solution for Decentralized, Multi-Tenant IoT Systems

  2022cites this paper
• MODIFICATION OF POLLARD RHO ALGORITHM USING NEGATION MAPPING

  2022cites this paper
• Efficient Privacy-Preserving Data Aggregation Scheme with Fault Tolerance in Smart Grid

  2022cites this paper
• Mobile and safe e-cash system based on blockchain

  2022cites this paper
• SoK: SCA-secure ECC in software - mission impossible?

  2022cites this paper
• Revisiting cycles of pairing-friendly elliptic curves

  2022cites this paper
• The Influence of Public-Key Cryptography on Mathematics

  2022cites this paper
• Efficient Loop Abort Fault Attacks on Supersingular Isogeny based Key Exchange (SIKE)

  2022cites this paper
• PBAG: A Privacy-Preserving Blockchain-Based Authentication Protocol With Global-Updated Commitment in IoVs

  2022cites this paper
• Quantum permutation pad for universal quantum-safe cryptography

  2022cites this paper
• On Random Number Generation for Kernel Applications

  2022cites this paper
• BalanceProofs: Maintainable Vector Commitments with Fast Aggregation

  2022cites this paper
• Computational investment in generation of elliptic curves randomly over large prime fields

  2022cites this paper
• A lightweight device-level Public Key Infrastructure with DRAM based Physical Unclonable Function (PUF) for secure cyber physical systems

  2022cites this paper
• BBARHS: Blockchain-Based Anonymous Ride-Hailing Scheme for Autonomous Taxi Network

  2022cites this paper
• Security Analysis of Elliptic Curves over Sextic Extension of Small Prime Fields

  2022cites this paper
• New Signature Scheme Based on Elliptic Curve and Factoring Problems Using Chaotic Map

  2022cites this paper
• On the Multi-user Security of Short Schnorr Signatures with Preprocessing

  2022cites this paper
• Pairing-Friendly Elliptic Curves: Revisited Taxonomy, Attacks and Security Concern

  2022cites this paper
• DiSSECT: Distinguisher of Standard & Simulated Elliptic Curves via Traits

  2022cites this paper
• Security limitations of Shamir’s secret sharing

  2022cites this paper
• XTR and Tori ∗

  2021cites this paper
• Efficient Zero-Knowledge Argument in Discrete Logarithm Setting: Sublogarithmic Proof or Sublinear Verifier

  2021cites this paper
• Iterated Inhomogeneous Polynomials

  2021cites this paper
• Computing Discrete Logarithms

  2021cites this paper
• History of integer factorization

  2021cites this paper
• SCA-secure ECC in software - mission impossible?

  2021cites this paper
• Pairing for Greenhorn: Survey and Future Perspective

  2021cites this paper
• Construction of metrics on the set of elliptic curves over a finite field

  2021cites this paper
• Speed Reading in the Dark: Accelerating Functional Encryption for Quadratic Functions with Reprogrammable Hardware

  2021cites this paper
• History of Cryptographic Key Sizes

  2021cites this paper
• Analysis of Crystals-Dilithium for BlockChain Security

  2021cites this paper
• Lattice Enumeration for Tower NFS: a 521-bit Discrete Logarithm Computation

  2021cites this paper
• An Efficient Double Parameter Elliptic Curve Digital Signature Algorithm for Blockchain

  2021influential citation
• A survey on Functional Encryption

  2021cites this paper