Recent progress on the elliptic curve discrete logarithm problem
From MaRDI portal
Publication:908041
DOI10.1007/s10623-015-0146-7zbMath1364.11164OpenAlexW2218139189WikidataQ61914006 ScholiaQ61914006MaRDI QIDQ908041
Steven D. Galbraith, Pierrick Gaudry
Publication date: 2 February 2016
Published in: Designs, Codes and Cryptography (Search for Journal in Brave)
Full work available at URL: https://hal.inria.fr/hal-01215623/file/DCC-survey.pdf
discrete logarithm problem (DLP)elliptic curve discrete logarithm problem (ECDLP)index-calculusPollard rhosummation polynomials
Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Number-theoretic algorithms; complexity (11Y16) Elliptic curves (14H52) Curves over finite and local fields (11G20) Finite ground fields in algebraic geometry (14G15) Applications to coding theory and cryptography of arithmetic geometry (14G50)
Related Items (19)
On index calculus algorithms for subfield curves ⋮ Efficient Software Implementation of Laddering Algorithms Over Binary Elliptic Curves ⋮ An authenticated key scheme over elliptic curves for topological networks ⋮ The multi-base discrete logarithm problem: tight reductions and non-rewinding proofs for Schnorr identification and signatures ⋮ Fiat-Shamir and correlation intractability from strong KDM-secure encryption ⋮ The point decomposition problem over hyperelliptic curves, Toward efficient computation of discrete logarithms in even characteristic ⋮ Source-location privacy full protection in wireless sensor networks ⋮ Acceleration of Index Calculus for Solving ECDLP over Prime Fields and Its Limitation ⋮ Cryptocash, cryptocurrencies, and cryptocontracts ⋮ New results on quasi-subfield polynomials ⋮ Extending the GLS endomorphism to speed up GHS Weil descent using Magma ⋮ On the discrete logarithm problem for prime-field elliptic curves ⋮ Short Generators Without Quantum Computers: The Case of Multiquadratics ⋮ Can we beat the square root bound for ECDLP over \(\mathbb{F}_p^2\) via representation? ⋮ Complexity bounds on Semaev's naive index calculus method for ECDLP ⋮ Low weight discrete logarithm and subset sum in \(2^{0.65n}\) with polynomial memory ⋮ Koblitz curves over quadratic fields ⋮ A probabilistic analysis on a lattice attack against DSA ⋮ Still wrong use of pairings in cryptography
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On the discrete logarithm problem in elliptic curves. II
- First fall degree and Weil descent
- Using symmetries in the index calculus for elliptic curves discrete logarithm
- Index calculus for abelian varieties of small dimension and the elliptic curve discrete logarithm problem
- Deterministically generating Picard groups of hyperelliptic curves over finite fields
- A birthday paradox for Markov chains with an optimal bound for collision in the Pollard rho algorithm for discrete logarithm
- Elliptic codes over fields of characteristic 2
- Parallel collision search with cryptanalytic applications
- Efficient computation of zero-dimensional Gröbner bases by change of ordering
- Kangaroos, monopoly and discrete logarithms
- Constructive and destructive facets of Weil descent on elliptic curves
- On the last fall degree of zero-dimensional Weil descent systems
- Solving a 112-bit prime elliptic curve discrete logarithm problem on game consoles using sloppy reduction
- Complexity of a determinate algorithm for the discrete logarithm
- Speeding up elliptic curve discrete logarithm computations with point halving
- Elliptic curve discrete logarithm problem over small degree extension fields
- Analysis of the Xedni calculus attack
- A simple method for obtaining relations among factor basis elements for special hyperelliptic curves
- Computing elliptic curve discrete logarithms with improved baby-step giant-step algorithm
- A Generic Algorithm for Small Weight Discrete Logarithms in Composite Groups
- Solving the Discrete Logarithm of a 113-Bit Koblitz Curve with an FPGA Cluster
- Point Decomposition Problem in Binary Elliptic Curves
- Non-uniform Cracks in the Concrete: The Power of Free Precomputation
- Solving the Elliptic Curve Discrete Logarithm Problem Using Semaev Polynomials, Weil Descent and Gröbner Basis Methods – An Experimental Study
- Computing Small Discrete Logarithms Faster
- Mathematics of Public Key Cryptography
- Cover and Decomposition Index Calculus on Elliptic Curves Made Practical
- Improving the Complexity of Index Calculus Algorithms in Elliptic Curves over Binary Fields
- Solving a Discrete Logarithm Problem with Auxiliary Input on a 160-Bit Elliptic Curve
- Multi-user Collisions: Applications to Discrete Logarithm, Even-Mansour and PRINCE
- Collision of Random Walks and a Refined Analysis of Attacks on the Discrete Logarithm Problem
- Summation Polynomial Algorithms for Elliptic Curves in Characteristic Two
- Generic Hardness of the Multiple Discrete Logarithm Problem
- A Group Action on $${\mathbb Z}_p^{\times }$$ and the Generalized DLP with Auxiliary Inputs
- ANALYSIS OF POSSIBLE PRE-COMPUTATION AIDED DLP SOLVING ALGORITHMS
- On the Static Diffie-Hellman Problem on Elliptic Curves over Extension Fields
- On the discrete logarithm problem in elliptic curves
- On the discrete logarithm problem in class groups of curves
- On the Correct Use of the Negation Map in the Pollard rho Method
- Global Duality, Signature Calculus and the Discrete Logarithm Problem
- Improvement of Faugère et al.’s Method to Solve ECDLP
- A double large prime variation for small genus hyperelliptic index calculus
- Sub-cubic change of ordering for Gröbner basis
- Last Fall Degree, HFE, and Weil Descent Attacks on ECDLP
- A new approach to the discrete logarithm problem with auxiliary inputs
- Using Equivalence Classes to Accelerate Solving the Discrete Logarithm Problem in a Short Interval
- Security Analysis of the Strong Diffie-Hellman Problem
- Hard Problems of Algebraic Geometry Codes
- Another look at non-standard discrete log and Diffie-Hellman problems
- Oracle-Assisted Static Diffie-Hellman Is Easier Than Discrete Logarithms
- The Strong Law of Small Numbers
- Constructing Isogenies between Elliptic Curves Over Finite Fields
- Improving the parallelized Pollard lambda search on anomalous binary curves
- Slope packings and coverings, and generic algorithms for the discrete logarithm problem
- Generalising the GHS Attack on the Elliptic Curve Discrete Logarithm Problem
- On Polynomial Systems Arising from a Weil Descent
- Computing discrete logarithms in an interval
- On the Use of the Negation Map in the Pollard Rho Method
- Decomposition Attack for the Jacobian of a Hyperelliptic Curve over an Extension Field
- How long does it take to catch a wild kangaroo?
- Algorithmic Cryptanalysis
- Advances in Cryptology - EUROCRYPT 2004
- Handbook of Elliptic and Hyperelliptic Curve Cryptography
- Elliptic and Hyperelliptic Curves: A Practical Security Analysis
- Analysis on a generalized algorithm for the strong discrete logarithm problem with auxiliary inputs
- Symmetrized Summation Polynomials: Using Small Order Torsion Points to Speed Up Elliptic Curve Index Calculus
- Remarks on Cheon’s Algorithms for Pairing-Related Problems
- Do All Elliptic Curves of the Same Order Have the Same Difficulty of Discrete Log?
- Advances in Elliptic Curve Cryptography
- Algorithmic Number Theory
- Algorithmic Number Theory
- Advances in Cryptology - ASIACRYPT 2003
- Discrete logarithm problems with auxiliary inputs
This page was built for publication: Recent progress on the elliptic curve discrete logarithm problem
