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Individual discrete logarithm with sublattice reduction
The Number Field Sieve and its numerous variants is the best algorithm to compute discrete logarithms in medium and large characteristic finite...
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Efficient quantum algorithms for some instances of the semidirect discrete logarithm problem
The semidirect discrete logarithm problem (SDLP) is the following analogue of the standard discrete logarithm problem in the semidirect product...
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Lattice Enumeration and Automorphisms for Tower NFS: A 521-Bit Discrete Logarithm Computation
The tower variant of the number field sieve (TNFS) is known to be asymptotically the most efficient algorithm to solve the discrete logarithm problem...
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A Subexponential Quantum Algorithm for the Semidirect Discrete Logarithm Problem
Group-based cryptography is a relatively unexplored family in post-quantum cryptography, and the so-called Semidirect Discrete Logarithm Problem...
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Searching B-Smooth Numbers Using Quantum Annealing: Applications to Factorization and Discrete Logarithm Problem
Integer factorization and discrete logarithm problem, two problems of classical public-key cryptography, are vulnerable to quantum attacks,...
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On the Discrete Logarithm Problem in the Ideal Class Group of Multiquadratic Fields
In this work we show that the discrete logarithm problem in the ideal class group of the multiquadratic field...
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Cryptosystems Based on the Discrete Logarithm Problem
In the previous chapter we learned about the RSA public-key scheme, which is based on the hardness of factoring large integers.
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Practical Solving of Discrete Logarithm Problem over Prime Fields Using Quantum Annealing
This paper investigates how to reduce discrete logarithm problem over prime fields to the QUBO problem to obtain as few logical qubits as possible....
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Efficient Zero-Knowledge Arguments in Discrete Logarithm Setting: Sublogarithmic Proof or Sublinear Verifier
We propose three interactive zero-knowledge arguments for arithmetic circuit of size N in the common random string model, which can be converted to...
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Removable weak keys for discrete logarithm-based cryptography
We describe a novel type of weak cryptographic private key that can exist in any discrete logarithm-based public-key cryptosystem set in a group of...
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CDLS: Proving Knowledge of Committed Discrete Logarithms with Soundness
The works of CRYPTO ’18 [1] and SAC ’21 [15] exist in the \(\varSigma \)...
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Quantum Cryptanalysis Landscape of Shor’s Algorithm for Elliptic Curve Discrete Logarithm Problem
Shor’s algorithm is recognized as one of the most influential algorithms that shape the research interest in quantum computation and quantum...
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Comparison of the complexity of Diffie–Hellman and discrete logarithm problems
The article presents an algorithm for solving the discrete logarithm problem with an oracle, solving the Diffie–Hellman problem. Certified the...
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Improving the Gaudry–Schost algorithm for multidimensional discrete logarithms
The discrete logarithm problem arises from various areas, including counting the number of points of certain curves and diverse cryptographic...
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The One-More Discrete Logarithm Assumption in the Generic Group Model
The one more-discrete logarithm assumption (OMDL) underlies the security analysis of identification protocols, blind signature and multi-signature...
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An Improved Cryptanalysis Algorithm for Chebyshev Map-Based Discrete Logarithm Problem
Chebyshev map is a chaotic map frequently used in design of cryptography schemes and cryptosystems based on the hardness of the Chebyshev map-based...
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Lattice Enumeration for Tower NFS: A 521-Bit Discrete Logarithm Computation
The Tower variant of the Number Field Sieve (TNFS) is known to be asymptotically the most efficient algorithm to solve the discrete logarithm problem...
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Learning Disentangled Discrete Representations
Recent successes in image generation, model-based reinforcement learning, and text-to-image generation have demonstrated the empirical advantages of...