discrete logarithms
On post-processing in the quantum algorithm for computing short discrete logarithms
... We revisit the quantum algorithm for computing short discrete logarithms that was recently introduced by Eker˚ a and H˚ astad. By carefully analyzing the probability distribution induced by the algorithm, ...
19
Factor Base Discrete Logarithms in Kummer Extensions
... that in this case, a small number of degenerate relations (from the Borel subgroup) are enough to solve the factor base discrete logarithms. We disprove the conjecture, and design a new heuristic algorithm ...
19
Quantum algorithms for computing general discrete logarithms and orders with tradeoffs
... general discrete logarithms, this yields a reduction by up to a factor of two in the number of group operations evaluated quantumly in each run, at the expense of having to perform multiple ...of ...
52
Nearly Sparse Linear Algebra and application to Discrete Logarithms Computations
... Abstract. In this article 1 , we propose a method to perform linear algebra on a matrix with nearly sparse properties. More precisely, although we require the main part of the matrix to be sparse, we allow some dense ...
23
The Proof is in the Pudding: Proofs of Work for Solving Discrete Logarithms
... We propose a proof of work scheme that is useful for cryptanalysis, in particular, solving discrete logarithms. The security of the ECDSA digital signature scheme is based on the hardness of the elliptic ...
8
A new perspective on the powers of two descent for discrete logarithms in finite fields
... Abstract. A new proof is given for the correctness of the powers of two de- scent method for computing discrete logarithms. The result is slightly stronger than the original work, but more importantly we ...
9
Modifying Shors algorithm to compute short discrete logarithms
... computing discrete logarithms was originally described for F ∗ p , it may be generalized to any finite abelian group, provided the group operation may be implemented efficiently using quantum ...
26
Multisignature Scheme Based on Discrete Logarithms in the Plain Public Key Model
... In this paper, we also propose a new multisignature scheme based on Discrete Logarithms (DL) in the plain public key model. We show that this new scheme can resist existential forgeries against adaptive ...
8
Traps to the BGJT-Algorithm for Discrete Logarithms
... The discrete logarithm problem over finite fields is one of the most important candidates, besides the integer factorization ...of discrete logarithms underpins the security of the widely adopted ...
16
Computing Elliptic Curve Discrete Logarithms with Improved Baby-step Giant-step Algorithm
... curve discrete logarithms using either the baby-step giant-step algorithm (BSGS) or Pollard ...curve discrete logarithms in small groups or small ...
20
Computing small discrete logarithms faster
... small discrete logarithms are feasible even in “secure” groups, and are used as subroutines in several cryptographic protocols in the ...square-root discrete-logarithm methods for ...a ...
22
Collision Bounds for the Additive Pollard Rho Algorithm for Solving Discrete Logarithms
... proposed as an integer factorization method [30], was later modified to obtain one of the most commonly used methods for solving the discrete logarithm problem when G is a generic finite cyclic group [31]. In this ...
15
Computing Individual Discrete Logarithms Faster in $GF(p^n)$
... In 2003, ten years after Gordon’s algorithm, Joux and Lercier [17] were the first to dissociate in NFS relation collection plus linear algebra on one side and individual DL on the other side. They used the special-q ...
25
Discrete Logarithms and Mordell-Weil Groups
... During the course of constructing S , the Generalized Riemann Hypothesis and Szpiro’s conjecture are assumed to bound the primes in S using the expected rank of the lifted elliptic curve[r] ...
11
On Generating Coset Representatives of PGL_2(\F_q) in PGL_2(\F_{q^2})
... 3. Razvan Barbulescu, Pierrick Gaudry, Antoine Joux, and Emmanuel Thom´ e. A heuristic quasi-polynomial algorithm for discrete logarithm in finite fields of small characteristic. In Advances in Cryptology - ...
11
Sashimi: Cutting up CSI-FiSh secret keys to produce an actively secure distributed signing protocol
... from discrete logarithms, we can follow the same paradigm in creating an actively secure threshold variant as is done in the standard case of actively secure distributed Schnorr ...
15
Improving the Polynomial time Precomputation of Frobenius Representation Discrete Logarithm Algorithms - Simplified Setting for Small Characteristic Finite Fields
... of discrete logarithms in small characteristic finite fields has been greatly improved [Jou14,GGMZ13a,BGJT14], with the introduc- tion of a new family of Index Calculus algorithms for this ...a ...
21
Some experiments investigating a possible L(1/4) algorithm for the discrete logarithm problem in algebraic curves
... of discrete logarithms in Jacobians of algebraic curves has developed essen- tially in parallel to finite ...computing discrete logarithms in Jacobians of low degree curves has very much in ...
16
Drinfeld modules may not be for isogeny based cryptography
... curve discrete logarithm problem is a foun- dational assumption in public key ...module discrete logarithm problem is easy even on a classical ...Beyond discrete logarithms, elliptic curve ...
16
A Simplified Approach to Rigorous Degree 2 Elimination in Discrete Logarithm Algorithms
... In this paper, we revisit the method. More precisely, we provide a slightly modified strategy and a new algorithm and analysis for the so-called degree 2 elimination step. This yields a simpler analysis of its success ...
11