[PDF] Top 20 Discrete Logarithms and Mordell-Weil Groups
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Discrete Logarithms and Mordell-Weil Groups
... to Mordell, one knows that the abelian group of rational points E( Q ) of E is finitely generated, hence, E( Q ) ∼ = E( Q ) tor × Z r where E( Q ) tor is the torsion subgroup of E( Q ), and r is the rank of ... See full document
11
Computing small discrete logarithms faster
... Fully homomorphic encryption is still prohibitively slow, but there are much more efficient schemes achieving more limited forms of homomorphic encryp- tion. We highlight Freeman’s variant [11] of the scheme by Boneh, ... See full document
22
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 ... See full document
52
Computing Individual Discrete Logarithms Faster in $GF(p^n)$
... the discrete logarithm (DL) of x ∈ G is the element 1 ≤ a ≤ #G such that x = g a ...well-chosen groups, the exponentiation (g, a) 7→ g a is very fast but computing a from (g, x) is conjectured to be very ... See full document
25
Collision Bounds for the Additive Pollard Rho Algorithm for Solving Discrete Logarithms
... 1.5. Organization of the paper. The paper is organized as follows: in Section 2 we explain why the recent methods of Kim et al. [20, 21] are not applicable (in any obvious way) to the setting of the additive Pollard rho ... See full document
15
The Proof is in the Pudding: Proofs of Work for Solving Discrete Logarithms
... certain groups, including multiplicative groups modulo primes and elliptic curve ...of discrete log underlies the security of multiple important cryptographic algorithms, including the Diffie-Hellman ... See full document
8
On post-processing in the quantum algorithm for computing short discrete logarithms
... puting discrete logarithms that is more efficient than Shor’s original algorithm when the logarithm is ...short discrete logarithms in instantiations of cryptographic schemes based on the ... See full document
19
Computing Elliptic Curve Discrete Logarithms with Improved Baby-step Giant-step Algorithm
... of discrete logarithms in small intervals are used as subroutines in several cryptographic protocols in the ...generic discrete log- arithm method for decryption; the Henry-Henry-Goldberg ... See full document
20
Modified Baby Step Giant Step Algorithm to Solve Elliptic Curve Discrete Logarithm Problem (ECDLP)
... In this work, a modified version of Shanks’ algorithm to compute discrete logarithms in elliptic curve groups is presented. This algorithm is the elliptic curve analog of the new modified version of ... See full document
5
Improving the Polynomial time Precomputation of Frobenius Representation Discrete Logarithm Algorithms - Simplified Setting for Small Characteristic Finite Fields
... such groups, the proportion of discrete logarithms that are left unknown is 1/2 k ...available groups grows, this proportion quickly tends to ...such groups we expect to obtain all ... See full document
21
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 - ... See full document
11
Multisignature Scheme Based on Discrete Logarithms in the Plain Public Key Model
... We have proposed a Multisignature Scheme based on Discrete Logarithms (MSDL). We show that this new scheme can resist existential forgeries against adaptive chosen-message attacks in the random oracle ... See full document
8
A new perspective on the powers of two descent for discrete logarithms in finite fields
... compute discrete logarithms, following ideas from [EG02] and ...the discrete logarithm of an element h in base g, the idea is to collect relations between g, h, and elements of the factor base by ... See full document
9
The Special Number Field Sieve in $\F _{p^{n}}$, Application to Pairing-Friendly Constructions
... z should be B 0 -smooth and squarefree. The second condition implies that only degree one prime ideals will appear in the factorization of (¯ z). This is required since only logarithms of such ideals are computed ... See full document
15
Actions of discrete amenable groups on factors
... e groups, m is the Haar measure, but on in f in it e groups, such a mean, i f i t e x is ts , is never ...Abelian groups are amenable, since the in v a ria n t mean can be chosen by means o f the ... See full document
205
Precautionary saving in Spain during the Great Recession: evidence from a panel of uncertainty indicators
... Given that the EFF does not report unemployment rates (under any type of aggregation) nor the geographical location within the Spanish territory of households in the sample (such that we could assign the jobless rate of ... See full document
25
Closed Form Moment Formulae for the Lognormal SABR Model and Applications to Calibration Problems
... We study two calibration problems for the lognormal SABR model using the moment method and some new formulae for the moments of the logarithm of the forward prices/rates variable. The lognormal SABR model is a special ... See full document
15
Approximation properties for discrete groups
... free groups, finitely generated Cox- eter groups [19], and finitely generated right angled Artin groups for which the Salvetti complex is a CAT(0) cube ...cancellation groups act properly and ... See full document
13
The Tower Number Field Sieve
... Once this setting is done, the TNFS algorithm proceeds as usual. For many polynomials a(ι) − b(ι)x in R[x], we consider their two images in R[x]/f(x) and R[x]/g(x), and test them for smoothness as ideals. Each time the ... See full document
26
A study of exactness for discrete groups
... Guentner and Kaminker illustrated their theorem by showing that the Hilbert Space compression of a finite rank free group is 1 thus giving a new proof of exactness for free groups.. It s[r] ... See full document
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