Logic Geometry, Information Profile picture
Professional critic and mathematician. Doctorate in (a subarea of) mathematics. https://t.co/wMrzGxjiyd, https://t.co/85Qkws0fZ8, https://t.co/YUvA0gyxzI
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5 Apr
#GoldsteinQuantumInformation-7
"The idea that the wave function merely represents information, and does not describe an objective state of affairs, raises many questions and problems:
#Information about what?
• What about quantum interference? How can the terms of a
>
> quantum superposition interfere with each other, producing an observable interference pattern, if such a superposition is just an expression of our ignorance?

• The problem of vagueness: Quantum mechanics is supposed to be a fundamental physical theory. As such it should be
>
> precise. But if it is fundamentally about
#information, then it is presumably concerned directly either with mental events or, more likely, with the behavior of macroscopic variables. But the notion of the macroscopic is intrinsically vague.
• Simple physical #laws are to be
>
Read 4 tweets
5 Apr
#BernsteinHeningerLouValenta-4
"Contents of This Paper
Is it actually true that #QuantumComputers will kill RSA?
The question here is not whether quantum computers will be built, or will be affordable for attackers. This paper assumes that astonishingly scalable quantum computers
> will be built, making a qubit operation as inexpensive as a bit operation. Under this assumption, Shor’s algorithm easily breaks RSA 𝘢𝘴 𝘶𝘴𝘦𝘥 𝘰𝘯 𝘵𝘩𝘦 𝘐𝘯𝘵𝘦𝘳𝘯𝘦𝘵 𝘵𝘰𝘥𝘢𝘺. The question is whether RSA parameters can be adjusted so that
>
>all known quantum attack algorithms are infeasible while encryption and decryption remain feasible."

M.t. 'Inhalt des vorliegenden Aufsatzes

Ist es wirklich wahr, dass Quantenrechner #RSA töten werden?

Im vorliegenden Aufsatz wird nicht die Frage behandelt, ob Quantenrechner>
Read 4 tweets
5 Apr
#BernsteinHeningerLouValenta-3
"1 Introduction
The 1994 publication of #Shor’s algorithm prompted widespread claims that quantum computers would kill #cryptography, or at least public-key cryptography. For example:
• [15]: “Nobody knows exactly when #QuantumComputing will
>
> become a reality, but when and if it does, it will signal the end of traditional cryptography”.
• [37]: “If #QuantumComputers exist one day, Shor’s results will make all current known public-key cryptographic systems useless”.

>
>
• [29]: “It is already proven that quantum computers will allow to break #PublicKeyCryptography.”
• [20]: “When the first quantum factoring devices are built the security of public-key crypstosystems [sic] will vanish.”

But these claims go far beyond the actual

>
Read 6 tweets
5 Apr
#BernsteinHeningerLouValenta-2
"Abstract
This paper proposes #RSA parameters for which
1) key generation, encryption, decryption, signing, and verification are feasible on today’s #computers while
2) all known attacks are infeasible, even ASSUMING..scalable #QuantumComputers.
>
> As part of the performance analysis, this paper introduces a new algorithm to generate a batch of
primes. As part of the attack analysis, this paper introduces a new quantum factorization algorithm that is often much faster than #ShorsAlgorithm and much faster than pre-quantum
>factorization algorithms. Initial pqRSA implementation results are provided.

Keywords
Post-quantum #cryptography
RSA scalability
#ShorsAlgorithm
ECM
#GroversAlgorithm
Make RSA Great Again"

M.t. 'Zusammenfassung
Vorliegender Aufsatz schlägt Parameter für das RSA-Verfahren vor
>
Read 6 tweets
5 Apr
"On vous braquera.
..
"Ça sera un braquage.
On vous braquera votre épargne.
..
On sera au même plan de Liban."
(Olivier Delamarche, at 29m37s of v=MCQkep8BlP4)
"On va devenir un gros Kolkhoze."

(Olivier #Delamarche, at 31m07s of v=MCQkep8BlP4)
Read 4 tweets
4 Apr
Already bored by your new 18-core #Intel i9-7980XE that you bought for a measly two thousand bucks?

Then why not spend a couple of million dollars on a 4*10^5-core #processor with the size of a whole wafer?

forbes.com/sites/tiriasre…

#Cerebras
#Stanford
#WaferScaleEngine
Read 4 tweets
4 Apr
#FeffermanEtAlWorkOfStein-6
"Let us begin with Stein’s work on #interpolation of operators. As background, we state and prove a classical result:

Theorem I.1.1 (#Riesz convexity theorem). Suppose 𝑋, 𝑌 are measure spaces, and suppose 𝑇 is an operator that carries functions
>
> on 𝑋 to functions on 𝑌. Assume 𝑇 is bounded from 𝐿^𝑝₀(𝑋) to 𝐿^𝑟₀(𝑌), and from 𝐿^𝑝₁(𝑋) to 𝐿^𝑟₁(𝑌). (Here 𝑝₀, 𝑝₁, 𝑟₀, 𝑟₁ ∈ [1,∞].) Then 𝑇 is bounded from 𝐿^𝑝(X) to 𝐿^𝑟(𝑌) for 1/𝑝= 𝑡/𝑝₁+(1−𝑡)/𝑝₀, 1/𝑟= 𝑡/𝑟₁+(1−𝑡)/𝑟₀, 0⩽𝑡⩽1."

>
>

M.t. 'Beginnen wir mit den Arbeiten von Stein zum Thema Interpolation von Operatoren. Als Hintergrund beweisen wir ein klassisches Ergebnis:

Satz I.1.1 (Interpolationssatz von #Riesz und Thorin). Seien 𝑋 und 𝑌 Maßräume, und sei 𝑇 ein Operator, der auf 𝑋 definierte
>
Read 5 tweets
4 Apr
#FeffermanEtAlWorkOfStein-5
"For purposes of this article, #RepresentationTheory deals with the construction and classification of the irreducible unitary representations of a semisimple Lie group.

Classical #Fourieranalysis starts with the 𝐿ᵖ-boundedness of
>
> two fundamental operators, the maximal function
Read 9 tweets
4 Apr
#FeffermanEtAlWorkOfStein-4
"Part I. Selections from Stein’s classical results

contributed by C. Fefferman

The purpose of this survey article is to give the general reader some idea of the scope and originality of Eli Stein’s contributions to analysis up to the year 1991. His
>
> work deals with #RepresentationTheory, classical #FourierAnalysis, and #PartialDifferentialEquations. He was the first to appreciate the interplay among
these subjects, and to perceive the fundamental insights in each field arising from that interplay. No one else really
>
> understands all three fields; therefore, no on else
could have done the work I am about to describe. However, deep understanding of three fields of #mathematics is by no means sufficient to lead to Stein’s main ideas.
Rather, at crucial points, Stein has shown extraordinary
>
Read 8 tweets
4 Apr
#ShamirIPequalsPSPACE-4
1. Introduction
The class IP of languages that have efficient #InteractiveProofs of membership was introduced
by Goldwasser et al. [8], and in a slightly different form by Babai [1] (the equivalence between these models was established by Goldwasser and
>
> Sipser [7]). A language 𝐿 belongs to IP if a probabilistic polynomial[-]time verifier 𝑉 can be convinced by some prover 𝑃 to accept any 𝑥∈𝐿 with overwhelming probability. Goldreich et al. [6] showed that IP contains some languages believed not to be in NP, but its exact
>
> characterization remained a major open problem for seveal years. In a breakthrough paper, Lund et al. [10] made ingenious use of earlier results by Valiant [12], Toda [11] Beaver and Feigenbaum [2] and Lipton [9] to prove that IP contains the #PolynomialHierarchy PH.
>
Read 5 tweets
4 Apr
#Reitschuster
Bundesverfassungsgericht, 15. Januar 1958 - 1 BvR 400/51: "Das Grundrecht auf freie Meinungsäußerung ist als unmittelbarster Ausdruck der menschlichen Persönlichkeit in der Gesellschaft eines der vornehmsten Menschenrechte überhaupt (un des droits les plus précieux>
> de l"homme nach Artikel 11 der Erklärung der Menschen- und Bürgerrechte von 1789). Für eine freiheitlich-demokratische Staatsordnung ist es schlechthin konstituierend,..(BVerfGE 5, 85 [205]). Es ist in gewissem Sinn die Grundlage jeder Freiheit überhaupt, "the matrix, the
>
> indispensable condition of nearly every other form of #freedom" (Cardozo).

Aus dieser grundlegenden Bedeutung der Meinungsäußerungsfreiheit für den freiheitlich-demokratischen Staat ergibt sich, daß es vom Standpunkt dieses Verfassungssystems aus NICHT folgerichtig wäre,
>
Read 8 tweets
4 Apr
#ZuckerExactLatticeSums-4
"1. Introduction
Glasser (1973a, b) has recently revived much interest in the exact evaluation of lattice sums, It should be explained here what is meant by the ‘exact’ value of a lattice sum. Here we say a multiple sum has been evaluated if it can be
>
> expressed as the product of simple sums such as #DirichletSeries. For example it has been established that
where the sum on the left-hand side is over all integer values of 𝑙₁ and 𝑙₂ both positive and negative but excluding the case where both are zero. The right-hand side is the product of two well known #DirichletSeries namely
Read 7 tweets
4 Apr
#DailyMail 2021-04-02: "[Gaetz'] friend has been singing to the feds [..] #Gaetz's arrest is imminent as jailed tax collector #JoelGreenberg faces charges of having sex with same 17-year-old and 'making fake ID's with the congressman'"
Relevant context: threader.app/thread/1377798….

Of course, Mr. #Gaetz has to be presumed innocent. This is still early on in the case.
Mr. Gaetz has made himself unpopular with certain circles, on several occasions even. (Inter alia, in December 2019, during the #Impeachment-hearings.)

BTW, I can hardly believe he would be so stupid to use #Apple-payment processors for such transactions. Is this believable?
Read 4 tweets
4 Apr
#GalballyZelikLatticeSums-3
"1. Introduction
Lattice sums of the form
and various their extensions naturally appear in many branches of modern analysis including analytic number theory (e.g. for study the number of lattice points in spheres or balls), analysis of PDEs (e.g. for constructing #GreenFunctions for various differential operators in
>
> periodic domains, finding best constants in interpolation inequalities, etc.), harmonic analysis as well as in applications, e.g. for computing the electrostatic potential of a single ion in a #crystal (the so-called #MadelungConstants), see [1, 2, 3, 4, 9, 10, 11, 15] and
>
Read 6 tweets
4 Apr
#KipnisShamirOilAndVinegar-2
"Abstract.
Several multivariate algebraic signature schemes had been proposed in recent years, but most of them had been broken by exploiting the fact that their secret trapdoors are low rank algebraic structures. One of the few remaining variants is>
> #Patarin’s ”Oil & Vinegar” scheme, which is based on a system of 𝑛 quadratic forms in 2𝑛 variables of two flavors (𝑛 ”oil” variables and 𝑛 ”vinegar” variables). The security of the scheme depends on the difficulty of distinguishing between the two types, and does not seem
>
> to be susceptible to known low rank attacks. In this paper we describe two novel algebraic attacks which can efficiently separate the oil and vinegar variables, and thus forge arbitrary signatures."

M.t. 'Zusammenfassung
Mehrere multivariate algebraische Signierschemata
>
Read 5 tweets
3 Apr
#MayRSAvulnerabilities-17
"Actually, the idea of asymmetric #cryptography was already due to Whitfield #Diffie[,] but Rivest, Shamir and Adleman were the first who designed an asymmetric
cryptosystem¹. The idea of an asymmetric scheme is as follows:
Assume that Alice has a
>
>#public key 𝑘ₚ and a #secret key 𝑘ₛ.

She publishes 𝑘ₚ on the network, such that everyone can access her public key.

Now, if Bob wants to send a message 𝑚 to Alice,
he [(using a conjectural #TrapdoorFunction) LG,I] encrypts 𝑚 with Alice’s public key 𝑘ₚ.

In order to>
> recover 𝑚 from the ciphertext, Alice uses her secret key 𝑘ₛ in the decryption process.

In the case of the #RSA scheme, [this idea] is realized in the following way.
Alice chooses two large primes 𝑝 and 𝑞 and computes the product 𝑁 = 𝑝𝑞.

Then she selects
>
Read 7 tweets
2 Apr
#Videoverbrennung-191
[#censorship
#France
#history]

v=WRcP1vNXTEs "no longer available because the #YouTube account associated with this video has been terminated".

The heading was: "VIOLENTE Intrusion de l'Extrême Droite au Conseil Régional #Toulouse"

The description read:> Image
> "Huit membres du groupuscule d’extrême droite #ActionFrançaise se sont introduits dans l’enceinte du Conseil régional d’Occitanie à Toulouse, ce jeudi 25 mars. La Dépêche détaille les informations connues sur cet incident survenu en pleine séance plénière. Jeudi à 13h30, alors>
> que se déroule la séance plénière du Conseil régional, à Toulouse et en visio conférence à Montpellier, Carole Delga est en train de s’exprimer lorsqu’elle est interrompue par des cris et des bruits de lutte. "Ils étaient très agités et leurs gestes étaient violents,
>
Read 4 tweets
13 Feb
#Vielfalt:#Diversity

"Um das Grau des Betons zu kaschieren, wurde die Universität #Konstanz vollgestopft mit farbigen Elementen und Installationen." (Marc Reichwein, welt.de)

Symbolisch für die gesamte europäische Kultur nach 1945:
Compare #Princeton:
Read 5 tweets
12 Feb
The CCRL is not convinced of the truth of the claim of #FatFritz's superiority (yet):
The direct one-on-one comparison with the latest version of #Stockfish is remarkably undecided; the two engines appear to be practically equal in strength:
Also, Chessbase themselves admit that #FatFritz is but a Stockfish-clone, with a non-open-source neural-network-COMPONENT added, no doubt a carefully-crafted neural network. Still, Stockfish does the same. Fat Fritz 2.0 practically certainly is nothing revolutionary.
Read 6 tweets
12 Feb
archive.is/0U0Qm: "In dem Interview bekräftigt #Lütge auch seine Kritik an den Corona-Maßnahmen. Den #Lockdown halte er für „völlig unnötig und für nicht verhältnismäßig.“ Die Kollateralschäden seien „zu hoch“ – darunter fielen neben sozialen und psychischen Schäden auch>
> verpasste Vorsorgeuntersuchungen, die zu anderen Erkrankungen führten. Er äußert zudem die Vermutung, „die Politik“ wolle womöglich „durch drastische Anordnungen vom eigenen Impfversagen ablenken“. Auch die „einseitige Besetzung von Beratergremien“ sei „ein großes Problem“.

>
>
Auf Zahlen wie die der an oder mit Corona Verstorbenen angegsprochen[sic] behauptet Lütge, dies könne „man so nicht stehen lassen“, da diese Menschen „zum großen Teil nicht an Corona gestorben“, sondern lediglich „auf das Virus positiv getestet worden“ seien.

>
Read 4 tweets