Key agreement: security / division

Some key agreement schemes, such as Diffie--Hellman key agreement, reduce to Rabi--Sherman key agreement, in which Alice sends $ab$ to Charlie, Charlie sends $bc$ to Alice, they agree on key $a(bc) = (ab)c$, where multiplicative notation here indicates some specialized associative binary operation. All non-interactive key agreement schemes, where each peer independently determines a single delivery to the other, reduce to this case, because the ability to agree implies the existence of an associative operation. By extending the associative operation’s domain, the key agreement scheme can be enveloped into a mathematical ring, such that all cryptographic values are ring elements, and all key agreement computations are ring multiplications. (A smaller envelope, a semigroup instead of a ring, is also possible.) Security relies on the difficulty of division: here, meaning an operator $/$ such that $((ab)/b)b = ab$. Security also relies on the difficulty of the less familiar wedge operation $[ab, b, bc] \mapsto abc$. When Rabi--Sherman key agreement is instantiated as Diffie--Hellman key agreement: its multiplication amounts to modular exponentiation; its division amounts to the discrete logarithm problem; the wedge operation amounts to the computational Diffie--Hellman problem. Ring theory is well-developed and implies efficient division algorithms in some specific rings, such as matrix rings over fields. Semigroup theory, though less widely-known, also implies efficient division in specific semigroups, such as group-like semigroups. The rarity of key agreement schemes with well-established security suggests that easy multiplication with difficult division (and wedges) is elusive. Reduction of key agreement to ring or semigroup multiplication is not a panacea for cryptanalysis. Nonetheless, novel proposals for key agreement perhaps ought to run the gauntlet of a checklist for vulnerability to well-known division strategies that generalize across several forms of multiplication. Ambitiously applying this process of elimination to a plethora of diverse rings or semigroups might also, if only by a fluke, leave standing a few promising schemes, which might then deserve a more focused cryptanalysis

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum

Proceedings of the 21st International Congress of Aesthetics, Possible Worlds of Contemporary Aesthetics Aesthetics Between History, Geography and Media

The Faculty of Architecture, University of Belgrade and the Society for Aesthetics of Architecture and Visual Arts of Serbia (DEAVUS) are proud to be able to organize the 21st ICA Congress on “Possible Worlds of Contemporary Aesthetics: Aesthetics Between History, Geography and Media”. We are proud to announce that we received over 500 submissions from 56 countries, which makes this Congress the greatest gathering of aestheticians in this region in the last 40 years. The ICA 2019 Belgrade aims to map out contemporary aesthetics practices in a vivid dialogue of aestheticians, philosophers, art theorists, architecture theorists, culture theorists, media theorists, artists, media entrepreneurs, architects, cultural activists and researchers in the fields of humanities and social sciences. More precisely, the goal is to map the possible worlds of contemporary aesthetics in Europe, Asia, North and South America, Africa and Australia. The idea is to show, interpret and map the unity and diverseness in aesthetic thought, expression, research, and philosophies on our shared planet. Our goal is to promote a dialogue concerning aesthetics in those parts of the world that have not been involved with the work of the International Association for Aesthetics to this day. Global dialogue, understanding and cooperation are what we aim to achieve. That said, the 21st ICA is the first Congress to highlight the aesthetic issues of marginalised regions that have not been fully involved in the work of the IAA. This will be accomplished, among others, via thematic round tables discussing contemporary aesthetics in East Africa and South America. Today, aesthetics is recognized as an important philosophical, theoretical and even scientific discipline that aims at interpreting the complexity of phenomena in our contemporary world. People rather talk about possible worlds or possible aesthetic regimes rather than a unique and consistent philosophical, scientific or theoretical discipline