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Lattice in universal algebra
universal algebra, Post's lattice denotes the lattice of all clones on a two-element set {0, 1}, ordered by inclusion. It is named for Emil Post, who published
Post's_lattice
Cryptographic primitives that involve lattices
construction itself or in the security proof. Lattice-based constructions support important standards of post-quantum cryptography. Unlike more widely used
Lattice-based_cryptography
Set whose pairs have minima and maxima
A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra. It consists of a partially ordered
Lattice_(order)
Optimization problem in computer science
In computer science, lattice problems are a class of optimization problems related to mathematical objects called lattices. The conjectured intractability
Lattice_problem
Semiconductor company
Lattice Semiconductor Corporation is an American semiconductor company specializing in the design and manufacturing of low-power field-programmable gate
Lattice_Semiconductor
Type of observation mast on warships
observation and to spot fall of shot. The purpose of the lattice structure was to make the posts less vulnerable to shells from enemy ships, and to better
Lattice_mast
Mathematical operation
mathematics, the goal of lattice basis reduction is to find a basis with short, nearly orthogonal vectors when given an integer lattice basis as input. This
Lattice_reduction
Project by NIST to standardize post-quantum cryptography
over NTRU-Lattice-Based Digital Signature Algorithm. On March 11, 2025 NIST released Hamming Quasi-Cyclic (HQC) as the fifth algorithm for post-quantum
NIST Post-Quantum Cryptography Standardization
NIST_Post-Quantum_Cryptography_Standardization
Mathematical object
discrete mathematics, ideal lattices are a special class of lattices and a generalization of cyclic lattices. Ideal lattices naturally occur in many parts
Ideal_lattice
Cryptography secured against quantum computers
indicated that NTRU may have more secure properties than other lattice based algorithms. Two lattice-based algorithms, ML-KEM (commonly known as Kyber) and ML-DSA
Post-quantum_cryptography
Class of computational fluid dynamics methods
The lattice Boltzmann methods (LBM), originated from the lattice gas automata (LGA) method (Hardy-Pomeau-Pazzis and Frisch-Hasslacher-Pomeau models), is
Lattice_Boltzmann_methods
Computational problem used in cryptography
problems are two average-case problems that are used in lattice-based cryptography constructions. Lattice-based cryptography began in 1996 from a seminal work
Short integer solution problem
Short_integer_solution_problem
Concept in universal algebra in mathematics
considered). The lattice of clones on a two-element set is countable, and has been completely described by Emil Post (see Post's lattice, which traditionally
Clone_(algebra)
American mathematician and logician (1897 – 1954)
Emil Leon Post (/poʊst/; February 11, 1897 – April 21, 1954) was an American mathematician and logician. He is best known for his work in the field that
Emil_Leon_Post
Freestanding framework tower
A lattice tower, or truss tower, is a freestanding vertical framework tower. This construction is widely used in transmission towers carrying high-voltage
Lattice_tower
True when either but not both inputs are true
{y}})\cdot (x+y)} Zhegalkin polynomial x ⊕ y {\displaystyle x\oplus y} Post's lattices 0-preserving yes 1-preserving no Monotone no Affine yes Self-dual no
Exclusive_or
American writer and public speaker
and contains several new ideas, including Integral post-metaphysics and the Wilber-Combs lattice. In 2006, he published "Integral Spirituality", in which
Ken_Wilber
Quantum-safe key encapsulation mechanism
ML-KEM (Module-Lattice-Based Key-Encapsulation Mechanism), also known by its original name Kyber, is a key encapsulation mechanism (KEM) designed to be
ML-KEM
Historic house in Massachusetts, United States
typical of Queen Anne houses. It has a wraparound porch with turned posts, lattice railing, and a sunburst motif in the gabled pediment above the steps
Henry_N._Fisher_House
Digital signature resilient to quantum cryptography
hard problems in lattices are being created to replace the commonly used RSA and elliptic curve signatures. A subset of these lattice based scheme are
Ring learning with errors signature
Ring_learning_with_errors_signature
American defense technology company
border system. In June 2018, Lattice surveillance towers were informally tested on a Texas rancher's private land. Lattice was operated remotely by an
Anduril_Industries
Historic site in Queensland, Australia
with thick sills from which extend the verandah posts. Lattice infill panels are fixed in between the posts below arched valences. The main roof is clad
Monkton,_Brisbane
Logical connective AND
the short-circuit and control structure; In set theory, intersection. In lattice theory, logical conjunction (greatest lower bound). And is usually denoted
Logical_conjunction
Concept in cryptography
a set of post-quantum cryptographic algorithms which are based on the difficulty of solving certain mathematical problems involving lattices. Unlike older
Ring learning with errors key exchange
Ring_learning_with_errors_key_exchange
Cryptographic method
acronym for Fast Fourier lattice-based compact signatures over NTRU. It was selected by the NIST at the fourth round of the post-quantum standardisation
Falcon_(signature_scheme)
Concept in mathematical logic
,\wedge ,\bot ,\nrightarrow ,\nleftrightarrow } . Post gave a complete description of the lattice of all clones (sets of operations closed under composition
Functional_completeness
System of logic lacking the excluded middle law
= (A, ∨, ∧, 0, 1, ¬) such that: (A, ∨, ∧, 0, 1) is a bounded distributive lattice, and ¬ is a De Morgan involution: ¬(x ∧ y) = ¬x ∨ ¬y and ¬¬x = x. (i.e
De_Morgan_algebra
Computational problem possibly useful for post-quantum cryptography
(and all other lattice problems) in ideal lattices is as hard as in regular lattices." The difficulty of these problems on regular lattices is provably NP-hard
Ring_learning_with_errors
Logical connective OR
Zhegalkin polynomial x ⊕ y ⊕ x y {\displaystyle x\oplus y\oplus xy} Post's lattices 0-preserving yes 1-preserving yes Monotone yes Affine no Self-dual
Logical_disjunction
Logical operation
Metaphysics Research Lab, Stanford University, retrieved 2024-03-22 Emil Leon Post (1941). The Two-Valued Iterative Systems of Mathematical Logic. Annals of
Sheffer_stroke
Binary operation that is true if and only if both operands are false
polynomial 1 ⊕ x ⊕ y ⊕ x y {\displaystyle 1\oplus x\oplus y\oplus xy} Post's lattices 0-preserving no 1-preserving no Monotone no Affine no Self-dual no
Logical_NOR
Outdoor garden feature forming a shaded walkway
passageway, or sitting area of vertical posts or pillars that usually support crossbeams and a sturdy open lattice, often upon which woody vines are trained
Pergola
Post-quantum signature scheme
BLISS (short for Bimodal Lattice Signature Scheme) is a digital signature scheme proposed by Léo Ducas, Alain Durmus, Tancrède Lepoint and Vadim Lyubashevsky
BLISS_signature_scheme
In mathematics, the Barnes–Wall lattice B W 16 {\displaystyle BW_{16}} , discovered by Eric Stephen Barnes and G. E. (Tim) Wall, is the 16-dimensional
Barnes–Wall_lattice
Public-key cryptosystem that uses lattice-based cryptography
NTRU is an open-source public-key cryptosystem that uses lattice-based cryptography to encrypt and decrypt data. It consists of two algorithms: NTRUEncrypt
NTRU
Logical operation
{\displaystyle \lnot {x}} Zhegalkin polynomial 1 ⊕ x {\displaystyle 1\oplus x} Post's lattices 0-preserving no 1-preserving no Monotone no Affine yes Self-dual yes
Negation
Type of connective in logic
Zhegalkin polynomial q p ⊕ q r ⊕ r {\displaystyle qp\oplus qr\oplus r} Post's lattices 0-preserving yes 1-preserving yes Monotone no Affine no Self-dual no
Conditioned_disjunction
Indices. May 10, 2021. Retrieved May 19, 2021. "PTC Set to Join S&P 500; Lattice Semiconductor & Progyny to Join S&P MidCap 400; Domtar to Join S&P SmallCap
List_of_S&P_500_companies
Kind of microscopy
Lattice light-sheet microscopy is a modified version of light sheet fluorescence microscopy that increases image acquisition speed while decreasing damage
Lattice light-sheet microscopy
Lattice_light-sheet_microscopy
Logical connective
Zhegalkin polynomial 1 ⊕ x ⊕ x y {\displaystyle 1\oplus x\oplus xy} Post's lattices 0-preserving no 1-preserving yes Monotone no Affine no Self-dual no
Material_conditional
Series of programmable-logic devices from Lattice Semiconductor
The GAL22V10 is a series of programmable-logic devices from Lattice Semiconductor, implemented as CMOS-based generic array logic ICs, and available in
GAL22V10
Indices. April 27, 2021. Retrieved June 3, 2021. "PTC Set to Join S&P 500; Lattice Semiconductor & Progyny to Join S&P MidCap 400; Domtar to Join S&P SmallCap
List_of_S&P_400_companies
rustication. Verandah with hipped ogee roof, fretwork fringe, square wooden posts and lattice work railing. 4 panel single door (Edwardian type) with plain fanlight
List of heritage sites in Graaff-Reinet
List_of_heritage_sites_in_Graaff-Reinet
Iranian-made drone
Industries, which uses a suite of sensors powered by the company's AI Lattice system to detect and track threats, then passes information to Anvil interceptors
HESA_Shahed_136
Public-key cryptosystem
Mathematics: 167–226. doi:10.1137/S0097539702403773. FIPS 203: Module-Lattice-Based Key-Encapsulation Mechanism Standard (PDF), NIST, 2024-08-13, doi:10
Key_encapsulation_mechanism
Tree data structure that partitions a 2D area
insertion have been studied under the name weighted planar stochastic lattices. Point quadtrees are constructed as follows. Given the next point to insert
Quadtree
Logical operator in propositional calculus
{y}})} Zhegalkin polynomial 1 ⊕ x ⊕ y {\displaystyle 1\oplus x\oplus y} Post's lattices 0-preserving no 1-preserving yes Monotone no Affine yes Self-dual no
Logical_equality
3D computer graphics software
used for simulating liquids, like water being poured into a cup. It uses Lattice Boltzmann methods (LBM) to simulate fluids and allows for plenty of adjustment
Blender_(software)
Clock that monitors the resonant frequency of atoms
clocks such as trapped-ion or fountain clocks, and optical clocks such as lattice clocks, use a sequential interrogation protocol[clarification needed] rather
Atomic_clock
(PDF). April 27, 2021. Retrieved May 5, 2021. "PTC Set to Join S&P 500; Lattice Semiconductor & Progyny to Join S&P MidCap 400; Domtar to Join S&P SmallCap
List_of_S&P_600_companies
fact several allusions are made to dove-cotes, with their "windows" or latticed openings. But in olden times as well as now, besides the legions of pigeons
Animals_in_the_Bible
Mountain pass and archaeological site in Colorado, USA
near the top of the peak along with the leg stubs used for the beacon's lattice tower. There have been many documented airplane and helicopter crashes
Rollins_Pass
Improvised armor developed during Russo-Ukrainian war
"mangals" in Russian and Ukrainian or "cope cages" in English) refer to metal lattices that surround ground military vehicles to provide additional protection
Anti-drone_mesh
Algorithm for public-key cryptography
Ed25519 Ed448 ECMQV EKE ElGamal signature scheme MQV Schnorr SPEKE SRP STS Lattice/SVP/CVP/LWE/SIS BLISS Kyber NewHope NTRUEncrypt NTRUSign RLWE-KEX RLWE-SIG
RSA_cryptosystem
Structure used to support an overhead power line
tall structure used to support an overhead power line. It is usually a lattice or tubular tower made of steel. In electrical grids, transmission towers
Transmission_tower
German-born theoretical physicist (1879–1955)
1926. In 1907, Einstein proposed a model of matter where each atom in a lattice structure is an independent harmonic oscillator. In the Einstein model
Albert_Einstein
Physical phenomenon
During nuclear magnetic resonance observations, spin–lattice relaxation is the mechanism by which the longitudinal component of the total nuclear magnetic
Spin–lattice_relaxation
Defensive wall in Bronze and Iron Age hill forts
characterized by vertical wooden posts set into the front stone facing. The rampart is constructed from a timber lattice filled with earth or rubble. The
Pfostenschlitzmauer
Steel lattice television tower in Dudelange
steel framework FM radio and television transmission tower, also called a lattice tower, with a triangular cross section located near Dudelange in Luxembourg
Dudelange_Radio_Tower
Digital signature scheme
Ed25519 Ed448 ECMQV EKE ElGamal signature scheme MQV Schnorr SPEKE SRP STS Lattice/SVP/CVP/LWE/SIS BLISS Kyber NewHope NTRUEncrypt NTRUSign RLWE-KEX RLWE-SIG
Merkle_signature_scheme
Tower in Paris, France
Eiffel Tower (/ˈaɪfəl/ EYE-fəl; French: Tour Eiffel [tuʁ ɛfɛl] ) is a lattice tower on the Champ de Mars in Paris, France. It is named after the engineer
Eiffel_Tower
Method of exchanging cryptographic keys
problem, the discrete logarithm problem, and the period-finding problem. A post-quantum variant of Diffie-Hellman algorithm was proposed in 2023, and relies
Diffie–Hellman_key_exchange
Chemical element with atomic number 82 (Pb)
conductivity was not recorded. Diamond cubic structures with lattice parameters around the lattice parameter of silicon exists both in thin lead and tin films
Lead
Mathematics award
Mathematics" Archived 23 May 2013 at the Wayback Machine, The Jerusalem Post Fuller-Wright, Liz (5 July 2022). "Princeton mathematician June Huh awarded
Fields_Medal
United States historic place
additional supports added in the 19th and 20th centuries. Built with a Town lattice design, the bridge has reinforced trusswork visible on the interior. At
Bull's_Bridge
Topics referred to by the same term
Module-Lattice cryptography: ML-DSA, the Module-Lattice-Based Digital Signature Standard for post-quantum cryptography ML-KEM, the Module-Lattice-Based
ML
Panel made by weaving branches
Wattle is a lattice made by weaving flexible branches around upright stakes. The wattle may be made into an individual panel, commonly called a hurdle
Wattle_(construction)
Proposed superconducting material
"Cu-doped Pb10(PO4)6O, and V doped SrTiO3 -- a tutorial on electron-crystal lattice coupling in insulating materials with transition metal dopants". arXiv:2308
LK-99
Class of membrane-less organelles within biological cells
PMC 10107566. PMID 37359769. Choi, J.M.; Dar, F.; Pappu, R.V. (2019). "LASSI: A lattice model for simulating phase transitions of multivalent proteins". PLOS Computational
Biomolecular_condensate
Form of carbon
nitrogen). Small numbers of defects or impurities—about one per million of lattice atoms—can color a diamond blue (boron), yellow (nitrogen), brown (defects)
Diamond
Electricity generation by nuclear fusion
fusion power included using bombs to initiate reactions. See Project PACER. Lattice confinement fusion (LCF): Deuteron-saturated metals are exposed to gamma
Fusion_power
2025 play by Conor McPherson
It contains London's largest hydraulic stage and its ceiling contains a lattice of metal rods capable of supporting up to four tonnes. Audience seats—some
The_Hunger_Games:_On_Stage
United States historic place
and lattice below. The vertical posts are made of two channels connected by lattice bracing connecting them on both sides. Struts connecting the posts are
State Street Bridge (Bridgeport, Michigan)
State_Street_Bridge_(Bridgeport,_Michigan)
Equation in Fourier analysis
^{n})} (L1 for L1 space) and Λ {\displaystyle \Lambda } is a unimodular lattice in R n {\displaystyle \mathbb {R} ^{n}} . Then the periodization of f {\displaystyle
Poisson_summation_formula
Prefecture and commune in France
Toulouse is the home of Bonhoure Radio Tower, a 61-metre-tall (200 ft) lattice tower used for FM and TV transmission. In 2001 a 100-kilometre (62 mi)
Toulouse
US AI military intelligence program
2024 Anduril and Palantir announced a consortium that links Anduril's Lattice Mesh with Maven Smart System and Palantir's AI Platform to move tactical
Project_Maven
Town lattice Kesler Covered Bridge Homer, Banks County 1925 (Collapsed between 1978-1981) 69 feet (21 m) Broad River King post to one side, Queen post to
List of covered bridges in Georgia
List_of_covered_bridges_in_Georgia
Season of television series
Display) Result Cristy Creamy Mushroom & Leek Picnic Pies 5th 'Autumnal Lattice' Decorative Pies Star Baker Dan Lamb Keema Picnic Pies 1st 'Journey Around
The Great British Bake Off series 14
The_Great_British_Bake_Off_series_14
Bridge whose load-bearing superstructure is composed of a truss
bridge to protect the structure. In 1820, a simple form of truss, Town's lattice truss, was patented, and had the advantage of requiring neither high labor
Truss_bridge
IEEE standardization project for public-key cryptography
Traditional public-key cryptography (IEEE Std 1363-2000 and 1363a-2004) Lattice-based public-key cryptography (IEEE Std 1363.1-2008) Password-based public-key
IEEE_P1363
Asymmetric encryption algorithm developed by Robert McEliece
much acceptance in the cryptographic community, but is a candidate for "post-quantum cryptography", as it is immune to attacks using Shor's algorithm
McEliece_cryptosystem
Palace and fortress complex in Granada, Spain
room is also covered by a unique vault ceiling consisting of a wooden lattice shaped into an interlacing geometric motif and filled with pieces of coloured
Alhambra
Rigid structure that consists of two-force members only
lower aerodynamic drag. American architect Ithiel Town designed Town's Lattice Truss as an alternative to heavy-timber bridges. His design, patented in
Truss
Song
Open Thy Lattice Love was a song composed by Stephen Foster on February 1, 1844, in Pittsburgh, Pennsylvania. Susan E. Robinson was the last remaining
Open_Thy_Lattice_Love_(song)
Ed25519 Ed448 ECMQV EKE ElGamal signature scheme MQV Schnorr SPEKE SRP STS Lattice/SVP/CVP/LWE/SIS BLISS Kyber NewHope NTRUEncrypt NTRUSign RLWE-KEX RLWE-SIG
Niederreiter_cryptosystem
Japanese and English actress (born 1986)
featuring Beck, where she played a dancer gradually transformed into a 3-D lattice. Later that year she appeared in the music video for Frank Ocean's song
Sonoya_Mizuno
Bridge in Piedmont, Alabama
(19-meter) covered bridge was a rare construction of Multiple King-post truss with Town Lattice over a single span. The Coldwater Covered Bridge, also located
Tallahatchee_Covered_Bridge
French viennoiserie
Knafeh Kitchener bun Klobásník Knieküchle Kolach Kroštule Kürtőskalács Lattice Leipziger Lerche London Cheesecake Lukhmi Ma'amoul Mandelkubb Mantecada
Pain_au_chocolat
History of Istanbul under Ottoman rule
(sometimes the sultan attended, observing from a small lodge separated by a lattice, allowing him to see and hear everything while remaining unseen). Initially
Istanbul during the Ottoman Empire
Istanbul_during_the_Ottoman_Empire
Marble mausoleum in Agra, India
stars made of red sandstone, surrounded by a border. The building has many lattice windows or jalis with interlocking hexagonal patterns. The gateway arches
Taj_Mahal
Method for evaluating stock options that divides time into discrete intervals
In quantitative finance, a lattice model is a numerical approach to the valuation of derivatives in situations requiring a discrete time model. For dividend
Lattice_model_(finance)
In computational and mathematical biology, a biological lattice-gas cellular automaton (BIO-LGCA) is a discrete model for moving and interacting biological
BIO-LGCA
Communications tower in London, England
part of the GPO microwave network. It replaced a shorter, 1940s steel lattice tower on the roof of the Museum Telephone Exchange, so named for its proximity
BT_Tower
Lattice-based public key cryptosystem
is an NTRU lattice-based alternative to RSA and elliptic curve cryptography (ECC) and is based on the shortest vector problem in a lattice (which is not
NTRUEncrypt
Akita dog known for his loyalty (1923–1935)
grave is enclosed by a lattice fence made of bamboo.[298] Also, just outside his grave, at the right front corner of the lattice fence, is erected the
Hachikō
Hexagonal lattice allotrope of carbon
structure, is an allotrope of carbon with a hexagonal lattice, as opposed to the cubical lattice of conventional diamond. It is found in nature in meteorite
Lonsdaleite
Set of cryptographic algorithms by the NSA
and the overall delivery and timing of the announcement, in the absence of post-quantum standards, raised considerable speculation about whether NSA had
Commercial National Security Algorithm Suite
Commercial_National_Security_Algorithm_Suite
10 million ounces of gold resource. The gold occurs within the crystal lattice of arsenopyrite associated with other metal sulfides in veins, veinlets
Gold_mining_in_Alaska
Digital signature scheme
Ed25519 Ed448 ECMQV EKE ElGamal signature scheme MQV Schnorr SPEKE SRP STS Lattice/SVP/CVP/LWE/SIS BLISS Kyber NewHope NTRUEncrypt NTRUSign RLWE-KEX RLWE-SIG
Schnorr_signature
German physicist (1901–1976)
paper on electrodynamics in 1912 and Born had used them in his work on the lattice theory of crystals in 1921. While matrices were used in these cases, the
Werner_Heisenberg
POSTS LATTICE
POSTS LATTICE
Girl/Female
Biblical
The posts of a door, splendor, beauty.
Boy/Male
Tamil
King of poets, Name of Lord Ganesh
Surname or Lastname
English and Scottish
English and Scottish : patronymic from Pott 1, particularly common in northeastern England.
Boy/Male
Indian
Pillar, Post, Support
Girl/Female
Hindu, Indian, Marathi
Post; Pillar; A Goddess
Boy/Male
Indian, Tamil
King of Poets
Girl/Female
Tamil
One who poses all best qualities
Girl/Female
Tamil
Lord of poets, Lord Ganesh, Small poem
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Lord of Poets; Lord Ganesha
Biblical
the posts of a door; splendor; beauty
Boy/Male
African, Arabic, Muslim, Swahili
Support; Pillar; Post
Girl/Female
Greek
Favorite name with poets.
Boy/Male
Indian, Sanskrit
Lord of Poets
Girl/Female
Hindu
One who poses all best qualities
Boy/Male
Indian, Sanskrit
Lord of Poets
Boy/Male
Muslim
Pillar, Post, Support
Boy/Male
Indian, Sanskrit
Moon of Poets
Boy/Male
Muslim
Pillar, Post, Support
Boy/Male
Biblical
Lord of hosts.
Boy/Male
Indian
Pillar, Post, Support
POSTS LATTICE
POSTS LATTICE
POSTS LATTICE
POSTS LATTICE
POSTS LATTICE
POSTS LATTICE
POSTS LATTICE
a.
After death; as, post-mortem rigidity.
v. i.
To travel with post horses; figuratively, to travel in haste.
n.
A station, or one of a series of stations, established for the refreshment and accommodation of travelers on some recognized route; as, a stage or railway post.
n.
Same as King-post.
n.
A piece of timber, metal, or other solid substance, fixed, or to be fixed, firmly in an upright position, especially when intended as a stay or support to something else; a pillar; as, a hitching post; a fence post; the posts of a house.
v. t.
To hold up to public blame or reproach; to advertise opprobriously; to denounce by public proclamation; as, to post one for cowardice.
n.
An established conveyance for letters from one place or station to another; especially, the governmental system in any country for carrying and distributing letters and parcels; the post office; the mail; hence, the carriage by which the mail is transported.
v. t.
To carry, as an account, from the journal to the ledger; as, to post an account; to transfer, as accounts, to the ledger.
v. t.
To place in the care of the post; to mail; as, to post a letter.
n.
A station, office, or position of service, trust, or emolument; as, the post of duty; the post of danger.
v. t.
To assign to a station; to set; to place; as, to post a sentinel.
n.
See under 4th Post.
v. t.
To attach to a post, a wall, or other usual place of affixing public notices; to placard; as, to post a notice; to post playbills.
n.
One who posts bills; a billposter.
adv.
With post horses; hence, in haste; as, to travel post.
n.
One of two suspending posts in a roof truss, or other framed truss of similar form. See King-post.
n.
A post (generally a pillar of iron) supporting a lamp or lantern for lighting a street, park, etc.
n.
A post-temporal bone.