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Cryptographic methods built using trace zero varieties from algebraic geometry
Frey in 1998, trace zero cryptography refers to the use of trace zero varieties (TZV) for cryptographic purpose.[citation needed] Trace zero varieties are
Trace_zero_cryptography
Hash function that is suitable for use in cryptography
The resistance to such search is quantified as security strength: a cryptographic hash with n {\displaystyle n} bits of hash value is expected to have
Cryptographic_hash_function
German mathematician (born 1944)
contributions to elliptic-curve cryptography. Elliptic curves Fermat's Last Theorem Hyperelliptic curve cryptography Tate pairing Hellegouarch, Yves (1975)
Gerhard_Frey_(mathematician)
Cryptography based on quantum mechanical phenomena
Quantum cryptography is the science of exploiting quantum mechanical properties such as quantum entanglement, measurement disturbance, no-cloning theorem
Quantum_cryptography
Mathematical function
distinguishing cryptographically strong pseudorandom bits from truly random bits) is negligible in terms of the input x {\displaystyle x} = cryptographic key length
Negligible_function
Form of side channel attack
channel attack in which the attacker studies the power consumption of a cryptographic hardware device. These attacks rely on basic physical properties of
Power_analysis
Cryptocurrency aimed at privacy
privacy-focused cryptocurrency which features an encrypted ledger using zero-knowledge proofs. Launched in October 2016, Zcash was developed by cryptographers
Zcash
Arithmetic in a field with a finite number of elements
block codes such as BCH codes and Reed–Solomon error correction, in cryptography algorithms such as the Rijndael (AES) encryption algorithm, in tournament
Finite_field_arithmetic
Linux networking toolkit
lightweight multiuser IP tunnel based on elliptic-curve cryptography astraceroute: an autonomous system trace route utility with Geo-IP information Distribution
Netsniff-ng
American mathematician (born 1947)
understanding of Siegel zeroes, to the ABC conjecture, to modular forms on GL ( n ) {\displaystyle \operatorname {GL} (n)} , and to cryptography (Arithmetica cipher
Dorian_M._Goldfeld
Multi-party secure computation protocol
In cryptography, the anonymous veto network (or AV-net) is a multi-party secure computation protocol to compute the boolean-OR function. It was first proposed
Anonymous_veto_network
Privacy in blockchain systems
off-chain while recording only cryptographic commitments, such as hashes, on-chain. A zero-knowledge proof (ZKP) is a cryptographic method by which one party
Blockchain_privacy
Mathematical idealization of the trace left by a moving point
genus zero. Elliptic curves, which are nonsingular curves of genus one, are studied in number theory, and have important applications to cryptography. Coordinate
Curve
Information Theory by M. Wilde. C. H. Bennett and G. Brassard, “Quantum Cryptography: Public key distribution and coin tossing”, Proceedings of the IEEE International
Channel-state_duality
Hiding messages in other messages
Steganographia, a treatise on cryptography and steganography, disguised as a book on magic. The advantage of steganography over cryptography alone is that the intended
Steganography
Privacy protocol
ensuring more equitable mining among ordinary users. In April 2018, a cryptographic flaw was found in the Zerocoin protocol which allows an attacker to
Zerocoin_protocol
Electronic money corporation founded by David Chaum in 1990
proposed to construct a system of cryptographic protocols, in which a bank or the government would be unable to trace personal payments conducted online
DigiCash
Average uncertainty in variable's states
Pliam, John (1999). "Selected Areas in Cryptography". International Workshop on Selected Areas in Cryptography. Lecture Notes in Computer Science. Vol
Entropy_(information_theory)
Parameter in differential equations and dynamical systems
derivatives in the equation), generally requires k initial conditions to trace the equation's evolution through time. In other contexts, the term may refer
Initial_condition
"Zero" is the usual name for the number 0 in English. In British English "nought" is also used and in American English "naught" is used occasionally for
Names for the number 0 in English
Names_for_the_number_0_in_English
Computational hardness assumption
assumption) is a computational hardness assumption used in elliptic curve cryptography. In particular, the DLIN assumption is useful in settings where the decisional
Decision_Linear_assumption
System that regulates the formation of blocks on a blockchain
work (also written as proof-of-work, and abbreviated PoW) is a form of cryptographic proof in which one party (the prover) proves to others (the verifiers)
Proof_of_work
Computer hardware technology that uses quantum mechanics
applications during World War II; computers played a major role in wartime cryptography, and quantum physics was essential for nuclear physics used in the Manhattan
Quantum_computing
Software for automated reasoning about cryptography
properties of cryptographic protocols. The tool has been developed by Bruno Blanchet and others. Support is provided for cryptographic primitives including:
ProVerif
Secure communication method
distribution (QKD) is a secure communication method that implements a cryptographic protocol based on the laws of quantum mechanics, specifically quantum
Quantum_key_distribution
theory. See also: List of recreational number theory topics Topics in cryptography Composite number Highly composite number Even and odd numbers Parity
List_of_number_theory_topics
Mathematical curves that are isomorphic over algebraic closures
its twists have the same j-invariant. Applications of twists include cryptography, the solution of Diophantine equations, and when generalized to hyperelliptic
Twists_of_elliptic_curves
Physics phenomenon
down-conversion to develop entanglement swapping and demonstrate quantum cryptography with entangled photons. In 2022, the Nobel Prize in Physics was awarded
Quantum_entanglement
Greek cryptographer and computer scientist
and cryptography. From 2003, at the University of Connecticut, Kiayias focused his research on privacy and secure electronic voting using cryptography. In
Aggelos_Kiayias
Algebraic curve in mathematics
curve cryptography (ECC) and integer factorization. An elliptic curve is not an ellipse in the sense of a projective conic, which has genus zero: see elliptic
Elliptic_curve
Technique for anonymous communication over a computer network
able to determine its own location in the chain. Using asymmetric key cryptography, the originator obtains a public key from the directory node to send
Onion_routing
Term in quantum mechanics
correction". arXiv:quant-ph/9606012. C. A. Fuchs and J. van de Graaf, "Cryptographic Distinguishability Measures for Quantum Mechanical States", IEEE Trans
Fidelity_of_quantum_states
Open-source CPU instruction set architecture
are useful for cryptography and CRC checks of data integrity. Done well, a more specialised bit-manipulation subset can aid cryptographic, graphic, and
RISC-V
64-bit extension of the ARM architecture
(Neon) as standard features in both AArch32 and AArch64. It also adds cryptography instructions supporting AES, SHA-1/SHA-256 and finite field arithmetic
AArch64
Study of computation
cryptography include symmetric and asymmetric encryption, digital signatures, cryptographic hash functions, key-agreement protocols, blockchain, zero-knowledge
Computer_science
Malicious software used in ransom demands
encrypts the victim's personal data until a ransom is paid. Difficult-to-trace digital currencies such as paysafecard or Bitcoin and other cryptocurrencies
Ransomware
1941 Japanese crash landing in Hawaii, US
the Pearl Harbor attack, crash-landed his battle-damaged aircraft, an A6M2 Zero "B11-120", from the carrier Hiryu, in a Ni'ihau field near where Hawila Kaleohano
Niʻihau_incident
American-Canadian speculative fiction novelist (born 1948)
Humanities and the Digital Forensics Lab, and Quinn DuPont, a PhD student of cryptography from the University of Toronto, in calling for the aid of cryptographers
William_Gibson
Parallel computing platform and programming model
parallel, such as: cryptographic hash functions machine learning molecular dynamics simulations physics engines The origins of CUDA trace to the early 2000s
CUDA
Array of numbers
and are pure rotations by an angle zero. The complex analog of an orthogonal matrix is a unitary matrix. The trace, tr(A) of a square matrix A is the
Matrix_(mathematics)
coding theory (cyclic redundancy codes and BCH codes), cryptography (public key cryptography by the means of elliptic curves), and computational number
Factorization of polynomials over finite fields
Factorization_of_polynomials_over_finite_fields
prime order group that is suitable for public key cryptography, including Elliptic curve cryptography. Let s {\displaystyle s} be their shared (low-entropy)
Password Authenticated Key Exchange by Juggling
Password_Authenticated_Key_Exchange_by_Juggling
Free and open-source software project for enabling anonymous communication
In 2021, the Tor Project was awarded the Levchin Prize for real-world cryptography. Privacy software Tor Project. "Tor Project Mission Statement". Tor Project
The_Tor_Project
Open-source software
API keys or access tokens. Teleport uses identity-based cryptography to issue cryptographic identities to users, machines, workloads, devices, and protected
Teleport_(software)
Mathematical concept
congruent to zero modulo p {\displaystyle p} . When q = p > 3 {\displaystyle q=p>3} this is equivalent to having the trace of Frobenius equal to zero (by the
Supersingular_elliptic_curve
Mathematics problem
"Puzzles Column", The Emissary, Spring 2004: 3 Richard E. Blahut (2014), Cryptography and Secure Communication, Cambridge University Press, pp. 29–30 Christoph
100_prisoners_problem
K L M N O P Q R S T U V W X Y Z See also References External links 0-day—Zero-day vulnerability 1GL—First-generation programming language 1NF—First normal
List of computing and IT abbreviations
List_of_computing_and_IT_abbreviations
128-bit number used to identify information in computer systems
While the probability that a UUID will be duplicated is not zero, it is close enough to zero to be negligible. Thus, anyone can create large numbers of
Universally_unique_identifier
2010 novel by Hannu Rajeniemi
near-baseline humanity exist on the mobile cities of Mars, where advanced cryptography and an obsessive privacy culture ensure that the Sobornost cannot upload
The_Quantum_Thief
List of x86 microprocessor instructions
USPTO/Zhaoxin, Patent application US2023/006718: Processor with a hash cryptographic algorithm and data processing thereof, pages 13 and 45, Mar 2, 2023
List_of_x86_instructions
Method of externally opening ports on a firewall
combination with knock attempt-limiting, longer or more complex sequences and cryptographic hashes, makes successful port access attempts extremely difficult. Once
Port_knocking
Aspect of quantum information science
{U}}_{D}(\mu )} , are greater than or equal to zero. At least one of the values in the sum of the trace will be positive, the one where D {\textstyle D}
Quantum_energy_teleportation
Special-use top-level internet domain
potentially be valid version 2 addresses (though as the output of a cryptographic hash, a randomly selected string of this form having a corresponding
.onion
Unreproducible object used in digital security
used in applications with high-security requirements, more specifically cryptography, Internet of things (IOT) devices and privacy protection. PUFs can also
Physical_unclonable_function
Cross-platform instant messaging service
has organized two cryptography contests to challenge its own security. Third parties were asked to break the service's cryptography and disclose the information
Telegram_(software)
Files on Jeffrey Epstein and his affiliates
[email protected], spanning from 2002 through 2022. The outlet used cryptographic verification, metadata analysis, and corroboration with external sources
Epstein_files
Branch of physics seeking to explain chaotic dynamical systems in terms of quantum theory
as the ratio of the Planck constant to the action of the system tends to zero. If this is true, then there must be quantum mechanisms underlying classical
Quantum_chaos
compete in solving applied problems related to vulnerability detection, cryptography, malware analysis, and other aspects of information security. The qualifying
Security_Analyst_Summit
Privacy-focused cryptocurrency
markets, ransomware, cryptojacking, and other organized crime. Monero's roots trace back to CryptoNote v2, a cryptocurrency protocol first introduced in a white
Monero
IBM's 64-bit instruction set architecture implemented by its mainframe computers
includes a 64-bit instruction address An 8-KiB prefix storage area (PSA) Cryptographic Facility IEEE Binary-floating-point instructions added by ESA/390 IEEE
Z/Architecture
Process of "purifying" entangled quantum states
and Bob) in order to allow reliable quantum teleportation or quantum cryptography. Entanglement entropy quantifies entanglement. Several different definitions
Entanglement_distillation
Family of RISC-based computer architectures
Armv8-A makes VFPv3/v4 and advanced SIMD (Neon) standard. It also adds cryptography instructions supporting AES, SHA-1/SHA-256 and finite field arithmetic
Arm_architecture_family
Doughnut-shaped surface of revolution
Toric section Toric variety Toroid Toroidal and poloidal Torus-based cryptography Torus knot Umbilic torus Villarceau circles Nociones de Geometría Analítica
Torus
System where only the inputs and outputs can be viewed, and not its implementation
purpose. In cryptography to capture the notion of knowledge obtained by an algorithm through the execution of a cryptographic protocol such as a zero-knowledge
Black_box
Singaporean technology, defence and engineering company
specialises in high-assurance hardware encryption and quantum-safe cryptography, while operating managed Security Operations Centres (SOCs) for critical
ST_Engineering
finite field extension L/K, by using the field trace. This requires the property that the field trace TrL/K provides a non-degenerate quadratic form over
Dual basis in a field extension
Dual_basis_in_a_field_extension
Overview article
originated in earlier releases of Windows. CryptoAPI is replaced by Cryptography API: Next Generation. GINA is succeeded by Credential Providers (with
Security and safety features new to Windows Vista
Security_and_safety_features_new_to_Windows_Vista
Data that remains after deleting it
IEEE Standard for Sanitizing Storage, August 2022 Computer forensics Cryptography Data erasure Data recovery Electronic waste Encryption File deletion
Data_remanence
Digital asset using a distributed ledger
a type of cryptographic electronic money called ecash. Later, in 1995, he implemented it through Digicash, an early form of cryptographic electronic
Cryptocurrency
Major naval battle in the Pacific Theater of World War II
18 A6M2 Zero fighters; Zuikaku 63 total – 21 kankō, 22 kanbaku, 20 Zeros; Shōhō 18 total – 6 kankō, 4 Mitsubishi A5M Type 96 fighters, 8 Zeros (Lundstrom
Battle_of_the_Coral_Sea
Free and open-source anonymity network based on onion routing
technique is called onion routing. Using Tor makes it more difficult to trace a user's internet activity by preventing any single point on the internet
Tor_(network)
Description of a quantum-mechanical system
used instead. A density matrix is a positive semi-definite operator whose trace is equal to 1. (The term "density operator" is also used, particularly when
Schrödinger_equation
Theory of stochastic partial differential equations
the Poincaré–Bendixson theorem. Another object of interest is the sharp trace of the GTO, W = T r ( − 1 ) k ^ M ^ t t ′ = ∑ α ( − 1 ) k α e − ( t − t
Supersymmetric theory of stochastic dynamics
Supersymmetric_theory_of_stochastic_dynamics
Computer malware timeline
Laboratory of Cryptography of Systems Security (CrySyS). 14 October 2011. "Statement on Duqu's initial analysis". Laboratory of Cryptography of Systems Security
Timeline of computer viruses and worms
Timeline_of_computer_viruses_and_worms
are considered precursors to the modern Internet. 1970s: Public-key cryptography is invented and developed by James H. Ellis, Clifford Cocks, Malcolm
Timeline of historic inventions
Timeline_of_historic_inventions
Contact tracing app by the Australian Department of Health
Retrieved 24 June 2020. Apple, Inc (April 2020). "Exposure Notification - Cryptography Specification" (PDF). Apple. Retrieved 22 May 2020. Hendry, Justin (23
COVIDSafe
equestrian trying to make the Olympic team; also the creator of the cryptography code that links computers and secret communications worldwide. Cast :
List of The Six Million Dollar Man episodes
List_of_The_Six_Million_Dollar_Man_episodes
Branch of elementary mathematics
the application of number theory to fields like physics, biology, and cryptography. Influential theorems in number theory include the fundamental theorem
Arithmetic
Virtual marketplace in the darknet
payment services such as PayPal and Western Union allowed law enforcement to trace payments and it was subsequently shut down by the FBI in 2012. The first
Darknet_market
Videoconferencing software
have access to end-to-end encryption after all. On September 7, 2020, cryptography researcher Nadim Kobeissi accused Zoom's security team of failing to
Zoom_(software)
Malicious software
dissertation was on the subject of computer viruses. The combination of cryptographic technology as part of the payload of the virus, exploiting it for attack
Malware
Currency stored on electronic systems
is a sub-type of digital currency and a digital asset that relies on cryptography to chain together digital signatures of asset transfers, peer-to-peer
Digital_currency
Integer side lengths of a right triangle
square divisible by 16. Primitive Pythagorean triples have been used in cryptography as random sequences and for the generation of keys. Boolean Pythagorean
Pythagorean_triple
Process in quantum computing
P_{i}X_{i}.} Note that, while this procedure perfectly corrects the output when zero or one flips are introduced by the channel, if more than one qubit is flipped
Quantum_error_correction
Unique digital identifier that is recorded on a blockchain
confers little more than use as a status symbol. NFTs function like cryptographic tokens, but unlike cryptocurrencies, NFTs are not usually mutually interchangeable
Non-fungible_token
American international information security company
under the names Whoppix, IWHAX, and Auditor. It was designed to delete any trace of its usage. The distribution was widely known and used by security experts
Offensive_Security
Elementary particle with negative charge
known as nucleosynthesis, forming isotopes of hydrogen and helium, with trace amounts of lithium. This process peaked after about five minutes. Any leftover
Electron
Formulation of classical mechanics
for a definite integral to be zero is if the integrand equals zero, each of the coefficients of δqj must also be zero. Then we obtain the equations of
Lagrangian_mechanics
Marked objects for finding random numbers
Dice can be used to generate random numbers for use in passwords and cryptography applications. The Electronic Frontier Foundation describes a method by
Dice
Measure of a civilization's evolution
pristine—supporting a flourishing natural biosphere, with little or no visible trace of industry or artificial modification. Transhumanists Paul Hughes and John
Kardashev_scale
Processor register which changes or controls the general behavior of a CPU
priority and the remaining 60 bits are reserved and must be written with zeros. System software can use the TPR register to temporarily block low-priority
Control_register
Malware
files stored on local and mounted network drives using RSA public-key cryptography, with the private key stored only on the malware's control servers. The
CryptoLocker
Mass surveillance program run by the NSA
spokesperson Zabiullah Mujahid said, "We knew about their past efforts to trace our system. We have used our technical resources to foil their efforts and
PRISM
Branch of mathematics
geometry. Algebraic geometry has applications in many areas, including cryptography and string theory. Complex geometry studies the nature of geometric structures
Geometry
Modular computer malware discovered in 2012
the Iranian National CERT, Kaspersky Lab and CrySyS Lab (Laboratory of Cryptography and System Security) of the Budapest University of Technology and Economics
Flame_(malware)
Protection of computer systems from information disclosure, theft or damage
the access of individuals using user account access controls and using cryptography can protect systems files and data, respectively. Firewalls are by far
Computer_security
On generating functions from counting points on algebraic varieties over finite fields
Chapter 6, Theorem 5.1 in Koblitz, Neal (7 May 2004). Algebraic Aspects of Cryptography. Springer. p. 146. ISBN 3-540-63446-0. Chapter 7, Paragraph §7B in Mumford
Weil_conjectures
Structure of Bipartite Quantum States - Insights from Group Theory and Cryptography". arXiv:quant-ph/0604183. Cambridge PhD thesis. Hay03 Patrick Hayden;
Squashed_entanglement
Form of social engineering
28, 2006. "GP4.3 – Growth and Fraud — Case #3 – Phishing". Financial Cryptography. December 30, 2005. Archived from the original on January 22, 2019. Retrieved
Phishing
1945 attacks in Japan during WWII
as the Genbaku (A-bomb) dome, which was only 150 m (490 ft) from ground zero (the hypocenter). The ruin was named Hiroshima Peace Memorial and was made
Atomic bombings of Hiroshima and Nagasaki
Atomic_bombings_of_Hiroshima_and_Nagasaki
TRACE ZERO-CRYPTOGRAPHY
TRACE ZERO-CRYPTOGRAPHY
Male
Finnish
Short form of Finnish Antero, TERO means "man; warrior."
Surname or Lastname
English
English : perhaps a variant of Treece.
Male
Finnish
Finnish form of German Erich, EERO means "ever-ruler."Â
Male
Italian
 Short form of Italian Raniero, NERO means "wise warrior." Compare with another form of Nero.
Female
English
Feminine variant spelling of English unisex Tracy, TRACEE means "place of Thracius."
Girl/Female
Latin American English Irish
Grace.
Girl/Female
American, Arabic, Australian, British, Chinese, Christian, Danish, English, French, German, Gujarati, Indian, Irish, Jamaican, Latin, Muslim, Portuguese, Swedish
Mercy; God's Favor; Grace; Grace of God; Kindness; Thanks; Love; Favour; Blessing; Charm; Good will
Male
English
Short form of English unisex Tracy, TRACE means "place of Thracius."
Surname or Lastname
English
English : probably from Middle English, Old French brace ‘arm’, also denoting a piece of armor covering the arm. In most cases it is probably a metonymic occupational name for a maker or seller of armor, specifically armor designed to protect the upper arms, but it could also have been a nickname for someone with strong arms (compare Armstrong) or a deformed or otherwise noticeable arm.
Female
English
Feminine variant spelling of English unisex Tracy, TRACIE means "place of Thracius."
Surname or Lastname
English
English : nickname from Middle English, Old French grace ‘charm’, ‘pleasantness’ (Latin gratia).English : from the female personal name Grace, which was popular in the Middle Ages. This seems in the first instance to have been from a Germanic element grīs ‘gray’ (see Grice 1), but was soon associated by folk etymology with the Latin word meaning ‘charm’.
Female
English
Feminine variant spelling of English unisex Tracy, TRACI means "place of Thracius."
Boy/Male
American, Anglo, Australian, British, Chinese, English, French
Fighter; Brave
Female
Greek
(ἩÏá½¼) Greek name derived form the word hÄ“rÅs, HERO means "hero." In mythology, this is the name of the lover of Leandros (Latin Leander).
Boy/Male
Arabic, Australian, German, Greek, Kurdish
Empty; Void
Male
English
English surname transferred to unisex forename use, from a Norman baronial name TRACY means "place of Thracius."
Boy/Male
Anglo Saxon American English French
Brave.
Male
Spanish
Spanish name derived from Latin juniperus, JUNÃPERO means "juniper tree."
Male
English
Variant spelling of English unisex Tracy, TRACEY means "place of Thracius."
Boy/Male
Arabic
Empty.
TRACE ZERO-CRYPTOGRAPHY
TRACE ZERO-CRYPTOGRAPHY
Girl/Female
Hindu, Indian, Tamil, Telugu
Rising of End
Boy/Male
Indian, Sanskrit
Liberal
Boy/Male
Indian, Sanskrit
Whitish; Washed; Purified
Surname or Lastname
English (Lancashire, Cheshire)
English (Lancashire, Cheshire) : unexplained; perhaps of Irish origin, a variant of Kehir, Keher, Munster and Connacht variants of Cahir, an Anglicized form of Gaelic Ó Cathaoir, from an old Irish personal name.
Boy/Male
Tamil
Jewel
Boy/Male
Tamil
Adviteeya | அதà¯à®µà®¿à®¤à®¿à®¯
Unique, The first one. no second, The Sun or one which has no end
Surname or Lastname
English
English : variant of Highley.
Girl/Female
Hindu
Goddess
Girl/Female
Indian
Polite, Obedience
Boy/Male
Indian
Radiating the beauteous light, Matchless light, Flame
TRACE ZERO-CRYPTOGRAPHY
TRACE ZERO-CRYPTOGRAPHY
TRACE ZERO-CRYPTOGRAPHY
TRACE ZERO-CRYPTOGRAPHY
TRACE ZERO-CRYPTOGRAPHY
n.
A large and valuable fish of the Mackerel family, of the genus Scomberomorus. Two species are found in the West Indies and less commonly on the Atlantic coast of the United States, -- the common cero (Scomberomorus caballa), called also kingfish, and spotted, or king, cero (S. regalis).
v. t.
A mark left by anything passing; a track; a path; a course; a footprint; a vestige; as, the trace of a carriage or sled; the trace of a deer; a sinuous trace.
v. t.
To follow the tracks or traces of; to pursue by following the marks of the feet; to trace; to trail; as, to track a deer in the snow.
v. t.
To add grace notes, cadenzas, etc., to.
v. t.
To trace out; to track; also, to draw out; to protact.
n.
One who, or that which, traces.
n.
A mark or impression left by the foot, either of man or beast; trace; vestige; footprint.
v.
The trade winds.
pl.
of Zero
v. t.
Hence, to follow the trace or track of.
v. t.
To supply with heavenly grace.
n.
Fig.: The lowest point; the point of exhaustion; as, his patience had nearly reached zero.
v. t.
To run a race with.
n.
A mark left by something that has passed along; as, the track, or wake, of a ship; the track of a meteor; the track of a sled or a wheel.
n.
A tract or area, as of land.
v. t.
To mark out; to draw or delineate with marks; especially, to copy, as a drawing or engraving, by following the lines and marking them on a sheet superimposed, through which they appear; as, to trace a figure or an outline; a traced drawing.
v. t.
To cause to contend in a race; to drive at high speed; as, to race horses.
n.
Course; way; as, the track of a comet.
v.
Track; trace.
imp. & p. p.
of Trace