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Showing 1–30 of 204 reference entries

Physics · Information · MeasurementScientific records

Build an inspectable physics record, test and revise a bounded cart model, preserve processing history, and plan findable data with appropriate sharing conditions.

MethodMathematics & logic · InformationClassical propositions and connectives

Classical logic combines truth-valued propositions using defined connectives.

DefinitionMathematics & logic · InformationSets, membership and basic operations

A set specifies membership without counting duplicate listings.

DefinitionMathematics & logic · InformationFunctions, domain and codomain

A function assigns exactly one output to each input in its domain.

DefinitionMathematics & logic · InformationMathematical induction

A base case and general successor step establish a predicate on all nonnegative integers.

MethodMathematics & logic · InformationComplex numbers

A complex number has real coordinates a and b and an imaginary unit satisfying i²=−1.

DefinitionMathematics & logic · Information · PhysicsLinear maps and matrix representation

A linear map preserves linear combinations and has a matrix once bases are chosen.

DefinitionMathematics & logic · InformationProbability space and axioms

A probability assigns nonnegative, normalised, countably additive weights to events.

DefinitionMathematics & logic · InformationConditional probability and independence

Conditioning restricts attention to an event of positive probability.

DefinitionMathematics & logic · InformationExpected value of a discrete random variable

Expected value weights possible values by their probabilities.

DefinitionInformation · Mathematics & logicBits and unsigned binary encoding

A bit has two possible states; a fixed-width unsigned binary word encodes an integer.

DefinitionInformation · Mathematics & logicShannon entropy of a discrete distribution

Shannon entropy measures uncertainty in a specified probability distribution.

DefinitionInformationAlgorithm and decision procedure

An algorithm specifies effective steps; a decision procedure must terminate on every permitted input.

MethodInformation · Mathematics & logicUndecidability of the halting problem

No total algorithm decides halting for every program and input in a general computation model.

Mathematical statementInformation · Mathematics & logicAsymptotic upper bounds and big O

Big O bounds eventual growth up to a fixed constant factor.

DefinitionInformationFinite-alphabet mutual information

Mutual information measures statistical dependence in bits.

DefinitionInformationNear-lossless source coding threshold

Entropy bounds asymptotic compression for an iid source.

Mathematical statementInformationDiscrete memoryless channel capacity

Capacity is the maximal asymptotically reliable rate.

Mathematical statementInformationHamming distance and error correction

Separated codewords permit bounded symbol-error recovery.

Mathematical statementInformationInternet protocol layers

Protocol layers divide communication responsibilities.

DefinitionInformationTCP reliable byte-stream transport

TCP orders bytes and retransmits detected losses.

MethodInformationEncryption, hashes and message authentication

Cryptographic primitives serve distinct security properties.

DefinitionInformationPublic-key digital signatures

A signing key and a verification key have different roles.

DefinitionInformationComputable reductions and undecidability

Reduction direction determines which impossibility transfers.

Mathematical statementInformationDecision classes P and NP

Polynomial solving and polynomial verification differ.

DefinitionInformationNP-hardness and NP-completeness

NP-completeness combines verification and reduction hardness.

DefinitionInformationBounded-error randomized computation

Random choices permit a stated probability of error.

DefinitionInformationFinite graphs and trees

Graphs represent pairwise connections; trees impose acyclicity.

DefinitionInformationData-structure interfaces and operation costs

An interface defines operations; an implementation determines costs.

MethodInformationLoop invariants and total correctness

An invariant establishes correctness only with its proof obligations.

Method
DefinitionSource checked

Public-key digital signatures

Information

A signing key and a verification key have different roles.

Key knowledge

A digital signature is generated using a private key and checked using the corresponding public key to support message integrity and origin authentication. Signing does not itself conceal the message.

Conditions and scope

  • Verification relies on a trusted association between the public key and the claimed signer.
  • Key compromise, algorithm assumptions and protocol context limit conclusions; mathematical verification alone does not prove a person's identity or legal responsibility.
Sources · 1

References

Sources retain their recorded scope. A source link alone does not establish verification of every statement.

  1. Glossary: Digital signatureNISTReference guidecsrc.nist.govRead source

Evidence and review

Private-key generation/public-key verification, authenticity/integrity versus confidentiality; legal guarantees excluded.

2026-10-10 · NIST public/private signature definition; unqualified nonrepudiation excluded.

Related reference entries

Explore relationships within this area of study and its connections to other areas.

Showing 1–2 of 2 relationships

Scientific relationships · 2 / 2

The relationship type describes the connection. Its linked statements, sources and conditions define the scope.

  1. Related to
    Relationship sources · 2

    Linked statements

    • EUF-CMA signature security gives an adversary a public verification key and signing oracle, then tests whether it can produce a valid signature on a previously unsigned message. Strong unforgeability uses a stricter message/signature-pair criterion. This concerns cryptographic validity, not whether the signed statement is true, whether the key owner intended the act, or whether compromised signing software selected the right message.

    Public verification is coupled to a precise forgery experiment.

  2. Related to
    Relationship sources · 1

    Linked statements

    • In the synchronous oral-message Byzantine-generals model, agreement with at most f faulty participants requires at least 3f+1 participants, with identifiable senders and reliable delivery but no unforgeable transferred signature chain. Lamport, Shostak and Pease show that signed-message assumptions change the achievable boundary. A crash-majority protocol cannot inherit Byzantine guarantees merely by attaching a signature to each network packet.

    Signed-message reasoning assumes authenticated evidence.

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