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Cryptographic primitives that involve lattices
Lattice-based cryptography is the generic term for constructions of cryptographic primitives that involve lattices, either in the construction itself or
Lattice-based_cryptography
Cryptography secured against quantum computers
(2015-01-01). "McBits: fast constant-time code-based cryptography". Cryptology ePrint Archive. "Lattice Cryptography Library". Microsoft Research. 19 Apr 2016
Post-quantum_cryptography
Optimization problem in computer science
of cryptographic algorithms. In addition, some lattice problems which are worst-case hard can be used as a basis for extremely secure cryptographic schemes
Lattice_problem
Project by NIST to standardize post-quantum cryptography
schemes Lattice-based cryptography NIST hash function competition "Post-Quantum Cryptography PQC". 3 January 2017. "Post-Quantum Cryptography Standardization
NIST Post-Quantum Cryptography Standardization
NIST_Post-Quantum_Cryptography_Standardization
Mathematical object
they have a significant place in cryptography. Micciancio defined a generalization of cyclic lattices as ideal lattices. They can be used in cryptosystems
Ideal_lattice
Quantum-safe key encapsulation mechanism
learning with errors lattice problem as its basic trapdoor function. It won the NIST competition for the first post-quantum cryptography (PQC) standard. and
ML-KEM
Computational problem used in cryptography
two average-case problems that are used in lattice-based cryptography constructions. Lattice-based cryptography began in 1996 from a seminal work by Miklós
Short integer solution problem
Short_integer_solution_problem
Concept in cryptography
post-quantum cryptographic algorithms which are based on the difficulty of solving certain mathematical problems involving lattices. Unlike older lattice based cryptographic
Ring learning with errors key exchange
Ring_learning_with_errors_key_exchange
Digital signature resilient to quantum cryptography
Another approach to signatures based on lattices over Rings is a variant of the patented NTRU family of lattice based cryptography. The primary example of this
Ring learning with errors signature
Ring_learning_with_errors_signature
Periodic set of points
constant Lattice-based cryptography Lattice graph Lattice (module) Lattice (order) Mahler's compactness theorem Reciprocal lattice Unimodular lattice Gruber
Lattice_(group)
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
Computational problem possibly useful for post-quantum cryptography
problem even on a quantum computer, RLWE based cryptography may form the fundamental base for public-key cryptography in the future just as the integer factorization
Ring_learning_with_errors
Topics referred to by the same term
a field Lattice graph, a graph that can be drawn within a repeating arrangement of points Lattice-based cryptography, encryption systems based on repeating
Lattice
Israeli-American computer scientist
institute at New York University. He is best known for his work in lattice-based cryptography, and in particular for introducing the learning with errors problem
Oded Regev (computer scientist)
Oded_Regev_(computer_scientist)
protocol MSZ96 SARG04 Six-state protocol Falcon Hash-based cryptography Lattice-based cryptography McEliece cryptosystem ML-KEM NTRU NTRUEncrypt NTRUSign
List of cryptographic software
List_of_cryptographic_software
Cryptographic method
verifications per second. Post-quantum cryptography Lattice-based cryptography NTRU NIST Post-Quantum Cryptography Standardization Official website Thomas
Falcon_(signature_scheme)
Lattice-based cryptosystem
Goldreich–Goldwasser–Halevi (GGH) lattice-based cryptosystem is a broken asymmetric cryptosystem based on lattices. There is also a GGH signature scheme
GGH_encryption_scheme
Mathematical operation
Q. (2009). "Hermite's Constant and Lattice Algorithms". The LLL Algorithm. Information Security and Cryptography. Berlin, Heidelberg: Springer Berlin
Lattice_reduction
Problem in computer science
algorithms can perform for this task, as it can be applied to break lattice-based cryptography. The hidden shift problem states: Given an oracle O {\displaystyle
Hidden_shift_problem
Post-quantum signature scheme
Lepoint and Vadim Lyubashevsky in their 2013 paper "Lattice Signature and Bimodal Gaussians". In cryptography, a digital signature ensures that a message is
BLISS_signature_scheme
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
NTRU public-key cryptography digital signature algorithm
the NTRU Signature Algorithm, is an NTRU public-key cryptography digital signature algorithm based on the GGH signature scheme. The original version of
NTRUSign
Form of encryption that allows computation on ciphertexts
cryptosystem (polynomial-size branching programs) Craig Gentry, using lattice-based cryptography, described the first plausible construction for a fully homomorphic
Homomorphic_encryption
scheme is based on the hardness assumption of the ring learning with errors (RLWE) problem, the ring variant of very promising lattice-based hard problem
HEAAN
Identity-based cryptography is a type of public-key cryptography in which a publicly known string representing an individual or organization is used as
Identity-based_cryptography
Russian-American scientist
Technologies. He is best known for his work in cryptography (homomorphic encryption, lattice-based cryptography), chemical engineering (theory of filtration
Yuriy_Polyakov
Ability to easily switch cryptographic primitives
discrete logarithms include lattice-based cryptography, multivariate cryptography, hash-based cryptography, and code-based cryptography. System evolution and
Cryptographic_agility
Cryptographic protocol designed to resist quantum computer attacks
provide 128-bit "classical" security level. CECPQ2 Cryptography Lattice-based cryptography Quantum cryptography "NewHope Post-quantum key encapsulation". "Chrome:
NewHope
Topics referred to by the same term
filename extension Short integer solution problem, a problem in lattice-based cryptography Single-instance storage, information-storage space-saving mechanism
Sis
Hungarian-American computer scientist
establishing lower bounds in computational complexity and founding lattice-based cryptography." Ajtai received his Candidate of Sciences degree in 1976 from
Miklós_Ajtai
Cryptographic analysis
thesis showed that lattice point enumeration and lattice block reduction algorithms could be used to attack lattice-based cryptography. In 2021, "guess-and-determine"
Concrete_security
Algorithm in computational number theory
The Lenstra–Lenstra–Lovász (LLL) lattice basis reduction algorithm is a polynomial time lattice reduction algorithm invented by Arjen Lenstra, Hendrik
Lenstra–Lenstra–Lovász lattice basis reduction algorithm
Lenstra–Lenstra–Lovász_lattice_basis_reduction_algorithm
Practice and study of secure communication techniques
non-repudiation) are also central to cryptography. Practical applications of cryptography include electronic commerce, chip-based payment cards, digital currencies
Cryptography
encryption Elliptic-curve cryptography Lattice-based cryptography McEliece cryptosystem Multivariate cryptography Isogeny-based cryptography Corinne Bernstein
List_of_cryptosystems
IEEE standardization project for public-key cryptography
public-key cryptography. It includes specifications for: Traditional public-key cryptography (IEEE Std 1363-2000 and 1363a-2004) Lattice-based public-key
IEEE_P1363
Digital signature scheme
in 1997, based on solving the closest vector problem (CVP) in a lattice. The signer demonstrates knowledge of a good basis for the lattice by using it
GGH_signature_scheme
cross platform software library that provides implementations of lattice cryptography building blocks and homomorphic encryption schemes. PALISADE adopted
PALISADE_(software)
Approach to public-key cryptography
Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC
Elliptic-curve_cryptography
Public-key cryptographic pseudorandom function
In 2020, Esgin et al. proposed a post-quantum secure VRF based on lattice-based cryptography. VRFs provide deterministic pre-commitments for low entropy
Verifiable_random_function
Mathematical problem in cryptography
In cryptography, learning with errors (LWE) is a mathematical problem that is widely used to create secure encryption algorithms. It is based on the idea
Learning_with_errors
Complexity class
solution) problem, which is a generalization of the SIS problem from lattice-based cryptography, has been shown to be complete for PPP. Prior to that work, the
PPP_(complexity)
algorithms, such as lattice-based cryptographic schemes. Bertram, Linda A. / Dooble, Gunther van: Transformation of Cryptography - Fundamental concepts
Bibliography_of_cryptography
KYK-13 Lacida • Ladder-DES • Lamport signature • Lars Knudsen • Lattice-based cryptography • Laurance Safford • Lawrie Brown • LCS35 • Leo Marks • Leonard
Index of cryptography articles
Index_of_cryptography_articles
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
Algorithm for public-key cryptography
cryptosystem) such as RSAES-OAEP, and public-key key encapsulation. In RSA-based cryptography, a user's private key—which can be used to sign messages, or decrypt
RSA_cryptosystem
Electrical Engineer and Computer Scientist (born 1959)
Polynomial Multiplication via Fast Filtering and Applications to Lattice-Based Cryptography". IEEE Transactions on Computers. 72 (9): 2454–2466. arXiv:2110
Keshab_K._Parhi
Type of public-key encryption
Identity-based encryption (IBE), is an important primitive of identity-based cryptography. As such it is a type of public-key encryption in which the public
Identity-based_encryption
Proving validity without revealing other data
various cryptographic primitives, such as hash-based cryptography, pairing-based cryptography, multi-party computation, or lattice-based cryptography. Generally
Zero-knowledge_proof
Cryptography based on quantum mechanical phenomena
adversaries are McEliece and lattice-based schemes, as well as most symmetric-key algorithms. Surveys of post-quantum cryptography are available. Additional
Quantum_cryptography
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 Key-Encapsulation
ML
Mathematical scheme for verifying the authenticity of digital documents
known to the recipient. Digital signatures are a type of public-key cryptography, and are commonly used for software distribution, financial transactions
Digital_signature
Method of exchanging cryptographic keys
exchange is a mathematical method of securely generating a symmetric cryptographic key over a public channel and was one of the first protocols as conceived
Diffie–Hellman_key_exchange
American mathematician (born 1955)
the Joint Mathematics Meetings, speaking on The Mathematics of Lattice-based Cryptography The Association for Women in Mathematics named her as their Noether
Jill_Pipher
Digital signature scheme
In hash-based cryptography, the Merkle signature scheme is a digital signature scheme based on Merkle trees (also called hash trees) and one-time signatures
Merkle_signature_scheme
Non-federated cryptographic protocol
Protocol (formerly known as the TextSecure Protocol) is a non-federated cryptographic protocol that provides end-to-end encryption for voice and instant messaging
Signal_Protocol
cryptography, cryptographic hash functions can be divided into two main categories. In the first category are those functions whose designs are based
Security of cryptographic hash functions
Security_of_cryptographic_hash_functions
Set of cryptographic algorithms by the NSA
replacement for NSA Suite B Cryptography algorithms. It serves as the cryptographic base to protect US National Security Systems information up to the TOP
Commercial National Security Algorithm Suite
Commercial_National_Security_Algorithm_Suite
Cryptographic key management algorithm
session keys. It combines a cryptographic so-called "ratchet" based on the Diffie–Hellman key exchange (DH) and a ratchet based on a key derivation function
Double_Ratchet_Algorithm
applications on cryptography, as key exchange protocols, identity-based encryption, and broadcast encryption. There exist constructions of cryptographic 2-multilinear
Cryptographic_multilinear_map
Public-key cryptosystem
In cryptography, a key encapsulation mechanism (KEM) is a public-key cryptosystem that allows a sender to generate a short secret key and transmit it to
Key_encapsulation_mechanism
Cryptographic algorithm for digital signatures
In cryptography, the Elliptic Curve Digital Signature Algorithm (ECDSA) offers a variant of the Digital Signature Algorithm (DSA) which uses elliptic-curve
Elliptic Curve Digital Signature Algorithm
Elliptic_Curve_Digital_Signature_Algorithm
Digital verification standard
second phase computes a single key pair for one user. Choose an approved cryptographic hash function H {\displaystyle H} with output length | H | {\displaystyle
Digital_Signature_Algorithm
Mechanism for authenticating cryptographic keys
In cryptography, a web of trust is a concept used in PGP, GnuPG, and other OpenPGP-compatible systems to establish the authenticity of the binding between
Web_of_trust
In cryptography, the Niederreiter cryptosystem is a variation of the McEliece cryptosystem developed in 1986 by Harald Niederreiter. It applies the same
Niederreiter_cryptosystem
Key agreement protocol
It is a variant of the Diffie–Hellman protocol using elliptic-curve cryptography. The following example illustrates how a shared key is established. Suppose
Elliptic-curve_Diffie–Hellman
Hypothesis in computational complexity theory
average-case assumptions used in cryptography (including RSA, discrete log, and some lattice problems) can be based on worst-case assumptions via
Computational hardness assumption
Computational_hardness_assumption
Israeli–American professor
is one of the principal contributors to the development of pairing-based cryptography, along with Matt Franklin of the University of California, Davis.
Dan_Boneh
Factorisation algorithm
coefficients. In cryptography, the Coppersmith method is mainly used in attacks on RSA when parts of the secret key are known and forms a base for Coppersmith's
Coppersmith_method
Digital signature scheme
BLS digital signature, also known as Boneh–Lynn–Shacham (BLS), is a cryptographic signature scheme which allows a user to verify that a signer is authentic
BLS_digital_signature
System that can issue, distribute and verify digital certificates
distribute, use, store and revoke digital certificates and manage public-key cryptography set-ups. The purpose of a PKI is to facilitate the secure storage and/or
Public_key_infrastructure
Function computed by two parties that emulates a random oracle
many useful applications in cryptography and information security. These include password-based key derivation, password-based key agreement, password-hardening
Oblivious pseudorandom function
Oblivious_pseudorandom_function
Cryptographic signature scheme
In cryptography, a Lamport signature or Lamport one-time signature scheme is a method for constructing a digital signature. Lamport signatures can be built
Lamport_signature
Asymmetric encryption algorithm developed by Robert McEliece
In cryptography, the McEliece cryptosystem is an asymmetric encryption algorithm developed in 1978 by Robert McEliece. It was the first such scheme to
McEliece_cryptosystem
American information security researcher
12, 1945) is a US-American information security researcher known for lattice-based access control (LBAC), intrusion detection systems (IDS), and other
Dorothy_E._Denning
Capability-based security Context-based access control (CBAC) Discretionary access control (DAC) Graph-based access control (GBAC) Lattice-based access control
Risk-based_authentication
Cryptographic hash function
In cryptography, SWIFFT is a collection of provably secure hash functions. It is based on the concept of the fast Fourier transform (FFT). SWIFFT is not
SWIFFT
Type of cryptosystem
A threshold cryptosystem, the basis for the field of threshold cryptography, is a cryptosystem in which the secret key is split into a number of pieces
Threshold_cryptosystem
Public-key cryptosystem
In cryptography, the ElGamal encryption system is a public-key encryption algorithm based on the Diffie–Hellman key exchange. It was described by Taher
ElGamal_encryption
Form of public key cryptography
small-dimension lattice, they recover the plaintext in under one second on a standard laptop. Schneier, Bruce (1996). Applied Cryptography. New York: John
Merkle–Hellman knapsack cryptosystem
Merkle–Hellman_knapsack_cryptosystem
Function used in computer cryptography
discrete logarithm of β to the base α. One writes k = logα β. Popular choices for the group G in discrete logarithm cryptography are the cyclic groups (Zp)×
One-way_function
Hybrid encryption in cryptography
{\displaystyle m=E^{-1}(k_{E};c)} SECG, Standards for efficient cryptography, SEC 1: Elliptic Curve Cryptography, Version 2.0, May 21, 2009. Gayoso Martínez, Hernández
Integrated_Encryption_Scheme
Cryptographic protocol
In cryptography, Combined Elliptic-Curve and Post-Quantum 2 (CECPQ2) is a quantum-secure modification to Transport Layer Security (TLS) 1.3 developed by
CECPQ2
American computer scientist
Her contributions in cryptography include non-malleable cryptography with Danny Dolev and Moni Naor in 1991, the first lattice-based cryptosystem with Miklós
Cynthia_Dwork
Non-commutative cryptography is the area of cryptology where the cryptographic primitives, methods and systems are based on algebraic structures like semigroups
Non-commutative_cryptography
Short sequence of bytes used to authenticate or look up a longer public key
In public-key cryptography, a public key fingerprint is a short sequence of bytes used to identify a longer public key. Fingerprints are created by applying
Public_key_fingerprint
Matrix form in linear algebra
Micciancio, Daniele; Goldwasser, Shafi (2012-12-06). Complexity of Lattice Problems: A Cryptographic Perspective. Springer Science & Business Media. ISBN 9781461508977
Hermite_normal_form
Computer hardware technology that uses quantum mechanics
break on a classical computer. Quantum cryptography replaces conventional encryption algorithms with techniques based on quantum mechanics such as entanglement
Quantum_computing
Scheme often used with RSA encryption
In cryptography, optimal asymmetric encryption padding (OAEP) is a padding scheme often used together with RSA encryption. OAEP was introduced by Bellare
Optimal asymmetric encryption padding
Optimal_asymmetric_encryption_padding
Hyperelliptic curve cryptography is similar to elliptic curve cryptography (ECC) insofar as the Jacobian of a hyperelliptic curve is an abelian group in
Hyperelliptic curve cryptography
Hyperelliptic_curve_cryptography
Augmented password-authenticated key exchange protocol
Diffie–Hellman key exchange based on the client side having the user password and the server side having a cryptographic verifier derived from the password
Secure Remote Password protocol
Secure_Remote_Password_protocol
Digital signature scheme
In cryptography, a Schnorr signature is a digital signature produced by the Schnorr signature algorithm that was invented by Claus Schnorr. It is known
Schnorr_signature
American computer scientist
is an American scientist working in computer science, cyber security, cryptography, digital forensics, quantum computing, aerospace engineering, artificial
Chuck_Easttom
SPEKE (Simple Password Exponential Key Exchange) is a cryptographic method for password-authenticated key agreement. The protocol consists of little more
SPEKE
Digital signature algorithm
In cryptography, GMR is a digital signature algorithm named after its inventors Shafi Goldwasser, Silvio Micali and Ron Rivest. As with RSA the security
GMR_(cryptography)
1999 public-key cryptography algorithm
algorithm was a public-key cryptography algorithm published in early 1999 by 16-year-old Irishwoman Sarah Flannery, based on an unpublished work by Michael
Cayley–Purser_algorithm
Multiparty cryptographic process
Distributed key generation (DKG) is a cryptographic process in which multiple parties contribute to the calculation of a shared public and private key
Distributed_key_generation
Annual award
Conference in recognition of innovations and contributions in the field of cryptography. An award committee of experts, which is associated with the Cryptographer's
RSA Award for Excellence in Mathematics
RSA_Award_for_Excellence_in_Mathematics
Kane quantum computer quantum cryptography quantum decoherence quantum circuit universal quantum computer measurement based Quantum Computing timeline of
List of mathematical topics in quantum theory
List_of_mathematical_topics_in_quantum_theory
Unsolved problem in cryptography
In cryptography, the RSA problem summarizes the task of performing an RSA private-key operation given only the public key. The RSA algorithm raises a message
RSA_problem
Types of noise
inversely proportional to the square of frequency Pseudorandom noise, in cryptography, artificial signal that can pass for random Statistical noise, a colloquialism
Noise_(spectral_phenomenon)
LATTICE BASED-CRYPTOGRAPHY
LATTICE BASED-CRYPTOGRAPHY
LATTICE BASED-CRYPTOGRAPHY
LATTICE BASED-CRYPTOGRAPHY
LATTICE BASED-CRYPTOGRAPHY
LATTICE BASED-CRYPTOGRAPHY
LATTICE BASED-CRYPTOGRAPHY
LATTICE BASED-CRYPTOGRAPHY
LATTICE BASED-CRYPTOGRAPHY