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Application of group theory to cryptography
Group-based cryptography is a use of groups to construct cryptographic primitives. A group is a very general algebraic object and most cryptographic schemes
Group-based_cryptography
Technique in cryptography
Pairing-based cryptography is the use of a pairing between elements of two cryptographic groups to a third group with a mapping e : G 1 × G 2 → G T {\displaystyle
Pairing-based_cryptography
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
Lattice-based_cryptography
Cryptography secured against quantum computers
Post-quantum cryptography (PQC), sometimes referred to as quantum-proof, quantum-safe, or quantum-resistant, is the development of cryptographic algorithms
Post-quantum_cryptography
Torus-based cryptography involves using algebraic tori to construct a group for use in ciphers based on the discrete logarithm problem. This idea was first
Torus-based_cryptography
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
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
Branch of mathematics that studies the properties of groups
chemistry, and materials science. Group theory is also central to public key cryptography. The early history of group theory dates from the 19th century
Group_theory
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
International standard
around certificate-based key management, such as the profile defined by the PKIX working group. CMS is used as the key cryptographic component of many
Cryptographic_Message_Syntax
Group type in algebra
thanks to finitely generated groups with property T Algorithmic problems in combinatorial group theory Group-based cryptography attempts to make use of hard
Finitely_generated_group
Project by NIST to standardize post-quantum cryptography
Post-Quantum Cryptography Standardization is a program and competition by NIST to update their standards to include post-quantum cryptography. It was announced
NIST Post-Quantum Cryptography Standardization
NIST_Post-Quantum_Cryptography_Standardization
Cryptographic system with public and private keys
are generated with algorithms based on mathematical problems termed one-way functions. Security of public-key cryptography depends on keeping the private
Public-key_cryptography
Used for encoding or decoding ciphertext
file, which, when processed through a cryptographic algorithm, can encode or decode cryptographic data. Based on the used method, the key can be different
Key_(cryptography)
Newsgroup relevant to the discussion of cryptography and related issues
sci.crypt.research — a similar, moderated group, focusing on research into cryptography. It was founded based on a charter by Peter Gutmann. sci.crypt
Cryptography_newsgroups
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
Number of standards related to cryptography
There are a number of standards related to cryptography. Standard algorithms and protocols provide a focus for study; standards for popular applications
Cryptography_standards
Group of public-key cryptography standards
Public Key Cryptography Standards (PKCS) are a group of public-key cryptography intervendor standards first developed by RSA Security, with involvement
PKCS
Cryptography standards organization
In cryptography, the Standards for Efficient Cryptography Group (SECG) is an international consortium founded by Certicom in 1998. The group exists to
SECG
San Francisco based cryptography company
Cryptography Research, Inc. was a San Francisco based cryptography company specializing in applied cryptographic engineering, including technologies for
Cryptography_Research
Term applied to cryptographic systems that are highly resistant to cryptanalysis
Strong cryptography or cryptographically strong are general terms used to designate the cryptographic algorithms that, when used correctly, provide a very
Strong_cryptography
Cryptography, the use of codes and ciphers, began thousands of years ago. Until recent decades, it has been the story of what might be called classical
History_of_cryptography
Type of functions designed for being unsolvable by root-finding algorithms
it suitable for use in cryptography. It is also referred to as a cryptographic random number generator (CRNG). Most cryptographic applications require random
Cryptographically secure pseudorandom number generator
Cryptographically_secure_pseudorandom_number_generator
Articles related to cryptography include: A5/1 • A5/2 • ABA digital signature guidelines • ABC (stream cipher) • Abraham Sinkov • Acoustic cryptanalysis
Index of cryptography articles
Index_of_cryptography_articles
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
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
World Wide Web Consortium cryptography standard
The Web Cryptography API is the World Wide Web Consortium’s (W3C) recommendation for a low-level interface that would increase the security of web applications
Web_Cryptography_API
Computer communications authentication algorithm
In cryptography, an HMAC (sometimes expanded as either keyed-hash message authentication code or hash-based message authentication code) is a specific
HMAC
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
Hyperelliptic curve cryptography is similar to elliptic curve cryptography (ECC) insofar as the Jacobian of a hyperelliptic curve is an abelian group in which to
Hyperelliptic curve cryptography
Hyperelliptic_curve_cryptography
Adding data to a message prior to encryption to hide its length
In cryptography, padding is any of a number of distinct practices which all include adding data to the beginning, middle, or end of a message prior to
Padding_(cryptography)
Laws relating to encryption
Cryptography is the practice and study of encrypting information, or in other words, securing information from unauthorized access. There are many different
Cryptography_law
Measure of cryptographic strength
In cryptography, security level is a measure of the strength that a cryptographic primitive — such as a cipher or hash function — achieves. Security level
Security_level
Form of encryption that allows computation on ciphertexts
(polynomial-size branching programs) Craig Gentry, using lattice-based cryptography, described the first plausible construction for a fully homomorphic
Homomorphic_encryption
Transfer from the United States to another country of technology related to cryptography
The export of cryptography from the United States to other countries has experienced various levels of restrictions over time. World War II illustrated
Export of cryptography from the United States
Export_of_cryptography_from_the_United_States
Cryptographic protocol
these attacks. Anshel–Anshel–Goldfeld key exchange Group-based cryptography Non-commutative cryptography Also referred to as the colored Burau key agreement
Algebraic_Eraser
Digital signature scheme
and Blind Signatures Based on the Gap-Diffie-Hellman-Group Signature Scheme". In Desmedt, Yvo G. (ed.). Public Key Cryptography — PKC 2003. Lecture Notes
BLS_digital_signature
Placeholder characters
fictional characters commonly used as placeholders in discussions about cryptographic systems and protocols, and in other science and engineering literature
Alice_and_Bob
Algorithm for solving the discrete logarithm problem
a finite abelian group by Daniel Shanks. The discrete log problem is of fundamental importance to the area of public key cryptography. Many of the most
Baby-step_giant-step
Multiparty cryptographic process
Multisignatures and Blind Signatures Based on the Gap-Diffie-Hellman-Group Signature Scheme" (PDF). Public Key Cryptography — PKC 2003. Lecture Notes in Computer
Distributed_key_generation
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
Standard for cryptographic certificates
In cryptography, X.509 is an International Telecommunication Union (ITU) standard defining the format of public key certificates. X.509 certificates are
X.509
Israeli–American professor
(/boʊˈneɪ/; Hebrew: דן בונה) is an Israeli–American professor in applied cryptography and computer security at Stanford University. In 2016, Boneh was elected
Dan_Boneh
Cryptography primitive
function mode of operation has been broken and is not suitable for cryptographic use. Based on StepRightUp, it was designed by Joan Daemen and Craig Clapp
Panama_(cryptography)
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
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
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
Problem of inverting exponentiation in groups
cryptography, such as ElGamal, base their security on the hardness assumption that the discrete logarithm problem (DLP) over carefully chosen groups has
Discrete_logarithm
Message-digest hashing algorithm
a cryptographic hash function; however it has been found to suffer from extensive vulnerabilities. It remains suitable for other non-cryptographic purposes
MD5
British designation for intelligence from decrypted enemy communications
(India), SCU13 and SCU14. The cryptographic element of each SLU was supplied by the RAF and was based on the TYPEX cryptographic machine and one-time pad systems
Ultra_(cryptography)
Internet puzzle and mystery
uses non-puzzle-based recruiting methods, but created the Cicada puzzles because they were looking for potential members with cryptography and computer security
Cicada_3301
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
Iranian-American mathematician
US-UK based quantum start-up), and LifeNome Inc., a biotech company. Applications of Group Theory in Cryptography: Post-quantum Group-based Cryptography. American
Delaram_Kahrobaei
Type of code
smaller set of symbols, which is useful for telegraphy, steganography, and cryptography. The device was originally used for fire signalling, allowing for the
Polybius_square
Function that derives secret keys from a secret value
In cryptography, a key derivation function (KDF) is a cryptographic algorithm that derives one or more secret keys from a secret value such as a master
Key_derivation_function
In cryptography, the white-box model refers to an extreme attack scenario, in which an adversary has full unrestricted access to a cryptographic implementation
White-box_cryptography
Cryptography algorithm
itself is only suitable for the secure cryptographic transformation (encryption or decryption) of one fixed-length group of bits called a block. A mode of
Block cipher mode of operation
Block_cipher_mode_of_operation
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
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
Information used for message authentication and integrity checking
In cryptography, a message authentication code (MAC), sometimes known as an authentication tag, is a short piece of information used for authenticating
Message_authentication_code
Cryptographic hash function
RIPEMD (RIPE Message Digest) is a family of cryptographic hash functions developed in 1992 (the original RIPEMD) and 1996 (other variants). There are
RIPEMD
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
The sub-group hiding assumption is a computational hardness assumption used in elliptic curve cryptography and pairing-based cryptography. It was first
Sub-group_hiding
Mathematical object
lattices also form the basis for quantum computer attack resistant cryptography based on the Ring Learning with Errors. These cryptosystems are provably
Ideal_lattice
Algorithm for encrypting and decrypting information
In cryptography, a cipher (or cypher) is an algorithm for performing encryption or decryption—a series of well-defined steps that can be followed as a
Cipher
Elliptic curve used in Internet cryptography
In cryptography, Curve25519 is an elliptic curve used in elliptic-curve cryptography (ECC) offering 128 bits of security (256-bit key size) and designed
Curve25519
Public-key exchange protocol
the user's long-term private key, and depending on the underlying cryptographic group setting, the entire private key may be recovered by the attacker
MQV
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
American cryptographer (born 1947)
member of the Theory of Computation Group, and founder of MIT CSAIL's Cryptography and Information Security Group. Rivest was a founder of RSA Data Security
Ron_Rivest
Number of bits in a key used by a cryptographic algorithm
In cryptography, key size or key length refers to the number of bits in a key used by a cryptographic algorithm (such as a cipher). Key length defines
Key_size
South Korean cryptographer
Jung Hee Cheon is also one of the inventors of braid cryptography, a group-based cryptography scheme, and was previously known for his work on an efficient
Jung_Hee_Cheon
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
Books on cryptography have been published sporadically and with variable quality for a long time. This is despite the paradox that secrecy is of the essence
Bibliography_of_cryptography
Model of computation
available. Other names used are bare model and plain model. Cryptographic schemes are usually based on complexity assumptions, which state that some problems
Standard_model_(cryptography)
Early unclassified symmetric-key block cipher
been highly influential in the advancement of cryptography. Developed in the early 1970s at IBM and based on an earlier design by Horst Feistel, the algorithm
Data_Encryption_Standard
Encryption technique
one-time pad (OTP) is an encryption technique that cannot be cracked in cryptography. It requires the use of a single-use pre-shared key that is larger than
One-time_pad
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
In cryptography, an accumulator is a one way membership hash function. It allows users to certify that potential candidates are a member of a certain set
Accumulator_(cryptography)
German cipher machine during World War II
is encrypted with a different cryptographic key, making it highly resistant to conventional cryptographic attacks based on patterns the keys leave in
Enigma_machine
The tables below compare cryptography libraries that deal with cryptography algorithms and have application programming interface (API) function calls
Comparison of cryptography libraries
Comparison_of_cryptography_libraries
Cryptographic protocols for securing data in transit
Transport Layer Security (TLS) is a cryptographic protocol designed to provide communications security over a computer network, such as the Internet.
Transport_Layer_Security
Batch cryptography is a field of cryptology focused on the design of cryptographic protocols that perform operations—such as encryption, decryption, key
Batch_cryptography
Process of converting plaintext to ciphertext
In cryptography, encryption (more specifically, encoding) is the process of transforming information in a way that, ideally, only authorized parties can
Encryption
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
Substitution cipher based on linear algebra
In classical cryptography, the Hill cipher is a polygraphic substitution cipher based on linear algebra. Invented by Lester S. Hill in 1929, it was the
Hill_cipher
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
Swiss tech company
spin-off of the Group of Applied Physics at the University of Geneva. the firm is structured in three business units: The quantum safe cryptography division
ID_Quantique
Cryptographic key agreement scheme
Station-to-Station (STS) protocol is a cryptographic key agreement scheme. The protocol is based on classic Diffie–Hellman, and provides mutual key and
Station-to-Station_protocol
Simple encryption method
Rome, and used by Julius Caesar in the 1st century BC (see timeline of cryptography). ROT13 may be referred to as Rotate13, ROT-13, rotate by 13 places,
ROT13
Schnorr group is used. In general, YAK can use any prime order group that is suitable for public key cryptography, including elliptic curve cryptography. Let
YAK_(cryptography)
Study of analyzing information systems in order to discover their hidden aspects
is used to breach cryptographic security systems and gain access to the contents of encrypted messages, even if the cryptographic key is unknown. In
Cryptanalysis
SPEKE (Simple Password Exponential Key Exchange) is a cryptographic method for password-authenticated key agreement. The protocol consists of little more
SPEKE
Stream cipher
In cryptography, RC4 (also known as ARC4 or ARCFOUR, meaning Alleged RC4, see below) is a stream cipher. While it is remarkable for its simplicity and
RC4
Authenticated encryption mode
In cryptography, Galois/Counter Mode (GCM) is a mode of operation for symmetric-key cryptographic block ciphers that provides both encryption and message
Galois/Counter_Mode
Study of the frequency of letters or groups of letters in a ciphertext
of letters or groups of letters in a ciphertext. The method is used as an aid to breaking classical ciphers. Frequency analysis is based on the fact that
Frequency_analysis
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
Authenticated encryption with associated data algorithm
7634. Proposed Standard. "Do the ChaCha: better mobile performance with cryptography". The Cloudflare Blog. 2015-02-23. Retrieved 2021-12-28. A. Langley;
ChaCha20-Poly1305
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
British cryptographer
Officer at Zama. He is a cryptographer with interests in the theory of cryptography and its application in practice. Smart received a BSc degree in mathematics
Nigel_Smart_(cryptographer)
Periodic set of points
cryptanalysis of many public-key encryption schemes, and many lattice-based cryptographic schemes are known to be secure under the assumption that certain
Lattice_(group)
GROUP BASED-CRYPTOGRAPHY
GROUP BASED-CRYPTOGRAPHY
Boy/Male
Tamil
Commander of group
Boy/Male
Indian, Kannada, Sanskrit
Group Leader
Boy/Male
Hindu, Indian, Sanskrit
Group; Organisation; Gathering
Boy/Male
Muslim
Smiling
Surname or Lastname
Scottish
Scottish : habitational name from a place in the parish of Gamrie, near Banff. The place is situated on a headland affording some sheltered anchorage, and is said to get its name from Middle English true hope; however, when first recorded in 1296 it already appears as Trup, so it is more likely to be of the same origin as Thorpe.English : variant of Throop.
Boy/Male
Indian, Sanskrit
Conquering a Group
Boy/Male
Afghan, African, Arabic, Australian, Chinese, Greek, Indian, Muslim
Brave
Girl/Female
Arabic
Soul; Group Leader
Boy/Male
Muslim
Group of people
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Commander of Group
Boy/Male
Muslim/Islamic
Smiling
Boy/Male
Hindu, Indian
Group of God
Girl/Female
Arabic
Soul; Group Leader
Boy/Male
Indian
Group of people
Surname or Lastname
English
English : metonymic occupational name for a dealer in coarse meal, Old English grūt, Old Norse grautr ‘porridge’.
Boy/Male
Arabic, Australian
Smiling
Girl/Female
Bengali, Indian
Group of Lights
Girl/Female
British, English
Based
Boy/Male
Arabic
Group; Army
Boy/Male
Muslim/Islamic
Brave
GROUP BASED-CRYPTOGRAPHY
GROUP BASED-CRYPTOGRAPHY
Surname or Lastname
English (Northumberland and Durham)
English (Northumberland and Durham) : nickname for a vain or haughty man, from Middle English prod, prud ‘proud’ (late Old English prūd, from the oblique form of Old French proz).
Boy/Male
Assamese, Gujarati, Hindu, Indian, Malayalam, Marathi, Punjabi, Sikh
The Ocean
Girl/Female
Hindu
Splendor
Boy/Male
Arabic, Australian, Lebanese
Alone
Male
Hebrew
Variant spelling of Hebrew Gabriyel, GAVRIEL means "man of God" or "warrior of God."Â
Boy/Male
Gujarati, Hindu, Indian
The Sun
Boy/Male
Tamil
Maargit | மாரà¯à®•à¯€à®¤
Pearl
Girl/Female
Hindu
Royalty
Surname or Lastname
English
English : habitational name, perhaps from a place in Devon called Cheston, although the surname is found mainly in East Anglia rather than Devon.
Surname or Lastname
English
English : from a pet form of Ellis.
GROUP BASED-CRYPTOGRAPHY
GROUP BASED-CRYPTOGRAPHY
GROUP BASED-CRYPTOGRAPHY
GROUP BASED-CRYPTOGRAPHY
GROUP BASED-CRYPTOGRAPHY
v. t.
To fill up or finish with grout, as the joints between stones.
a.
Reduced; lowered; restrained; as, to speak with bated breath.
n.
Any comprehensive group of animals or plants including several subordinate related groups.
n.
To form a group of; to arrange or combine in a group or in groups, often with reference to mutual relation and the best effect; to form an assemblage of.
n.
Arrangement in a group or in groups; grouping.
n.
An assemblage of objects in a certain order or relation, or having some resemblance or common characteristic; as, groups of strata.
n.
A rustic play; -- called also prisoner's base, prison base, or bars.
n.
A pie; baked food.
a.
Having a base, or having as a base; supported; as, broad-based.
n.
A cluster, crowd, or throng; an assemblage, either of persons or things, collected without any regular form or arrangement; as, a group of men or of trees; a group of isles.
a.
Deep or grave in sound; as, the base tone of a violin.
a.
Alloyed with inferior metal; debased; as, base coin; base bullion.
a.
Morally low. Hence: Low-minded; unworthy; without dignity of sentiment; ignoble; mean; illiberal; menial; as, a base fellow; base motives; base occupations.
n.
An inflammatory affection of the larynx or trachea, accompanied by a hoarse, ringing cough and stridulous, difficult breathing; esp., such an affection when associated with the development of a false membrane in the air passages (also called membranous croup). See False croup, under False, and Diphtheria.
n.
Same as Prison base.
n.
Wearing, or protected by, bases.
a.
Of little, or less than the usual, height; of low growth; as, base shrubs.
a.
Not held by honorable service; as, a base estate, one held by services not honorable; held by villenage. Such a tenure is called base, or low, and the tenant, a base tenant.
imp. & p. p.
of Base