See also
 | This cryptography-related article is a stub. You can help Wikipedia by expanding it. |
In cryptography, the Standards for Efficient Cryptography Group (SECG) is an international consortium founded by Certicom in 1998. The group exists to develop commercial standards for efficient and interoperable cryptography based on elliptic curve cryptography (ECC).
| | This cryptography-related article is a stub. You can help Wikipedia by expanding it. |
In cryptography, key size, key length, or key space refer to the number of bits in a key used by a cryptographic algorithm.
Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC allows smaller keys compared to non-EC cryptography to provide equivalent security.
In cryptography, the Elliptic Curve Digital Signature Algorithm (ECDSA) offers a variant of the Digital Signature Algorithm (DSA) which uses elliptic-curve cryptography.
Scott A. Vanstone was a mathematician and cryptographer in the University of Waterloo Faculty of Mathematics. He was a member of the school's Centre for Applied Cryptographic Research, and was also a founder of the cybersecurity company Certicom. He received his PhD in 1974 at the University of Waterloo, and for about a decade worked principally in combinatorial design theory, finite geometry, and finite fields. In the 1980s he started working in cryptography. An early result of Vanstone was an improved algorithm for computing discrete logarithms in binary fields, which inspired Don Coppersmith to develop his famous exp(n^{1/3+ε}) algorithm.
The Centre for Applied Cryptographic Research (CACR) is a group of industrial representatives, professors, and students at the University of Waterloo in Waterloo, Ontario, Canada who work and do research in the field of cryptography.
NSA Suite B Cryptography was a set of cryptographic algorithms promulgated by the National Security Agency as part of its Cryptographic Modernization Program. It was to serve as an interoperable cryptographic base for both unclassified information and most classified information.
IEEE P1363 is an Institute of Electrical and Electronics Engineers (IEEE) standardization project for public-key cryptography. It includes specifications for:
Patent-related uncertainty around elliptic curve cryptography (ECC), or ECC patents, is one of the main factors limiting its wide acceptance. For example, the OpenSSL team accepted an ECC patch only in 2005, despite the fact that it was submitted in 2002.
The Microsoft Windows platform specific Cryptographic Application Programming Interface is an application programming interface included with Microsoft Windows operating systems that provides services to enable developers to secure Windows-based applications using cryptography. It is a set of dynamically linked libraries that provides an abstraction layer which isolates programmers from the code used to encrypt the data. The Crypto API was first introduced in Windows NT 4.0 and enhanced in subsequent versions.
Elliptic-curve Diffie–Hellman (ECDH) is a key agreement protocol that allows two parties, each having an elliptic-curve public–private key pair, to establish a shared secret over an insecure channel. This shared secret may be directly used as a key, or to derive another key. The key, or the derived key, can then be used to encrypt subsequent communications using a symmetric-key cipher. It is a variant of the Diffie–Hellman protocol using elliptic-curve cryptography.
Integrated Encryption Scheme (IES) is a hybrid encryption scheme which provides semantic security against an adversary who is able to use chosen-plaintext or chosen-ciphertext attacks. The security of the scheme is based on the computational Diffie–Hellman problem.
Two variants of IES are specified: Discrete Logarithm Integrated Encryption Scheme (DLIES) and Elliptic Curve Integrated Encryption Scheme (ECIES), which is also known as the Elliptic Curve Augmented Encryption Scheme or simply the Elliptic Curve Encryption Scheme. These two variants are identical up to the change of an underlying group.
Alfred Menezes is co-author of several books on cryptography, including the Handbook of Applied Cryptography, and is a professor of mathematics at the University of Waterloo in Canada.
Victor Saul Miller is an American mathematician as a Principal Computer Scientist in the Computer Science Laboratory of SRI International. He received his B.A. in mathematics from Columbia University in 1968, and his Ph.D. in mathematics from Harvard University in 1975. He was an assistant professor in the Mathematics Department of the University of Massachusetts Boston from 1973 to 1978. In 1978 he joined the IBM 801 project in the Computer Science Department of the Thomas J. Watson Research Center in Yorktown Heights, New York, and moved to the Mathematics Department in 1984. From 1993-2022 he was on the Research Staff of Center for Communications Research (CCR) of the Institute for Defense Analyses in Princeton, New Jersey, U.S. In 2022 he was a Research Scientist in that Statistics and Privacy Group of Meta Platforms.
In cryptography, implicit certificates are a variant of public key certificate. A subject's public key is reconstructed from the data in an implicit certificate, and is then said to be "implicitly" verified. Tampering with the certificate will result in the reconstructed public key being invalid, in the sense that it is infeasible to find the matching private key value, as would be required to make use of the tampered certificate.
Dual_EC_DRBG is an algorithm that was presented as a cryptographically secure pseudorandom number generator (CSPRNG) using methods in elliptic curve cryptography. Despite wide public criticism, including the public identification of the possibility that the National Security Agency put a backdoor into a recommended implementation, it was for seven years one of four CSPRNGs standardized in NIST SP 800-90A as originally published circa June 2006, until it was withdrawn in 2014.
In cryptography, Curve25519 is an elliptic curve used in elliptic-curve cryptography (ECC) offering 128 bits of security and designed for use with the elliptic curve Diffie–Hellman (ECDH) key agreement scheme. It is one of the fastest curves in ECC, and is not covered by any known patents. The reference implementation is public domain software.
The following outline is provided as an overview of and topical guide to cryptography:
In cryptography, post-quantum cryptography (PQC) refers to cryptographic algorithms that are thought to be secure against a cryptanalytic attack by a quantum computer. The problem with currently popular algorithms is that their security relies on one of three hard mathematical problems: the integer factorization problem, the discrete logarithm problem or the elliptic-curve discrete logarithm problem. All of these problems could be easily solved on a sufficiently powerful quantum computer running Shor's algorithm or even faster and less demanding alternatives.
Discrete logarithm records are the best results achieved to date in solving the discrete logarithm problem, which is the problem of finding solutions x to the equation given elements g and h of a finite cyclic group G. The difficulty of this problem is the basis for the security of several cryptographic systems, including Diffie–Hellman key agreement, ElGamal encryption, the ElGamal signature scheme, the Digital Signature Algorithm, and the elliptic curve cryptography analogues of these. Common choices for G used in these algorithms include the multiplicative group of integers modulo p, the multiplicative group of a finite field, and the group of points on an elliptic curve over a finite field.
The Commercial National Security Algorithm Suite (CNSA) is a set of cryptographic algorithms promulgated by the National Security Agency as a replacement for NSA Suite B Cryptography algorithms. It serves as the cryptographic base to protect US National Security Systems information up to the top secret level, while the NSA plans for a transition to quantum-resistant cryptography.