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 to provide equivalent security, compared to cryptosystems based on modular exponentiation in Galois fields, such as the RSA cryptosystem and ElGamal cryptosystem.
Public-key cryptography, or asymmetric cryptography, is the field of cryptographic systems that use pairs of related keys. Each key pair consists of a public key and a corresponding private key. Key pairs are generated with cryptographic algorithms based on mathematical problems termed one-way functions. Security of public-key cryptography depends on keeping the private key secret; the public key can be openly distributed without compromising security.
Ronald Linn Rivest is a cryptographer and computer scientist whose work has spanned the fields of algorithms and combinatorics, cryptography, machine learning, and election integrity. He is an Institute Professor at the Massachusetts Institute of Technology (MIT), and a member of MIT's Department of Electrical Engineering and Computer Science and its Computer Science and Artificial Intelligence Laboratory.
Articles related to cryptography include:
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 key of a user is some unique information about the identity of the user. This means that a sender who has access to the public parameters of the system can encrypt a message using e.g. the text-value of the receiver's name or email address as a key. The receiver obtains its decryption key from a central authority, which needs to be trusted as it generates secret keys for every user.
The Paillier cryptosystem, invented by and named after Pascal Paillier in 1999, is a probabilistic asymmetric algorithm for public key cryptography. The problem of computing n-th residue classes is believed to be computationally difficult. The decisional composite residuosity assumption is the intractability hypothesis upon which this cryptosystem is based.
IEEE P1363 is an Institute of Electrical and Electronics Engineers (IEEE) standardization project for public-key cryptography. It includes specifications for:
The external Diffie–Hellman (XDH) assumption is a computational hardness assumption used in elliptic curve cryptography. The XDH assumption holds if there exist certain subgroups of elliptic curves which have useful properties for cryptography. Specifically, XDH implies the existence of two distinct groups with the following properties:
- The discrete logarithm problem (DLP), the computational Diffie–Hellman problem (CDH), and the computational co-Diffie–Hellman problem are all intractable in and .
- There exists an efficiently computable bilinear map (pairing) .
- The decisional Diffie–Hellman problem (DDH) is intractable in .
In cryptography, a Lamport signature or Lamport one-time signature scheme is a method for constructing a digital signature. Lamport signatures can be built from any cryptographically secure one-way function; usually a cryptographic hash function is used.
Paulo Licciardi Barreto is a Brazilian-American cryptographer and one of the designers of the Whirlpool hash function and the block ciphers Anubis and KHAZAD, together with Vincent Rijmen. He has also co-authored a number of research works on elliptic curve cryptography and pairing-based cryptography, including the eta pairing technique, identity-based cryptographic protocols, and the family of Barreto–Naehrig (BN) and Barreto–Lynn-Scott (BLS) pairing-friendly elliptic curves. More recently he has been focusing his research on post-quantum cryptography, being one of the discoverers of quasi-dyadic codes and quasi-cyclic moderate-density parity-check (QC-MDPC) codes to instantiate the McEliece and Niederreiter cryptosystems and related schemes.
Reihaneh "Rei" Safavi-Naini is the NSERC/Telus Industrial Research Chair and the Alberta Innovates Strategic Chair in Information Security at the University of Calgary, Canada.
Willy Susilo is an Australian cybersecurity scientist and cryptographer. He is a Distinguished Professor at the School of Computing and Information Technology, Faculty of Engineering and Information Sciences University of Wollongong, Australia.
A 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.
Lattice-based cryptography is the generic term for constructions of cryptographic primitives that involve lattices, either in the construction itself or in the security proof. Lattice-based constructions support important standards of post-quantum cryptography. Unlike more widely used and known public-key schemes such as the RSA, Diffie-Hellman or elliptic-curve cryptosystems — which could, theoretically, be defeated using Shor's algorithm on a quantum computer — some lattice-based constructions appear to be resistant to attack by both classical and quantum computers. Furthermore, many lattice-based constructions are considered to be secure under the assumption that certain well-studied computational lattice problems cannot be solved efficiently.
Cryptography, or cryptology, is the practice and study of techniques for secure communication in the presence of adversarial behavior. More generally, cryptography is about constructing and analyzing protocols that prevent third parties or the public from reading private messages. Modern cryptography exists at the intersection of the disciplines of mathematics, computer science, information security, electrical engineering, digital signal processing, physics, and others. Core concepts related to information security are also central to cryptography. Practical applications of cryptography include electronic commerce, chip-based payment cards, digital currencies, computer passwords, and military communications.
The following outline is provided as an overview of and topical guide to cryptography:
Identity-based cryptography is a type of public-key cryptography in which a publicly known string representing an individual or organization is used as a public key. The public string could include an email address, domain name, or a physical IP address.
Post-quantum cryptography (PQC), sometimes referred to as quantum-proof, quantum-safe, or quantum-resistant, is the development of cryptographic algorithms that are thought to be secure against a cryptanalytic attack by a quantum computer. The problem with popular algorithms currently used in the market 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.
In cryptography, Curve448 or Curve448-Goldilocks is an elliptic curve potentially offering 224 bits of security and designed for use with the elliptic-curve Diffie–Hellman (ECDH) key agreement scheme.
SM9 is a Chinese national cryptography standard for Identity Based Cryptography issued by the Chinese State Cryptographic Authority in March 2016. It is represented by the Chinese National Cryptography Standard (Guomi), GM/T 0044-2016 SM9. The standard contains the following components:
