Lattice problemIn computer science, lattice problems are a class of optimization problems related to mathematical objects called lattices. The conjectured intractability of such problems is central to the construction of secure lattice-based cryptosystems: lattice problems are an example of NP-hard problems which have been shown to be average-case hard, providing a test case for the security of cryptographic algorithms.
Homomorphic encryptionHomomorphic encryption is a form of encryption that allows computations to be performed on encrypted data without first having to decrypt it. The result of the computations are left in an encrypted form which, when decrypted, result in an output that is identical to that of the operations performed on the unencrypted data. Homomorphic encryption can be used for privacy-preserving outsourced storage and computation.
National Institute of Standards and TechnologyThe National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical science laboratory programs that include nanoscale science and technology, engineering, information technology, neutron research, material measurement, and physical measurement.Lattice (group)Periodic set of points A lattice in the Euclidean plane In geometry and group theory, a lattice in the real coordinate space R n {\displaystyle \mathbb {R} ^{n}} is an infinite set of lattice points having the following properties: Coordinate-wise addition or subtraction of two points in the lattice produces another lattice point. The lattice points are all separated by some minimum distance (isolated).
Cryptographic primitiveCryptographic primitives are well-established, low-level cryptographicalgorithms that are frequently used to build cryptographic protocols for computer security systems. These routines include, but are not limited to, one-way hash functions and encryption functions. RationaleWhen creating cryptographic systems, designers use cryptographic primitives as their most basic building blocks.
Post-quantum cryptographyCryptography secured against quantum computersPost-quantum cryptography (PQC), sometimes referred to as quantum-proof, quantum-safe, or quantum-resistant, is the development of cryptographic algorithms (usually public-key algorithms) that are currently thought, but not proven, to be secure against a cryptanalytic attack by a quantum computer.
Elliptic-curve cryptographyElliptic-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 finite fields, such as the RSA cryptosystem and ElGamal cryptosystem. Elliptic curves are applicable for key agreement, digital signatures, pseudo-random generators and other tasks.
Shor's algorithmQuantum algorithm for integer factorizationShor's algorithm is a quantum algorithm for finding the prime factors of an integer. It was developed in 1994 by the American mathematician Peter Shor. It is one of the few known quantum algorithms with compelling potential applications and strong evidence of superpolynomial speedup compared to best known classical (non-quantum) algorithms.
Computational hardness assumptionIn computational complexity theory, a computational hardness assumption is the hypothesis that a particular problem cannot be solved efficiently (where efficiently typically means "in polynomial time"). It is not known how to prove (unconditional) hardness for essentially any useful problem.
RSA cryptosystemThe RSA (Rivest–Shamir–Adleman) cryptosystem is a family of public-key cryptosystems (one of the oldest), widely used for secure data transmission. The initialism "RSA" comes from the last-names of Ron Rivest, Adi Shamir and Leonard Adleman, who publicly described the algorithm in 1977. An equivalent system was developed secretly in 1973 at Government Communications Headquarters (GCHQ), the British signals intelligence agency, by the English mathematician Clifford Cocks.
Quantum computingA quantum computer is a computer that represents and processes information using quantum states. Quantum computations exploit phenomena such as superposition, interference, and entanglement. Quantum computers have the potential to complete some calculations exponentially faster than classical computers. For example, a large-scale quantum computer could break widely used encryption schemes and aid physicists in performing physical simulations.
Diffie–Hellman key exchangeDiffie–Hellman (DH) key 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 by Ralph Merkle and named after Whitfield Diffie and Martin Hellman. DH is one of the earliest practical examples of public key exchange implemented within the field of cryptography.*As an Amazon Associate I earn from qualifying purchases.