Finite field arithmeticIn mathematics, finite field arithmetic is arithmetic in a finite field (a field containing a finite number of elements) contrary to arithmetic in a field with an infinite number of elements, like the field of rational numbers. There are infinitely many different finite fields. Their number of elements is necessarily of the form pn where p is a prime number and n is a positive integer, and two finite fields of the same size are isomorphic.
Primitive root modulo nIn modular arithmetic, a number g is a primitive root modulo n if every number a coprime to n is congruent to a power of g modulo n. That is, g is a primitive root modulo n if for every integer a coprime to n, there is some integer k for which gk ≡ a (mod n). Such a value k is called the index or discrete logarithm of a to the base g modulo n. So g is a primitive root modulo n if and only if g is a generator of the multiplicative group of integers modulo n.
International Association for Cryptologic ResearchThe International Association for Cryptologic Research (IACR) is a non-profit scientific organization that furthers research in cryptology and related fields. The IACR was organized at the initiative of David Chaum at the CRYPTO '82 conference. The IACR organizes and sponsors three annual flagship conferences, four area conferences in specific sub-areas of cryptography, and one symposium: Crypto (flagship) Eurocrypt (flagship) Asiacrypt (flagship) Fast Software Encryption (FSE) Public Key Cryptography (PKC) Cryptographic Hardware and Embedded Systems (CHES) Theory of Cryptography (TCC) Real World Crypto Symposium (RWC) Several other conferences and workshops are held in cooperation with the IACR.
RSA Factoring ChallengeThe RSA Factoring Challenge was a challenge put forward by RSA Laboratories on March 18, 1991 to encourage research into computational number theory and the practical difficulty of factoring large integers and cracking RSA keys used in cryptography. They published a list of semiprimes (numbers with exactly two prime factors) known as the RSA numbers, with a cash prize for the successful factorization of some of them. The smallest of them, a 100-decimal digit number called RSA-100 was factored by April 1, 1991.
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. In addition, some lattice problems which are worst-case hard can be used as a basis for extremely secure cryptographic schemes.
Dialectica interpretationIn proof theory, the Dialectica interpretation is a proof interpretation of intuitionistic logic (Heyting arithmetic) into a finite type extension of primitive recursive arithmetic, the so-called System T. It was developed by Kurt Gödel to provide a consistency proof of arithmetic. The name of the interpretation comes from the journal Dialectica, where Gödel's paper was published in a 1958 special issue dedicated to Paul Bernays on his 70th birthday.
Gödel's completeness theoremGödel's completeness theorem is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability in first-order logic. The completeness theorem applies to any first-order theory: If T is such a theory, and φ is a sentence (in the same language) and every model of T is a model of φ, then there is a (first-order) proof of φ using the statements of T as axioms. One sometimes says this as "anything universally true is provable".
Multiplicative orderIn number theory, given a positive integer n and an integer a coprime to n, the multiplicative order of a modulo n is the smallest positive integer k such that . In other words, the multiplicative order of a modulo n is the order of a in the multiplicative group of the units in the ring of the integers modulo n. The order of a modulo n is sometimes written as . The powers of 4 modulo 7 are as follows: The smallest positive integer k such that 4k ≡ 1 (mod 7) is 3, so the order of 4 (mod 7) is 3.
Broadwell (microarchitecture)Broadwell is the fifth generation of the Intel Core Processor. It is Intel's codename for the 14 nanometer die shrink of its Haswell microarchitecture. It is a "tick" in Intel's tick–tock principle as the next step in semiconductor fabrication. Like some of the previous tick-tock iterations, Broadwell did not completely replace the full range of CPUs from the previous microarchitecture (Haswell), as there were no low-end desktop CPUs based on Broadwell.
Nehalem (microarchitecture)Nehalem nəˈheɪləm is the codename for Intel's 45 nm microarchitecture released in November 2008. It was used in the first-generation of the Intel Core i5 and i7 processors, and succeeds the older Core microarchitecture used on Core 2 processors. The term "Nehalem" comes from the Nehalem River. Nehalem is built on the 45 nm process, is able to run at higher clock speeds, and is more energy-efficient than Penryn microprocessors. Hyper-threading is reintroduced, along with a reduction in L2 cache size, as well as an enlarged L3 cache that is shared among all cores.
