Cryptographic hash functionA cryptographic hash function (CHF) is a hash algorithm (a map of an arbitrary binary string to a binary string with a fixed size of bits) that has special properties desirable for a cryptographic application: the probability of a particular -bit output result (hash value) for a random input string ("message") is (as for any good hash), so the hash value can be used as a representative of the message; finding an input string that matches a given hash value (a pre-image) is unfeasible, assuming all input str
Quadratic sieveThe quadratic sieve algorithm (QS) is an integer factorization algorithm and, in practice, the second fastest method known (after the general number field sieve). It is still the fastest for integers under 100 decimal digits or so, and is considerably simpler than the number field sieve. It is a general-purpose factorization algorithm, meaning that its running time depends solely on the size of the integer to be factored, and not on special structure or properties.
Smooth numberIn number theory, an n-smooth (or n-friable) number is an integer whose prime factors are all less than or equal to n. For example, a 7-smooth number is a number whose every prime factor is at most 7, so 49 = 72 and 15750 = 2 × 32 × 53 × 7 are both 7-smooth, while 11 and 702 = 2 × 33 × 13 are not 7-smooth. The term seems to have been coined by Leonard Adleman. Smooth numbers are especially important in cryptography, which relies on factorization of integers.
General number field sieveIn number theory, the general number field sieve (GNFS) is the most efficient classical algorithm known for factoring integers larger than 10100. Heuristically, its complexity for factoring an integer n (consisting of ⌊log2 n⌋ + 1 bits) is of the form in O and L-notations. It is a generalization of the special number field sieve: while the latter can only factor numbers of a certain special form, the general number field sieve can factor any number apart from prime powers (which are trivial to factor by taking roots).
Collision resistanceIn cryptography, collision resistance is a property of cryptographic hash functions: a hash function H is collision-resistant if it is hard to find two inputs that hash to the same output; that is, two inputs a and b where a ≠ b but H(a) = H(b). The pigeonhole principle means that any hash function with more inputs than outputs will necessarily have such collisions; the harder they are to find, the more cryptographically secure the hash function is.
Pentium 4Pentium 4 is a series of single-core CPUs for desktops, laptops and entry-level servers manufactured by Intel. The processors were shipped from November 20, 2000 until August 8, 2008. It was removed from the official price lists starting in 2010, being replaced by Core 2. All Pentium 4 CPUs are based on the NetBurst microarchitecture. The Pentium 4 Willamette (180 nm) introduced SSE2, while the Prescott (90 nm) introduced SSE3. Later versions introduced Hyper-Threading Technology (HTT).
Special number field sieveIn number theory, a branch of mathematics, the special number field sieve (SNFS) is a special-purpose integer factorization algorithm. The general number field sieve (GNFS) was derived from it. The special number field sieve is efficient for integers of the form re ± s, where r and s are small (for instance Mersenne numbers). Heuristically, its complexity for factoring an integer is of the form: in O and L-notations.
PentiumPentium is a series of x86 architecture-compatible microprocessors produced by Intel. The original Pentium was first released on March 22, 1993. Pentium-branded processors released from 2009 to 2022 are considered entry-level products that Intel rates as "two stars", meaning that they are above the low-end Atom and Celeron series, but below the faster Intel Core lineup and workstation/server Xeon series. These later Pentium processors have little more than their name in common with earlier Pentiums, which were Intel's flagship processor for over a decade until the introduction of the Intel Core line in 2006.
Hash functionA hash function is any function that can be used to map data of arbitrary size to fixed-size values, though there are some hash functions that support variable length output. The values returned by a hash function are called hash values, hash codes, digests, or simply hashes. The values are usually used to index a fixed-size table called a hash table. Use of a hash function to index a hash table is called hashing or scatter storage addressing.
Pentium ProThe Pentium Pro is a sixth-generation x86 microprocessor developed and manufactured by Intel and introduced on November 1, 1995. It introduced the P6 microarchitecture (sometimes termed i686) and was originally intended to replace the original Pentium in a full range of applications. While the Pentium and Pentium MMX had 3.1 and 4.5 million transistors, respectively, the Pentium Pro contained 5.5 million transistors.
Pentium MThe Pentium M is a family of mobile 32-bit single-core x86 microprocessors (with the modified Intel P6 microarchitecture) introduced in March 2003 and forming a part of the Intel Carmel notebook platform under the then new Centrino brand. The Pentium M processors had a maximum thermal design power (TDP) of 5–27 W depending on the model, and were intended for use in laptops (thus the "M" suffix standing for mobile).
Integer factorizationIn number theory, integer factorization is the decomposition, when possible, of a positive integer into a product of smaller integers. If the factors are further restricted to be prime numbers, the process is called prime factorization, and includes the test whether the given integer is prime (in this case, one has a "product" of a single factor). When the numbers are sufficiently large, no efficient non-quantum integer factorization algorithm is known. However, it has not been proven that such an algorithm does not exist.
One-way compression functionIn cryptography, a one-way compression function is a function that transforms two fixed-length inputs into a fixed-length output. The transformation is "one-way", meaning that it is difficult given a particular output to compute inputs which compress to that output. One-way compression functions are not related to conventional data compression algorithms, which instead can be inverted exactly (lossless compression) or approximately (lossy compression) to the original data.
Pentium DPentium D is a range of desktop 64-bit x86-64 processors based on the NetBurst microarchitecture, which is the dual-core variant of the Pentium 4 manufactured by Intel. Each CPU comprised two cores. The brand's first processor, codenamed Smithfield and manufactured on the 90 nm process, was released on May 25, 2005, followed by the 65 nm Presler nine months later. The core implementation on the 90 nm "Smithfield" and later 65 nm "Presler" are designed differently but are functionally the same.
Shor's algorithmShor'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 (that is, non-quantum) algorithms. On the other hand, factoring numbers of practical significance requires far more qubits than available in the near future.
Prime numberA prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4.
Perfect hash functionIn computer science, a perfect hash function h for a set S is a hash function that maps distinct elements in S to a set of m integers, with no collisions. In mathematical terms, it is an injective function. Perfect hash functions may be used to implement a lookup table with constant worst-case access time. A perfect hash function can, as any hash function, be used to implement hash tables, with the advantage that no collision resolution has to be implemented.
Preimage attackIn cryptography, a preimage attack on cryptographic hash functions tries to find a message that has a specific hash value. A cryptographic hash function should resist attacks on its (set of possible inputs). In the context of attack, there are two types of preimage resistance: preimage resistance: for essentially all pre-specified outputs, it is computationally infeasible to find any input that hashes to that output; i.e., given , it is difficult to find an such that () = .
P6 (microarchitecture)The P6 microarchitecture is the sixth-generation Intel x86 microarchitecture, implemented by the Pentium Pro microprocessor that was introduced in November 1995. It is frequently referred to as i686. It was planned to be succeeded by the NetBurst microarchitecture used by the Pentium 4 in 2000, but was revived for the Pentium M line of microprocessors. The successor to the Pentium M variant of the P6 microarchitecture is the Core microarchitecture which in turn is also derived from P6.
Hash collisionIn computer science, a hash collision or hash clash is when two pieces of data in a hash table share the same hash value. The hash value in this case is derived from a hash function which takes a data input and returns a fixed length of bits. Although hash algorithms have been created with the intent of being collision resistant, they can still sometimes map different data to the same hash (by virtue of the pigeonhole principle). Malicious users can take advantage of this to mimic, access, or alter data.
