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Montgomery modular multiplication relies on a special representation of numbers called Montgomery form. The algorithm uses the Montgomery forms of a and b to efficiently compute the Montgomery form of ab mod N. The efficiency comes from avoiding expensive division operations. Classical modular multiplication reduces the double-width product ab ...
The following tables list the computational complexity of various algorithms for common mathematical operations . Here, complexity refers to the time complexity of performing computations on a multitape Turing machine. [ 1] See big O notation for an explanation of the notation used. Note: Due to the variety of multiplication algorithms, below ...
Order of operations. In mathematicsand computer programming, the order of operationsis a collection of rules that reflect conventions about which operations to perform first in order to evaluate a given mathematical expression. These rules are formalized with a ranking of the operations. The rank of an operation is called its precedence, and an ...
Basic Linear Algebra Subprograms ( BLAS) is a specification that prescribes a set of low-level routines for performing common linear algebra operations such as vector addition, scalar multiplication, dot products, linear combinations, and matrix multiplication. They are the de facto standard low-level routines for linear algebra libraries; the ...
Fast multipole method. The fast multipole method ( FMM) is a numerical technique that was developed to speed up the calculation of long-ranged forces in the n -body problem. It does this by expanding the system Green's function using a multipole expansion, which allows one to group sources that lie close together and treat them as if they are a ...
Memory ordering. Memory ordering is the order of accesses to computer memory by a CPU. Memory ordering depends on both the order of the instructions generated by the compiler at compile time and the execution order of the CPU at runtime. [ 1][ 2] However, memory order is of little concern outside of multithreading and memory-mapped I/O, because ...
The FMA instruction set is an extension to the 128 and 256-bit Streaming SIMD Extensions instructions in the x86 microprocessor instruction set to perform fused multiply–add (FMA) operations. [ 1] There are two variants: FMA4 is supported in AMD processors starting with the Bulldozer architecture. FMA4 was performed in hardware before FMA3 was.
Elliptic curve scalar multiplication is the operation of successively adding a point along an elliptic curve to itself repeatedly. It is used in elliptic curve cryptography (ECC). The literature presents this operation as scalar multiplication, as written in Hessian form of an elliptic curve. A widespread name for this operation is also ...