Near Quadratic Matrix Multiplication Modulo Composites
نویسنده
چکیده
We show how one can use non-prime-power, composite moduli for computing representations of the product of two n × n matrices using only n multiplications and additions.
منابع مشابه
Finding orthogonal vectors in discrete structures
Hopcroft’s problem in d dimensions asks: given n points and n hyperplanes in R, does any point lie on any hyperplane? Equivalently, if we are given two sets of n vectors each in R, is there a pair of vectors (one from each set) that are orthogonal? This problem has a long history and a multitude of applications. It is widely believed that for large d, the problem is subject to the curse of dime...
متن کاملDealing with performance/portability and performance/accuracy trade-offs in heterogeneous computing systems: A case study with matrix multiplication modulo primes
We present the study of two important trade-offs in heterogeneous systems (i.e., between performance versus portability and between performance and accuracy) for a relevant linear algebra problem, matrix multiplication modulo primes. Integer matrix linear algebra methods rely heavily on matrix multiplication modulo primes. Double precision is necessary for exact representation of sufficiently m...
متن کاملElliptic Curve Point Multiplication
New type of elliptic curve point multiplication is proposed, where complex multiplication by 2 − or by 2 ) 7 1 ( − ± is used instead of point duplication. This allows speeding up multiplication about 1.34 times. Using higher radix makes it possible to use one point duplication instead of two and to speed-up computation about 1.6 times. The method takes prime group order factorization: ρ ρ = r a...
متن کاملOn Primitive Points of Elliptic Curves with Complex Multiplication
Let E be an elliptic curve defined over Q and P ∈ E(Q) a rational point of infinite order. Suppose that E has complex multiplication by an order in the quadratic imaginary field k. Denote by ME,P the set of rational primes ` such that ` splits in k, E has good reduction at `, and P is a primitive point modulo `. Under the generalized Riemann hypothesis, we can determine the positivity of the de...
متن کاملFaster Modulo 2 + 1 Multipliers without Booth Recoding
This paper proposes an improvement to the fastest modulo 2 + 1 multiplier already published, without Booth recoding. Results show that by manipulating the partial products and modulo reduction terms and by inserting them adequately in the multiplication matrix, the performance of multiplication units can be improved more than 20%. This improvement is obtained at the expense of some extra circui...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Electronic Colloquium on Computational Complexity (ECCC)
دوره 10 شماره
صفحات -
تاریخ انتشار 2003