Number-Theoretic Transforms of Prescribed Length
نویسندگان
چکیده
منابع مشابه
Number-theoretic transforms of prescribed length
A new constructive method for finding all convenient moduli m for a number-theoretic transform with given length N and given primitive Nth root of unity modulo m is presented. This method is based on the prime factorization of cyclotomic polynomials with integer-valued argument or on the primitive divisors of integers. Many known results can be obtained as simple corollaries.
متن کاملFaster arithmetic for number-theoretic transforms
We show how to improve the efficiency of the computation of fast Fourier transforms over Fp where p is a word-sized prime. Our main technique is optimisation of the basic arithmetic, in effect decreasing the total number of reductions modulo p, by making use of a redundant representation for integers modulo p. We give performance results showing a significant improvement over Shoup’s NTL library.
متن کاملUnusual-Length Number-Theoretic Transforms Using Recursive Extensions of Rader’s Algorithm
A novel decomposition of NTT blocklengths is proposed using repeated applications of Rader’s algorithm to reduce the problem to that of realising a single small-length NTT. An efficient implementation of this small-length NTT is achieved by an initial basis conversion of the data, so that the new basis corresponds to the kernel of the small-length NTT. Multiplication by powers of the kernel bec...
متن کاملNumber Theoretic Transforms in Neural Network Image Classiication
Judicious use of number theory and abstract algebra can increase the eeciency of neural network pattern classiiers. We use the example of our neural network tissue classiication of MRI of the breast to illustrate that eecient pattern recognition algorithms can be designed from algebraic fundamentals. The algorithm is based on number theoretic transform speed-up of an FFT-based convolution scheme.
متن کاملPublic Key Cryptosystem based on Number Theoretic Transforms
In this paper a Public Key Cryptosystem is proposed using the number theoretic transforms (NTT) over a ring of integer modulo a composite number. The key agreement is similar to ElGamal public key algorithm. The security of the system is based on solution of multivariate linear congruence equations and discrete logarithm problem. In the proposed cryptosystem only fixed numbers of multiplication...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1986
ISSN: 0025-5718
DOI: 10.2307/2008183