A low complexity probabilistic test for integer multiplication
نویسندگان
چکیده
A probabilistic test for equality a = bc for given n-bit integers a, b, c is designed within complexity n(log logn) exp{O(log∗ n)}.
منابع مشابه
Complexity of finite field arithmetic
For integers, the parameter n is the bit-length, and for the finite field Fq we let n = log q. In the case of polynomial root-finding, d is the degree of the polynomial and we list bounds on the expected running time since these operations are most efficiently implemented using probabilistic algorithms. In Lecture 3 we addressed the cost of addition and subtraction in both Z and Fq, and the cos...
متن کاملOn the Complexity of Integer Multiplication in Branching Programs with Multiple Tests and in Read-Once Branching Programs with Limited Nondeterminism
Branching Programs (BPs) are a well-established computation and representation model for Boolean functions. Although exponential lower bounds for restricted BPs such as Read-Once Branching Programs (BP1s) have been known for a long time, the proof of lower bounds for important selected functions is sometimes difficult. Especially the complexity of fundamental functions such as integer multiplic...
متن کاملApplications of Fast Truncated Multiplication in Embedded Cryptography
Truncated Multiplications compute Truncated Products, contiguous subsequences of the digits of integer products. For an n-digit multiplication algorithm of time complexity O(n), with 1< α ≤ 2, there is a truncated multiplication algorithm, which is constant times faster when computing a short enough truncated product. Applying these fast truncated multiplications several cryptographic long inte...
متن کاملApplications of Fast Truncated Multiplication in Cryptography
Truncated multiplications compute truncated products, contiguous subsequences of the digits of integer products. For an n-digit multiplication algorithm of time complexity O(nα), with 1 < α ≤ 2, there is a truncated multiplication algorithm, which is constant times faster when computing a short enough truncated product. Applying these fast truncated multiplications, several cryptographic long i...
متن کاملFast Truncated Multiplication and its Applications in Cryptography
Truncated Multiplication computes a truncated product, a contiguous subsequence of the digits of the product of 2 long integers. We review a few truncated multiplication algorithms and adapt them to integers. They are a constant times faster than n-digit full multiplications of time complexity O(n), with 1< α ≤ 2, important in cryptography. For example, the least significant half products with ...
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:
- J. Complexity
دوره 26 شماره
صفحات -
تاریخ انتشار 2010