Topic
Multiplication
About: Multiplication is a research topic. Over the lifetime, 11189 publications have been published within this topic receiving 154839 citations. The topic is also known as: × & times.
Papers published on a yearly basis
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Papers
TL;DR: The trigonometric algorithms used in this computer and the instrumentation of these algorithms are discussed in this paper.
Abstract: The COordinate Rotation DIgital Computer(CORDIC) is a special-purpose digital computer for real-time airborne computation. In this computer, a unique computing technique is employed which is especially suitable for solving the trigonometric relationships involved in plane coordinate rotation and conversion from rectangular to polar coordinates. CORDIC is an entire-transfer computer; it contains a special serial arithmetic unit consisting of three shift registers, three adder-subtractors, and special interconnections. By use of a prescribed sequence of conditional additions or subtractions, the CORDIC arithmetic unit can be controlled to solve either set of the following equations: Y' = K(Y cos? + X sin?) X' = K(X cos? - Y sin?), or R = K?X2 + Y2 ? = tan-1 Y/X, where K is an invariable constant. This special arithmetic unit is also suitable for other computations such as multiplication, division, and the conversion between binary and mixed radix number systems. However, only the trigonometric algorithms used in this computer and the instrumentation of these algorithms are discussed in this paper.
2,852 citations
TL;DR: An algorithm is given for computer control of a digital plotter that may be programmed without multiplication or division instructions and is efficient with respect to speed of execution and memory utilization.
Abstract: An algorithm is given for computer control of a digital plotter.
The algorithm may be programmed without multiplication or division instructions and is efficient with respect to speed of execution and memory utilization.
2,505 citations
TL;DR: Experimental results show that the AOA provides very promising results in solving challenging optimization problems compared with eleven other well-known optimization algorithms.
2,204 citations
30 May 2010
TL;DR: A fully homomorphic encryption scheme, using only elementary modular arithmetic, that reduces the security of the scheme to finding an approximate integer gcd, and investigates the hardness of this task, building on earlier work of Howgrave-Graham.
Abstract: We construct a simple fully homomorphic encryption scheme, using only elementary modular arithmetic. We use Gentry’s technique to construct a fully homomorphic scheme from a “bootstrappable” somewhat homomorphic scheme. However, instead of using ideal lattices over a polynomial ring, our bootstrappable encryption scheme merely uses addition and multiplication over the integers. The main appeal of our scheme is the conceptual simplicity.
We reduce the security of our scheme to finding an approximate integer gcd – i.e., given a list of integers that are near-multiples of a hidden integer, output that hidden integer. We investigate the hardness of this task, building on earlier work of Howgrave-Graham.
2,001 citations
3 Dec 2017
TL;DR: A method to construct a homomorphic encryption scheme for approximate arithmetic that supports an approximate addition and multiplication of encrypted messages, together with a new rescaling procedure for managing the magnitude of plaintext.
Abstract: We suggest a method to construct a homomorphic encryption scheme for approximate arithmetic. It supports an approximate addition and multiplication of encrypted messages, together with a new rescaling procedure for managing the magnitude of plaintext. This procedure truncates a ciphertext into a smaller modulus, which leads to rounding of plaintext. The main idea is to add a noise following significant figures which contain a main message. This noise is originally added to the plaintext for security, but considered to be a part of error occurring during approximate computations that is reduced along with plaintext by rescaling. As a result, our decryption structure outputs an approximate value of plaintext with a predetermined precision.
1,933 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2022 | 8 |
| 2021 | 435 |
| 2020 | 548 |
| 2019 | 541 |
| 2018 | 495 |
| 2017 | 426 |