Number-theoretic transform

The Double-Base Number System (DBNS)

Published in Vassil Dimitrov, Graham Jullien, Roberto Muscedere, Multiple-Base Number System, 2017

Vassil Dimitrov, Graham Jullien, Roberto Muscedere

For the final part of this introduction to the DBNS, we discuss the representation of a DBNS number via the exponents of the two bases, rather than the position of the digits in a two-dimensional table. We have already used logarithms in Chapter 1, where the slide rule was described as an analog logarithmic processor, and where finite field logarithms—introduced as an index calculus—were used in a number theoretic transform. Arithmetic operations in a DBNS index calculus are carried out using the exponents directly, rather than the techniques discussed in Chapter 3, where direct manipulations of the digits in the tabular representation are used. The equivalent to this is the binary logarithmic number system (LNS), where a number, x, is represented by its logarithm log2x, where the arithmetic operations are carried out using the base 2 logarithm representation, rather than x itself.

Efficient Fully Homomorphic Encryption with Large Plaintext Space

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Journal Information

Published in IETE Technical Review, 2018

NingBo Li, TanPing Zhou, XiaoYuan Yang, YiLiang Han, YuJuan Sun

In LATINCRYPT'2015, Biasse and Ruiz proposed a new scheme BR15 [26], which introduces homomorphic member tests and parallelizes the bootstrapping process. However, BR15 is based on a special cyclotomic polynomial ring, which will affect the performance of FFT/NTT (Fast Fourier Transformation/Number Theoretic Transform) during bootstrapping. However, comparing to Helib [20], BR15 increases the number of parallels, which results in nearly 100 times improvement in performance.

Number-theoretic transform

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The Double-Base Number System (DBNS)

Efficient Fully Homomorphic Encryption with Large Plaintext Space