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Towards Total Encryption

Adding and Scalar Multiplying With Homomorphic Encryption

Prof Bill Buchanan OBE FRSE
3 min readDec 21, 2021

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I predict in a decade, we will process encrypted values. This will allow us to preserve the privacy of data but still use mathematical operations. For example, we could run machine learning models on encrypted data, without revealing the core data used underneath. For this we are likely to look towards full homomorphic encryption, and which supports all of the arithmetic operators. But many current applications just need to support adding and subtraction functions for homomorphic encryption. This will support partial homomorphic encryption. For this, Paillier provided a useful method [here]:

And here is a quick presentation:

Its citation count shows that although it was first published in 1999, it has been a slow-burner, and its impact has generally increased over the years:

The method

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Prof Bill Buchanan OBE FRSE
Prof Bill Buchanan OBE FRSE

Written by Prof Bill Buchanan OBE FRSE

Professor of Cryptography. Serial innovator. Believer in fairness, justice & freedom. Based in Edinburgh. Old World Breaker. New World Creator. Building trust.

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