Paillier - Partial Homomorphic EncryptionThe Paillier cryptosystem is a partial homomorphic encryption (PHE) method, and here two encrypted values can be added together, and the decryption of the result gives the addition [1]. If we take two values: \(m_1\) and \(m_2\), we get two encrypted values of Enc(\(m_1\)) and Enc(\(m_2\)). We can then multiply the two cipher values to get Enc(\(m_1+m_2\)). We can then decrypt to get \(m_1+m_2\). Along with this we can also subtract to Enc(\(m_1-m_2\)). This is achieved by taking the inverse modulus of Enc(\(m_2\)) and multiplying it with Enc(\(m_1\)). Finally we can perform a scalar multiply to get Enc(\(m_1 \cdot m_2\)) and which is generated from Enc\((m_1)^{m_2}\).
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Presentation
References
[1] Paillier, P. (1999, May). Public-key cryptosystems based on composite degree residuosity classes. In International conference on the theory and applications of cryptographic techniques (pp. 223-238). Springer, Berlin, Heidelberg [here].