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In: Computer Science

Would it be useful to have an encryption that is additive and multiplicative in Homomorphic?

Would it be useful to have an encryption that is additive and multiplicative in Homomorphic?

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Expert Solution

SOLUTION:- YES, It would be useful to have an encryption that is additive and multiplicative in Homomorphic because that The RSA and Goldwasser-Micali encryption schemes had multiplicative and additive homomorphisms over Z2, Although, in few applications it would be useful to have homomorphism over a larger ring such that, homomorphic addition could provide as a tallying mechanism for a voting scheme, an identical requirement also emerges in database operations.

Paillier encryption scheme that endorse such homomorphisms and utilizes n-th residuosity assumption and generalizes Goldwasser-Micali encryption scheme, obtaining additive homomorphism in Zn. In the same way, El Gamal encryption scheme permits one to execute multiplications in Zp . Normally we would like to endorse arbitrary number of additions & multiplications so we can implement any circuit utilizing just XOR (addition) and AND (multiplication) gates, therefore we can utilize both mechanisms such that one that endorse multiplication and one that endorse addition, and isomorphisms between them, so the multiplication of addition outcomes is easily feasible. Now, we can say that It would be useful to have an encryption that is additive and multiplicative in Homomorphic.

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