Benaloh cryptosystem

The Benaloh Cryptosystem is an extension of the Goldwasser-Micali cryptosystem (GM) created in 1994 by Josh (Cohen) Benaloh. The main improvement of the Benaloh Cryptosystem over GM is that longer blocks of data can be encrypted at once, whereas in GM each bit is encrypted individually.

Like many public key cryptosystems, this scheme works in the group ${\displaystyle (\mathbb {Z} /n\mathbb {Z} )^{*}}$ where n is a product of two large primes. This scheme is homomorphic and hence malleable.

Given block size r, a public/private key pair is generated as follows:

The public key is then ${\displaystyle y,n}$, and the private key is ${\displaystyle \phi ,x}$.

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