Paillier cryptosystem

The Paillier cryptosystem is a special way to hide and protect information that was created by Pascal Paillier in 1999. It is part of a larger group of tools called asymmetric algorithm used in public key cryptography. This means it uses two different keys—one that anyone can share and another that is kept secret—to keep data safe.

What makes the Paillier cryptosystem special is that it allows some basic math to be done on hidden information without revealing what that information actually is. This property is called being an additive homomorphic cryptosystem. For example, if you have the hidden numbers m₁ and m₂, someone can figure out the hidden number for m₁ + m₂ without ever knowing what m₁ or m₂ actually equals.

The safety of this system depends on a complex math problem called the decisional composite residuosity assumption, which is believed to be very hard to solve without the right secret key. Because of these properties, the Paillier cryptosystem is used in situations where privacy is important but some calculations still need to be made on hidden data.

Algorithm

The Paillier cryptosystem is a way to keep messages safe when sharing them online. It was made by Pascal Paillier in 1999. It uses math with big numbers to create a special lock and key.

To start, you pick two very big prime numbers. These help make a public key (used to lock messages) and a private key (used to unlock them). The system also uses another random number to help lock messages.

One cool thing about the Paillier cryptosystem is that you can do some work on locked messages without unlocking them. For example, you can add two locked messages together and still keep them locked. This makes it useful for things like online voting, where you can count votes without seeing who voted for what.