SafekipediaThe 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 method for secure communication that uses complex mathematics to protect information. It was created by Pascal Paillier in 1999 and works by using two large, random numbers to create a special kind of lock and key.
When setting up the system, you first choose two big prime numbers. These numbers are used to calculate a special product and other values that help create a public key (used for locking messages) and a private key (used for unlocking them). The system also uses a random number to help in the locking process.
One special feature of the Paillier cryptosystem is that it allows certain operations on locked messages without unlocking them first. For example, you can combine two locked messages to get a locked version of their sum, or you can lock a message multiple times to represent multiplication. These features make it useful for tasks like online voting, where you need to count votes without revealing who voted for what.
This article is a child-friendly adaptation of the Wikipedia article on Paillier cryptosystem, available under CC BY-SA 4.0.