Cryptography and Network Security

In this blog, we shed light on the need for Asymmetric Scalar Product Preserving Encryption (ASPE) , a scheme that enables retrieval of top k nearest points for a given query q. We begin with the motivation, then present the ASPE scheme, and finally demonstrate known-plaintext attack (KPA) on it. Motivation In our daily routine, we frequently interact with various online service providers such as hotel booking platforms, cab services, food delivery, and many more. But have you ever wondered how these services keep your data secure? Let’s take an example of booking an online cab (as shown in Figure 1). Suppose you open a cab-booking application and search for nearest available ride. Behind the scenes, the application stores locations of all cabs in an encrypted form so that they remain hidden from any potential adversary. When you enter your location, the app first encrypts it and then processes it against the encrypted locations of all cabs. After performing the computation securel...

Motivation: In 1978, Rivest, Adleman and Dertouzos [1] introduced the idea of performing computations directly on encrypted data without using secret key. This concept is known as homomorphic encryption. However, their first proposal supported only one type of operation, either addition or multiplication, on encrypted data. Such schemes are called partially homomorphic encryption (PHE). Later, in 1999, Paillier [2] improved this concept by designing an encryption scheme that allows both addition and multiplication on encrypted data, but only a limited number of times. This type of scheme is called somewhat homomorphic encryption (SHE). Paillier Encryption: Paillier encryption is a probabilistic asymmetric algorithm, which means it uses separate keys for encryption and decryption and also introduces randomness during encryption to ensure that the same message never encrypts to the same ciphertext. It supports important homomorphic properties that make it useful in privacy preserving app...