QPP (Quadrature permutation polynomial)

Quadrature Permutation Polynomial (QPP) is a cryptographic primitive used in symmetric key encryption algorithms. It is a construction that combines a permutation and a polynomial function to achieve confusion and diffusion properties in encryption.

QPP is primarily used in the context of block ciphers, where it operates on fixed-size blocks of data. The construction consists of two main components: a permutation layer and a polynomial layer.

1. Permutation Layer: The permutation layer of QPP is responsible for shuffling the bits of the input block to introduce confusion. It ensures that each bit of the input block affects multiple bits in the subsequent stages of the encryption process. The permutation layer can be implemented using various techniques, such as bitwise rotations, XOR operations, or lookup tables. The specific permutation used in QPP depends on the design and requirements of the encryption algorithm.
2. Polynomial Layer: The polynomial layer of QPP applies a polynomial function to the permuted block to introduce diffusion. It ensures that each bit of the output block depends on multiple bits of the input block, creating a complex relationship between the bits. The polynomial function used in QPP is typically a non-linear function that combines addition, multiplication, and other bitwise operations. The coefficients and structure of the polynomial function are carefully chosen to achieve cryptographic properties like confusion and diffusion.

The combination of the permutation and polynomial layers in QPP helps to achieve a high level of security in the encryption process. The permutation layer ensures that the relationship between the input and output bits is complex and non-linear, while the polynomial layer spreads the influence of each input bit across multiple output bits. This combination makes it difficult for an attacker to analyze the encryption algorithm and recover the original plaintext from the ciphertext without knowledge of the secret key.

QPP is often used as a component in the design of symmetric key encryption algorithms, such as block ciphers or stream ciphers. It is particularly effective when used in combination with other cryptographic techniques, such as key scheduling algorithms, substitution boxes (S-boxes), and additional rounds of encryption.

It's important to note that while QPP provides strong confusion and diffusion properties, its security also relies on the secrecy of the encryption key and the resistance of its individual components against various cryptanalysis techniques. Cryptographers continually analyze and evaluate new constructions, including QPP, to ensure their resistance against known attacks and to develop stronger encryption algorithms.