Encryption and Decryption in Conic Curves Cryptosystem Over Finite Field $$GF(2^n)$$ Using Tile Self-assembly

This paper proposes how to accomplish encryption and decryption in conic curves cryptosystem over finite field GF(\(2^n\)) using tile self-assembly. Two parameters in ciphertext could be obtained by two separate models of point-multiplication, one of which changes the seed configuration with inputs to adapt the demands. The decryption process is fulfilled by a new designed tile assembly model containing three sub-models that respectively perform the operation of point-multiplication, the operation of negative point and the operation of point-addition. Assembly time complexity of the model to decrypt is \(\varTheta (n^3)\) and the space complexity is \( \varTheta (n^6)\).