"It is known that the security of public key cryptosystems can be based on Vector Decomposition Problem (VDP). In this paper, the authors analyze this problem. In practice, it was shown that the Computational Diffie-Hellmann Problem (CDHP) is equivalent to VDP for super-singular elliptic curves. Moreover, VDP on a higher genus curve is hard if CDHP is hard on its one dimensional subspace. They propose an encryption scheme, which is homomorphic in nature, based on VDP."