2017, 26(5): 926-932.
doi: 10.1049/cje.2017.07.010
Abstract:
Several special properties of Smart and Vercauteren's encryption scheme are put forward. They are all based on the special parameter, which is a recommended modulus polynomial. These properties not only show that the secret key is deduced from an N-dimensional vector into its any entry, but also produce the triplet (grade-i reduced plaintext space, grade-i reduced ciphertext space, grade-i reduced secret key) for each i, where grade-i reduced secret key can decrypt grade-i reduced ciphertexts and can be efficiently computed from grade-i delegated key. At the same time, sequentially grade-(i+ 1) delegated key can be efficiently computed from grade-i delegated key. This work also discusses a sequential computation in opposite direction, i.e., computing grade-i delegated key from grade-(i + 1) delegated key. But the sequential computation in the opposite direction is difficult except at most the first steps of such sequential computation. Based on the properties given, we then propose a simple hierarchical encryption scheme with relatively small key and ciphertext sizes.