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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.
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 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, ie, 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 hierarchic al encryption scheme with relatively small key and ciphertext sizes.