中文摘要：

全同态签名方案在可验证外包计算等领域具有重要应用,但目前人们还没有提出基于身份的全同态签名方案.因此,本文给出了基于身份的全同态签名方案的安全定义,基于格问题构造了一个基于身份的层次型全同态签名方案,在标准模型下基于小整数解问题难解性严格证明了所提全同态签名方案满足选择性身份与选择性消息数据集合攻击下的存在性不可伪造性.

英文摘要：

Fully homomorphic signature schemes have important applications in verifiable outsource computations,etc.But there is no identity-based（leveled）fully homomorphic signature scheme up to the present day.Consequently,this paper gives the security definition of the identity-based fully homomorphic signature scheme.Then,it constructs an identity-based leveled fully homomorphic signature scheme by using the lattice problems.Moreover,it strictly proves that the proposed fully homomorphic signature scheme satisfies the existential unforgeability against selective identity and selective message dataset attacks under the intractability of the small integer solution problem in the standard model.