This paper proposes a privacy preservation method based on random projection to overcome the curse of dimensionality in privacy preserving data mining.To prevent leaks of random matrix which can lead to the reconstruction attack

it first proposes the concepts of secure subspace and secure subspace mapping.Then

it constructs a secure subspace mapping using hash technique

which is implemented by a random projection matrix

and it achieves a low distortion embedding while preserving the data privacy.Finally

it proves that the secure subspace can preserve the Euclidean distance and inner product between any two original points.The experimental results show that the proposed technique can ensure the data quality in different data mining applications effectively under the precondition of preserving data privacy.