<p><span style="font-size: small;"><span>The low cost availability of smart devices and broadband connection has led to rapid growth of communication over Internet. As of today the internet based communication service is widely used in various application services such as in E-Mail transaction of sensitive data (medical data), online money transaction etc. all these services requires a strong security. There has been continuous ongoing research by various cryptanalyst to enhance security of cryptography especially in semi-untrusted server. However, performance, computation time and ease of use play a significant role in using the algorithm for implementation. Proxy re-encryption plays a significant role in protecting data that are stored in semi-untrusted server. Many existing Proxy re-encryption technique induces high computation overhead due to adoption of public key cryptography such RSA (Rivet Shamir Adleman), ECC (Elliptical Curve Cryptography) etc. and it suffer from quantum attack. To address this lattice based cryptography is adopted by various approaches which is based on Learning With Error which shows resilience against quantum attacks such Chosen Cipher data attack and Chosen Plain Text attack. The drawback with existing lattice cryptography based approach is that they are unidirectional and adopts bilinear pairing which compromise security and induces high computation cost. To address this work present a Bidirectional Proxy Re-encryption scheme by adopting lattice based cryptography technique. Experiment is conducted for computation overhead by varying key and data size which attained significant performance improvement over existing Proxy Re-encryption scheme.</span><br /></span></p>