Questions on determining the security parameter

[bluefrogGG]

Hi, I have tried to use the LWE estimator in particular to measure the security parameter for a custom parameter set. I attempted to see if the output security parameter is equal with that listed in some FHE related papers and Homomorphic Encryption Standard, and I noticed they are not necessarily the same or similar. The estimator sometimes gives more conservative, and the other times gives higher estimate of the security parameter. Both estimators used in this library and Homomorphic Encryption Standard seem to be based on the same paper [APS15], and I am not sure if I can simply accept the result of HElib's lwe estimator.

Thanks in advance. I would appreciate any help..

[APS15] Martin R. Albrecht, Rachel Player and Sam Scott. On the concrete hardness of Learning with
Errors. Journal of Mathematical Cryptology. Volume 9, Issue 3, Pages 169–203, ISSN (Online) 1862-2984,
October 2015