# How to identify the difference between two cryptographic schemes in terms of security?

I am currently working on a project, that requires using encryption libraries namely (LibScarab and FHEW). I want to know how can I compare the two schemes in terms of security (I already compared between them in terms of execution time). All I know that LibScarab uses SV scheme, while FHEW uses LWE scheme. Can I get help in how to bring comparisons between two schemes to decide which one is more secure?

Security of the Smart-Vercauteren scheme is based on the Short Generator Principal Ideal Problem (SG-PIP), whilst FHEW is based on (ring)-LWE. There have recently been several attacks on SG-PIP that are much faster than the best known LWE attacks, so it would seem that FHEW currently has stronger security foundations.

In particular, Cramer, Ducas, Peikert and Regev described a subexponential attack that solves SG-PIP in $O(2^{n^{2/3 + \varepsilon}})$ time.

http://eprint.iacr.org/2015/313.pdf

I don't know whether LibScarab takes this attack into account, but I suspect at least the original SV parameters are much weaker than first suggested.

There are also polynomial time quantum attacks on SG-PIP that are referenced in that work, whereas there are currently no known efficient quantum algorithms for (ring)-LWE.

• Thanks a lot,but I know that FHEW ae usig standard LWE encryption scheme not the ring-LWE. However, the SV is using the ideal lattice based. So if I want to compare between scheme in mathmatical representation ( security bit) do you think that I could make something work a round this attack ?? – Never too late Apr 1 '16 at 8:22

To compare two schemes in terms of security, you need to know the security models of your schemes, i.e. being ind-cpa or ind-cca, etc.