Lattice problem such as NTRU problem and LWE problem is widely used as the security base of post-quantum cryptosystems. And currently doing lattice reduction by BKZ algorithm is the most efficient way to solve it. In this paper, we give several further improvements on BKZ algorithm, which can be used for different SVP subroutines base on both enumeration and sieving. These improvements in combination provide a speed up of 2^{3~4} in total. It is significant in concrete attacks. Using these new techniques, we solved the 656 dimensional ideal lattice challenge in only 380 thread hours (also with a enumeration based SVP subroutine), much less than the previous records (which costs 4600 thread hours in total). With these improvements enabled, we can still simulate the new BKZ algorithm easily. One can also use this simulator to find the blocksize strategy (and the corresponding cost) to make Pot of the basis (defined in section 5.2) decrease as fast as possible, which means the length of the first basis vector decrease the fastest if we accept the GSA assumption. It is useful for analyzing concrete attacks on lattice-based cryptography.

Often times, the ability to distinguish between random data and a public key can leads to an attack against the cryptosystem itself. In this paper, we will show experimentally a very efficient distinguisher based on the distribution of ranks of the symmetric matrices associated with the central map in the multivariate cryptosystem HFE when the degree D of the central map is very small.

Our purpose is to compare how much the F5 algorithm can gain in efficiency compared to the F4 algorithm. This can be achieve as the F5 algorithm uses the concept of signatures to foresee potential useless computation which the F4 algorithm might make represented by zero rows in the reduction of a large matrix. We experimentally show that this is a modest increase in efficiency for the parameters we tested.