Nowadays, alternative models of elliptic curves like Montgomery, Edwards, twisted Edwards, Hessian, twisted Hessian, Huff’s curves and many others are very popular and many people use them in cryptosystems which are based on elliptic curve cryptography. Most of these models allow to use fast and complete arithmetic which is especially convenient in fast implementations that are side-channel attacks resistant. Montgomery, Edwards and twisted Edwards curves have always order of group of rational points divisible by 4. Huff’s curves have always order of rational points divisible by 8. Moreover, sometimes to get fast and efficient implementations one can choose elliptic curve with even bigger cofactor, for example 16. Of course the bigger cofactor is, the smaller is the security of cryptosystem which uses such elliptic curve. In this article will be checked what influence on the security has form of cofactor of elliptic curve and will be showed that in some situations elliptic curves with cofactor divisible by 2m are vulnerable for combined small subgroups and side-channel attacks.
The aim of this publication is to present practical application of the R. Kolman’s quality rating method used in the evaluation of aluminium alloys. The results of studies of the mechanical and physical properties of the three selected test materials are discussed. To find the best material, the quality level of each of the tested materials was assessed using quality ratings proposed by R. Kolman. The results of the conducted analysis have proved that the best material was an AKII MM alloy, i.e. a casting AK11 aluminium alloy from the 4XXX series.