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 study was carried out in Polish goat population to estimate the prevalence of the nasal cavity infection with various staphylococcal species including methicillin-resistant Staphylococcus aureus (MRSA), investigate the potential permissive role of small ruminant lentivirus (SRLV) infection and determine the level of clonality of S. aureus nasal isolates. Nasal swabs and blood samples were collected from 1300 clinically healthy adult goats from 21 Polish goat herds. Blood samples were serologically screened for SRLV. Staphylococci were isolated from nasal swabs and identified using classical microbiological methods, MALDI-TOF, multiplex-PCR, and their clonality was assessed using PFGE. Antimicrobial resistance was determined on the basis of minimum inhibitory concentration and by demonstration of the presence of the mecA gene encoding the multiplex-PCR PBP2a protein and of the five main types of staphylococcal cassette chromosome mec. The apparent prevalence of staphylococcal and S. aureus infection of the nasal cavity was 29.1% (CI 95%: 26.9%, 31.5%) and 7.3% (CI 95%: 6.1%, 8.8%), respectively. No relationship was found between the SRLV-infection and the presence of any staphylococcal species including S. aureus (p=0.143). Only 9.8% of S. aureus isolates were resistant to amoxicillin/clavulanic acid and 5.9% to chloramphenicol and ciprofloxacin. All tested isolates proved to be phenotypically and genotypically sensitive to methicillin, which yielded the apparent prevalence of MRSA of 0% (CI 95%: 0%, 7.0%). S. aureus isolates show high genetic similarity within goat herds, however vary considerably between herds. Goats do not appear to be an important source of S. aureus for humans in Poland.