چكيده انگليسي :
HIMMO A Key Predistribution Scheme Tahereh Mohammadbeigi Dehaghi t mohammadbeigi@math iut ac ir 2017 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Reza Rezaeian Farashahi farashahi@cc iut ac ir Advisor Dr Omran Ahmadi Darvishvand oahmadid@ipm ir 2010 MSC 14H52 14G50 94A60 11T71 Keywords HI problem MMO problem HIMMO lattice AbstractPairwise key establishment practically and e ectively is of great importance for industrial expansionof large networks with limited resources such as wireless sensors In these networks the nodes areextremely limited with regard to computing power energy and bandwidth In this thesis chapter 5 we review HIMMO as a lightweight key predistribution for establishment of a common key amongtwo nodes It is the rst e cient key predistribution scheme which has two highly secure and highlye cient features Highly secure that means large collusions of nodes are tolerated and highly e cientmeans that the time required for key establishment is very short Actually key establishment is donein a fraction of second only even if devices are very limited such as 8 bit CPUs and if the memoryfootprint is low The HIMMO scheme is suggestive of Blundo et al s key predistribution scheme Key establishment in Blundo et al s scheme is done e ciently as it comes up to the evaluation ofa polynomial over a nite eld Key establishment among two nodes in HIMMO scheme comes upto the evaluation of an individual low degree univariate polynomial for every node which is also verye cient The di erence is that the Blundo et al s scheme entirely breaks down when the number ofcolluding nodes is larger than the degree of the polynomial but the HIMMO scheme is designed tobe resistant against any number of colluding nodes In chapter 3 we study the Mixing Modular Operations MMO problem as recovering two polynomialsf Zp x and g Zq x with known degree where p and q are two un known possitive integers byusing of the values of f t mod p g t mod q that are calculated in many points t Z Then westudy if p and q are known the MMO problem can be reduced to nding a close vector in a lattice
