پديد آورنده :
محمدي نسب، هادي
عنوان :
مسئله لگاريتم گسسته خم هاي بيضوي و كاربرد آن در رمز نگاري
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
رياضي كاربردي
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
صفحه شمار :
دوازده، 167ص.: مصور، جدول
يادداشت :
ص.ع. به فارسي و انگليسي
استاد راهنما :
رضا رضائيان فراشاهي
استاد مشاور :
محمدرضا هوشمند اصل
توصيفگر ها :
الگوريتم پلارد رو , قرينه نقطه , نصف نقطه
تاريخ نمايه سازي :
94/2/16
استاد داور :
عمران احمدي درويشوند، ساره گلي
تاريخ ورود اطلاعات :
1396/09/27
چكيده انگليسي :
The elliptic curves discrete logarithm problem and its applications in cryptography Hadi Mohammadi Nasab hadi mohammadi@math iut ac ir 2015 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Reza Rezaeian Farashahi farashahi@cc iut ac ir Advisor Dr Mohammad Reza Hooshmand Asl hooshmandasl@yazd ac ir 2010 MSC 11T71 11G20 14Q20 68Q25 Keywords Elliptic curve discrete logarithm Pollarrd Rho method Point halving Negation map AbstractThe Elliptic curve discrete logarithm problem ECDLP is a signi cant problem in the epoch of moderncryptography The security of various cryptographic systems and protocols such as the Di e HellmanKey Exchange DHKE the US governments Digital Signature Algorithm DSA and the Schnorrsignature scheme relies on the intractability of solving the Elliptic curve discrete logarithm problem The elliptic curve cryptosystem ECC was proposed independently by Neal Koblitz and Victor Millerin 1985 In fact they utilize the group of points on an elliptic curve that is de ned over nite prime eld instead of the multiplicative groups of nite prime elds Afterwards several practical systemsbased on the ECDLP were designed such as various pairing based schemes Nowadays Pollard rhomethod and its parallelized versions are known as the best generic attack against the ECDLP Thesemethods can be used for any cyclic group and do not require to de ne any additional structure in theelliptic curve groups Pollard rho method is a randomized algorithm for computing discrete logarithms based on the BirthdayParadox More precisely an iteration function F G G is used to de ne a pseudo randoim sequenceYi by Yi 1 F Yi for i 0 1 2 with an initial value Y0 The sequence Y0 Y1 Y2 constitutesa walk in the group G Since the order of the group is nite the sequence will ultimately attain anelement that has occurred before which is called a collision The most advantageous of the Pollard s
استاد راهنما :
رضا رضائيان فراشاهي
استاد مشاور :
محمدرضا هوشمند اصل
استاد داور :
عمران احمدي درويشوند، ساره گلي
