16212

1672 دكتري

دكتري

جبر (رمز)

اصفهان : دانشگاه صنعتي اصفهان

1399

دوازده؛ 107ص.

رضا رضاييان فراشاهي

امير هاشمي

عمران احمدي درويش وند؛ علي رجايي؛ فريد بهرامي

1399/10/22

كتابنامه

رياضي

رياضي

1399/10/22

2661210

Hashing to Elliptic Curves over Finite Fields Mojtaba Fadavi mfadavi88@gmail com September 2020 Doctor of Philosophy Thesis Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranSupervisor Dr Reza Rezaeian Farashahi farashahi@iut ac ir Advisor Dr Amir Hashemi Amir Hashemi@iut ac irAbstractMany curve based cryptosystems and protocols require to efficiently encode bit stringsinto the points of a given elliptic curve such that the encoding function satisfies com putability regularity and samplability or generally admissibility But the availableadmissible encoding functions from Fq are restricted to the class of elliptic curves witha non trivial l torsion Fq rational point where l 2 3 Therefore there is no admissi ble encoding function to the class of many cryptographically interesting elliptic curvesof prime order In this thesis we present four types of admissible encoding functions First a 2 1 encoding function F 0 1 q 1 E Fq where E Fq is the Fq rational 2points of the elliptic curve E Second an injective encoding function to elliptic curveswith a non trivial Fq rational point of order two Third an injective encoding functionto binary elliptic curves and fourth an injective encoding function to ternary ellipticcurves Conversely occasionally we have to transmit points of a known curve through an inse cure channel Traditional methods for transferring points enable an adversary to recog nize patterns in the transmitted data Consequently one finds valuable information to

رضا رضاييان فراشاهي

امير هاشمي

عمران احمدي درويش وند؛ علي رجايي؛ فريد بهرامي