Algebraic Cryptanalysis of Small Scale Variants of the Grain-128AEAD cipher
Algebraická kryptoanalýza zjednodušených variant šifry Grain-128AEAD
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České vysoké učení technické v Praze
Czech Technical University in Prague
Czech Technical University in Prague
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Táto práca sa zaoberá algebraickou kryptoanalýzou, ktorá šifru Grain-128AEADv2, ďalej už len Grain, prevedie na sústavu polynomiálnych rovníc a následne ju vyrieši pomocou Groebnerových báz. Algebraická kryptoanalýza bude aplikovaná na zjednodušené varianty šifry Grain. Pre efektívnejší výpočet riešenia použijeme metódu Locality Sensitive Hashing pre zjednodušenie systému polynomiálnych rovníc. V rámci experimentov sme boli schopný prelomiť napríklad zmenšenú 16 bitovú variantu šifry s počtom kôl 64 a taktiež aj 24 bitovú variantu s počtom kôl 8. Čas generovania rovníc pre zmienenú 24 bitovú variantu trval približne 8 minút a výpočet riešenia 113 sekúnd. Taktiež sme aplikovali algoritmus Locality Sensitive Hashing a tým sme zrýchlili výpočet Groebnerových báz a riešenia. Napríklad pre 24 bitovú verziu s počtom kôl 8 sme boli schopný znížiť výpočet riešenia zo 113 sekúnd na 1,88 sekundy.
This master thesis deals with algebraic cryptanalysis which converts the Grain-128AEADv2 cipher, hereinafter referred to as Grain, into a system of polynomial equations and then solves it using Groebner bases. Algebraic cryptanalysis will be applied to small scale variants of Grain cipher. For a more efficient calculation of the solution, we will use the Locality Sensitive Hashing method for simplifying the system of polynomial equations. As part of the experiments, we were able to break, for example, a 16-bit small scale variant of the cipher with the number of rounds of 64, as well as the 24-bit variant with number of rounds of 8. The generation time of the equations for the mentioned 24-bit variant took approximately 8 minutes, and the calculation of the solution took 113 seconds. We also applied the Locality Sensitive Hashing algorithm and thereby accelerated the calculation of Groebner bases and solutions. For example, for the 24-bit version with the number of rounds of 8, we were able to reduce the calculation of the solution from 113 seconds to 1,88 seconds.
This master thesis deals with algebraic cryptanalysis which converts the Grain-128AEADv2 cipher, hereinafter referred to as Grain, into a system of polynomial equations and then solves it using Groebner bases. Algebraic cryptanalysis will be applied to small scale variants of Grain cipher. For a more efficient calculation of the solution, we will use the Locality Sensitive Hashing method for simplifying the system of polynomial equations. As part of the experiments, we were able to break, for example, a 16-bit small scale variant of the cipher with the number of rounds of 64, as well as the 24-bit variant with number of rounds of 8. The generation time of the equations for the mentioned 24-bit variant took approximately 8 minutes, and the calculation of the solution took 113 seconds. We also applied the Locality Sensitive Hashing algorithm and thereby accelerated the calculation of Groebner bases and solutions. For example, for the 24-bit version with the number of rounds of 8, we were able to reduce the calculation of the solution from 113 seconds to 1,88 seconds.
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Vysokoškolská závěrečná práce je dílo chráněné autorským zákonem. Je možné pořizovat z něj na své náklady a pro svoji osobní potřebu výpisy, opisy a rozmnoženiny. Jeho využití musí být v souladu s autorským zákonem v platném znění.
Vysokoškolská závěrečná práce je dílo chráněné autorským zákonem. Je možné pořizovat z něj na své náklady a pro svoji osobní potřebu výpisy, opisy a rozmnoženiny. Jeho využití musí být v souladu s autorským zákonem v platném znění.