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Showing result 1 - 5 of 10 essays matching the above criteria.

  1. 1. Homomorphic encryption

    University essay from KTH/Matematik (Avd.)

    Author : Daniel Sanaee; [2023]
    Keywords : Mathematics; Cryptography; Computer science; Group Theory; Matematik; Kryptografi; Datalogi; Gruppteori;

    Abstract : The problem of constructing a secure encryption scheme that allows for computation on encrypted data was an open problem for more than 30 years. In 2009, Craig Gentry solved the problem, constructing the first fully homomorphic encryption (FHE) scheme. READ MORE

  3. 2. How is Polly? Revisiting the Differential Attack on Polly Cracker after 20 years

    University essay from Lunds universitet/Matematikcentrum

    Author : Christoph Strobl; [2022]
    Keywords : Gröbner Bases; polly cracker; differential attack; asymmetric cryptography; multivariate cryptography; public-key cryptography; Mathematics and Statistics; Technology and Engineering;

    Abstract : För att skapa nya krypteringsalgoritmer är man alltid på jakt efter svårlösta matematiska problem. Men är alla problem lämpliga? Uppsatsen behandlar Gröbnerbaser över ändliga kroppar och visar att de är inte lämpliga för att bygga säkra krypteringsalgoritmer. READ MORE

  4. 3. A Prime or Not a Prime? That is the Question

    University essay from Lunds universitet/Matematik LTH; Lunds universitet/Matematik (naturvetenskapliga fakulteten)

    Author : Vetle Tjora; [2022]
    Keywords : primality testing; Lucas--Lehmer; number theory; cubic reciprocity; Mersenne primes; Mathematics and Statistics;

    Abstract : In this survey, we shall prove the Lucas–Lehmer primality test used to find the Mersenne primes. A proof of the Law of Cubic Reciprocity will also be presented, which will be applied in the proof of a generalisation of the Lucas–Lehmer primality test... READ MORE

  5. 4. On the Use of Elliptic Curves in Public-Key Cryptography

    University essay from Lunds universitet/Matematik LTH; Lunds universitet/Matematik (naturvetenskapliga fakulteten)

    Author : Christoph Strobl; [2020]
    Keywords : Elliptic Curves; Public-Key Cryptography; Index Calculus; Pohlig-Hellman; Diffie-Hellman Problem; Asymmetric Cryptography; Mathematics and Statistics;

    Abstract : Uppsatsen behandlar asymmetrisk kryptering över ändliga kropper och elliptiska kurver. Elliptiska kurver införs med hjälp av affint och projektivt rum. Uppsaten också ger en introduction till algoritmer som kan knäcka diskret logaritm problemet över kropper och elliptiska kurver.. READ MORE

  6. 5. Discreet Discrete Mathematics : Secret Communication Using Latin Squares and Quasigroups

    University essay from Umeå universitet/Institutionen för matematik och matematisk statistik

    Author : Christoffer Olsson; [2017]
    Keywords : Cryptology; Cryptography; Latin squares; Row-latin squares; Quasigroups; Secret sharing schemes; Kryptologi; Kryptografi; Latinska kvadrater; Rad-latinska kvadrater; Kvasigrupper; Hemlighetsdelning;

    Abstract : This thesis describes methods of secret communication based on latin squares and their close relative, quasigroups. Different types of cryptosystems are described, including ciphers, public-key cryptosystems, and cryptographic hash functions. There is also a chapter devoted to different secret sharing schemes based on latin squares. READ MORE