1. MMR Encryption Algorithm as an Alternative Encryption Algorithm to RSA Encryption Algorithm

    Remzi Aktay

    Kecioren Sehit Halil Isilar Middle School

    Abstract:     In this study, a public key encryption algorithm is tried to be developed. Unlike other public key encryption algorithms, it is desired to create a monitoring key next to the open and closed keys. While creating the algorithm, the equivalence of a^(10^(n-1))-b^(10^(n-1))≡0 (mod 10n) is used. Based on this equivalence, algorithms and keys have been created using modular arithmetic rules, Euclidean Algorithm, Euler Theorem, Euler Function, Factoring rules. The first difference of this algorithm from other algorithms is the observation key. In the event that private keys are stolen or cracked, hidden text or data cannot be accessed without a observation key. The second difference is that the receiver’s private key, public key and observation key can take infinite values. For now, it is not a problem for the keys to take limited values ​​in other algorithms. However, with the development and speed of the quantum computers, this will be a problem in the future. There are studies that have been successful in this regard. The third difference is that this algorithm has its own character code table. In addition, this algorithm is safer against side channel attacks.

    Keywords: Encryption, Private Key, Monitoring Key, Euclid Algorithm, Euler’s Theorem, Side Channel Attacks, Public Key Encryption.

    Pages: 301 – 309 | Full PDF Paper

  2. Coprime Integer Encryption Algorithm Upon Euler’s Totient Function’s Unsolved Problems

    Remzi Aktay

    Kecioren Sehit Halil Isilar Middle School

    Abstract:     For the natural number n > 1, Euler function gives the amount of natural numbers smaller than and coprime to n. However, there is no study to find out what these numbers are. In this study, the solution method of this problem which the Euler Function cannot respond to has been found. In this method, Groups, Cyclic Groups, Group Homomorphism and Group Isomorphism are used. In addition, Modular Arithmetic and Chinese Remainder Theorem were used. Thanks to the method found, at least two-levels encryption algorithm has been developed. In this algorithm, it is aimed to prevent related companies from backing up, especially in social media and various communication applications such as WhatsApp.

    Keywords: Abstract Algebra, Algorithm, Chinese Remainder Theorem, Cyclic Group, Group Isomorphism.

    Pages: 310 – 320 | Full PDF Paper