Asymmetric Encryption Algorithm

A method of asymmetrical encryption and transferring encrypted data, the method comprising:

• generating an encryption key represented by k∈Z;
• calculating an n that satisfies the following properties:
• i) k<n;
• ii) n=pt, n=2·pt where p is an odd prime number and t∈Z is a non-negative integer;
• and
• iii) For any β∈Z that satisfies I) and II) it must be the case that n≤β, wherein, if these properties have been met, U(n) is defined as a cyclic group of all integers relatively prime to n and less than n, and wherein U(n) is cyclic and U(n)=<a>={a0, a1, a2, . . . , aφ(n)-1};
• choosing an element, al, with 0≤l≤φ(n)−1 such that U(n)=<a>={a0, a1, a2, . . . , aφ(n)-1}={ε1, ε2, ε3, . . . , εh, . . . εφ(n)}, wherein εi<εj when i<j, to represent a plaintext of a selection of data, and wherein al=εh;
• encrypting the selection of data by performing the following steps:
• a) multiplying all elements ε1·ε2 . . . εh mod n≡c, where c is a component of a ciphertext;
• b) analyzing data to determine when c·εφ(n)≡−1 mod n, c·εφ(n)·εφ(n)−1≡−1 mod n, all the way to c·ε(φ(n)·εφ(n)−1 . . . εh+1≡−1 mod n;
• c) recording a number of instances where step a) is true, wherein the number of instances is defined as Σ;
• and
• d) generating a ciphertext, defined as C, wherein C=(c,Σ);
• sending C to one or more third parties over a network;
• and
• decrypting, by the one or more third parties, the ciphertext using the encryption key.