Asymmetric Encryption Algorithm

1. 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=p t , n=2·p t 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>={a 0 , a 1 , a 2 , . . . , a φ(n)-1 };

choosing an element, a l , with 0≤l≤φ(n)−1 such that U(n)=<a>={a 0 , a 1 , a 2 , . . . , a φ(n)-1 }={ε 1 , ε 2 , ε 3 , . . . , ε h , . . . ε φ(n) }, wherein ε i <ε j when i<j, to represent a plaintext of a selection of data, and wherein a l =ε h ;

encrypting the selection of data by performing the following steps:

a) multiplying all elements ε 1 ·ε 2 . . . ε h mod n≡c, where c is a component of a ciphertext;

b) analyzing data to determine when c·ε φ(n) ≡−1 mod n, c·ε φ(n) ·ε φ(n)−1 ≡−1 mod n, all the way to c·ε (φ(n) ·ε φ(n)−1 . . . ε h+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.

2. The method as recited in claim 1 , wherein the encrypting includes encrypting on an electronic device having at least one process and at least one memory.

3. The method as recited in claim 2 , wherein the electronic device is selected from the group consisting of: a desktop computer; a laptop computer; a smartphone; a tablet computer; and an automated teller machine.