US 12,149,606 B2
Methods and systems for encrypting rational numbers and adding randomness to RSA cryptosystems using P-ADIC numbers
David W. Honorio Araujo da Silva, Colorado Springs, CO (US); Carlos A. Paz de Araujo, Colorado Springs, CO (US); and Jordan Isabella Pattee, Colorado Springs, CO (US)
Assigned to Algemetric, Inc., Colorado Springs, CO (US)
Filed by Algemetric, Inc., Colorado Springs, CO (US)
Filed on Aug. 19, 2022, as Appl. No. 17/891,926.
Application 17/891,926 is a continuation of application No. PCT/US2021/050988, filed on Sep. 17, 2021.
Claims priority of provisional application 63/079,676, filed on Sep. 17, 2020.
Prior Publication US 2022/0407719 A1, Dec. 22, 2022
Int. Cl. H04L 9/00 (2022.01); H04L 9/30 (2006.01); H04L 9/32 (2006.01); H04L 9/08 (2006.01)
CPC H04L 9/008 (2013.01) [H04L 9/30 (2013.01); H04L 9/3033 (2013.01); H04L 9/3249 (2013.01); H04L 9/0869 (2013.01); H04L 9/3093 (2013.01)] 8 Claims
OG exemplary drawing
 
1. A computer implemented method for encrypting a rational number α with a RSA (Rivest-Shamir-Adleman) cryptosystem for communication between a source device and a destination device over a network, wherein said RSA cryptosystem has a public key e, two secret prime numbers p and q, a public key n such that n=pq, and the private keys ϕ(n) and d that are computed as ϕ(n)=(p−1)(q−1) and d=e−1 mod ϕ(n), the method comprising:
encoding, by said source device, said rational number α using p-adic based integer Hensel encoding as a function of a Hensel encoding value v, and said rational number α to obtain integer Hensel code h, where said rational number α is comprised of a fraction a/b with numerator a and denominator b, where said numerator a, said denominator b, and said Hensel encoding value v are pairwise coprime, and where an absolute value of said numerator a and said denominator b are less than said Hensel encoding value v;
encrypting, by said source device, said integer Hensel code h using RSA cryptosystem encryption processes to obtain ciphertext c;
sending, over the network by said source device, said ciphertext c to said destination device;
decrypting, by said destination device, said ciphertext c using RSA decryption processes to obtain said integer Hensel code h; and
decoding, by said destination device, said integer Hensel code h using an Extended Euclidean Algorithm (EEA) as a function of said Hensel encoding value v and said Hensel code h to obtain said corresponding rational number α.