US 12,261,932 B2
Methods and systems for public and private-key leveled fully homomorphic encryption without bootstrapping with Hensel codes
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, LLC, Colorado Springs, CO (US)
Filed on Feb. 18, 2022, as Appl. No. 17/676,096.
Claims priority of provisional application 63/150,884, filed on Feb. 18, 2021.
Prior Publication US 2022/0385448 A1, Dec. 1, 2022
Int. Cl. H04L 9/00 (2022.01); H04L 9/14 (2006.01)
CPC H04L 9/008 (2013.01) [H04L 9/14 (2013.01)] 8 Claims
OG exemplary drawing
 
1. A method for private-key Fully Homomorphic Encryption (FHE) communication of a message m between a source computing device and a destination computing device, the method comprising:
generating by said source computing device prime numbers p1 . . . p5 as a function of provided parameters λ and d;
setting by said source computing device a secret key sk to be comprised of said prime numbers p1 . . . p5 wherein said secret key is known to both of said source computing device and said destination computing device but not to other computing devices;
setting by said source computing device a public evaluation key evk to be equal to a product (Πi=15 pi) of said prime numbers p1 . . . p5 wherein said evk also equals a g of Hensel Code g-adic computations (Hg);
generating by said source computing device values s1, s2, s3, and δ as a function of said prime numbers p2 . . . p4, said parameter λ, and said value g;
encrypting by said source computing device said message m as ciphertext c in accord with Hensel Code encryption computation c=|Hg(s1·Hp1,p2,p3−1(0, s2, s3)+δp4)|g;
sending by said source computing device said ciphertext c to said destination computing device; and
decrypting by said destination computing device said ciphertext c back into said message m in accord with Hensel Code decryption computation m=Hp1−1(Hp1(Hp4−1(c))).