US 12,463,792 B2
Accelerated division of homomorphically encrypted data
Marcelo Blatt, Modiin (IL); and Yuval Harness, Ramat Hasharon (IL)
Assigned to Duality Technologies, Inc., Maplewood, NJ (US)
Filed by Duality Technologies, Inc., Maplewood, NJ (US)
Filed on Jun. 28, 2022, as Appl. No. 17/851,552.
Claims priority of provisional application 63/215,865, filed on Jun. 28, 2021.
Prior Publication US 2022/0416995 A1, Dec. 29, 2022
Int. Cl. H04L 9/00 (2022.01); G06F 17/17 (2006.01)
CPC H04L 9/008 (2013.01) [G06F 17/17 (2013.01); H04L 2209/08 (2013.01)] 4 Claims
OG exemplary drawing
 
1. A method executed at multiple computing devices connected via one or more network(s), the method comprising:
at a first computing device of the multiple computing devices:
securely storing unencrypted data and one or more private keys;
homomorphically encrypting the unencrypted data using the one or more private keys to generate a homomorphic encrypted ciphertext x;
at a second computing device of the multiple computing devices:
receiving, from the first computing device, over the one or more network(s) connecting the multiple computing devices, the homomorphic encrypted ciphertext x;
calculating a polynomial approximation of 1/x for a homomorphically encrypted ciphertext x without decrypting the denominator x of the polynomial approximation by:
receiving a first value, l, corresponding to a degree of the polynomial approximation to be calculated;
receiving a second value, α, and a third value, β, wherein the second value and the third value define a range over which the polynomial approximation is to be calculated; and
calculating the polynomial approximation of 1/x for the homomorphically encrypted ciphertext x using the expression using the expression:

OG Complex Work Unit Math
wherein ak(l)=2ξ0ak+1(l)+ak+2(l) for k=2l−3,2l−4, . . . ,1,0,
wherein

OG Complex Work Unit Math
 and
wherein Tk(x) is a Chebyshev polynomial of the first kind of degree K.