	US 12,192,354 B2
	Cryptographic method of secure comparison of two secret data x and y
Florian Bourse, Chatillon (FR); Olivier Sanders, Chatillon (FR); and Jacques Traore, Chatillon (FR)
Assigned to ORANGE, Issy-les-Moulineaux (FR)
Appl. No. 17/278,861
Filed by ORANGE, Issy-les-Moulineaux (FR)
PCT Filed Sep. 20, 2019, PCT No. PCT/FR2019/052213 § 371(c)(1), (2) Date Mar. 23, 2021, PCT Pub. No. WO2020/065185, PCT Pub. Date Apr. 2, 2020.
Claims priority of application No. 1858677 (FR), filed on Sep. 24, 2018.
Prior Publication US 2022/0038277 A1, Feb. 3, 2022
Int. Cl. H04L 29/06 (2006.01); H04L 9/06 (2006.01); H04L 9/30 (2006.01)

CPC H04L 9/302 (2013.01) [H04L 9/0643 (2013.01); H04L 2209/046 (2013.01); H04L 2209/46 (2013.01)]

13 Claims

1. A cryptographic method of securely comparing two secret integer data x and y, possessed by a first computing device and by a second computing device, respectively, said method comprising:

generating, by the first computing device, a Rivest Shamir Adleman (RSA) module denoted N;

computing, by the first computing device, a number C equal to g^b^{^ax}h1 where g is an element of a sub-group G of custom character

_Nof order b^d, h1 is an element of a sub-group H of custom character

_Nof order f, and a, b, d, and f denote integers such that b and f are mutually prime, and the data x and y are less than d/a;

sending, by the first computing device, the number C to the second computing device;

computing, by the second computing device, at least:

a number D equal to C^u·b^{^d−ay}(gh3)^vh2 where u and v denote two random integers, and h2 and h3 elements of the sub-group H; and

a first fingerprint of (gh3)^vcomputed using a hash function;

sending, by the second computing device to the first computing device, the number D and the first fingerprint;

computing, by the first computing device, the number (D^f)^f′ where f′ is the inverse of f modulo b^d;

obtaining, by the first computing device, on the basis of the number (D^f)^f′ computed, a second fingerprint using the hash function; and

determining, by the first computing device, that the data x is greater than or equal to the data y or that the data x is less than the data y as a function of the result of a comparison between the first fingerprint and the second fingerprint and without revealing the data x to the second computing device and the data y to the first computing device.