US 11,658,819 B2
Method for generating public key and secret key based on module-wavy and module-LWR and method of encryption and decryption using the keys
Joohee Lee, Seoul (KR); Junghee Cheon, Seoul (KR); Duhyeong Kim, Seoul (KR); and Aaram Yun, Ulsan (KR)
Assigned to ULSAN NATIONAL INSTITUTE OF SCIENCE AND TECHNOLOGY, Seoul (KR); and SEOUL NATIONAL UNIVERSITY R&DB FOUNDATION, Seoul (KR)
Filed by Seoul National University R&DB Foundation, Seoul (KR); and UNIST (Ulsan National Institute of Science and Technology), Ulsan (KR)
Filed on Jun. 18, 2020, as Appl. No. 16/904,806.
Application 16/904,806 is a continuation of application No. PCT/KR2018/016014, filed on Dec. 17, 2018.
Claims priority of application No. 10-2017-0183661 (KR), filed on Dec. 29, 2017.
Prior Publication US 2020/0322147 A1, Oct. 8, 2020
Int. Cl. H04L 9/30 (2006.01); H04L 9/08 (2006.01)
CPC H04L 9/3006 (2013.01) [H04L 9/0861 (2013.01); H04L 9/0894 (2013.01)] 1 Claim
OG exemplary drawing
 
1. A computer-implemented method of decrypting a ciphertext, the method comprising:
receiving, by a processor, a ciphertext c, over a network; and
decrypting, by a processor, the ciphertext c to obtain a message (m) which is

OG Complex Work Unit Math
s being a secret key;
wherein a public key and the secret key are generated by a method comprising:
a step of determining, by a processor, the secret key (s) by sampling from custom characterWTn(hs)d;
a step of determining, by a processor, an error vector (e) by sampling from (Dαqn)d and an error value (e′) by sampling from Dαqn;
a step of choosing, by a processor, a randomly uniform matrix A∈Rqd×d which satisfies A·s=e (mod q);
a step of choosing, by a processor, a random column vector b∈Rqd which satisfies

OG Complex Work Unit Math
and
a step of determining, by a processor, (A∥b)∈Rqd×(d+1) as the public key (pk);
wherein the ciphertext c is generated by a method comprising a step of receiving, by a processor, the public key (pk) and a message (m∈R2); and a step of generating, by a processor, the ciphertext by

OG Complex Work Unit Math
wherein a column vector (r) is determined by sampling from custom characterWTn(hs)d; and wherein:
α is an error parameter which satisfies 0<α<1;
q is a positive integer;
p is a positive integer less than q;
d is a positive integer;
n is a power of 2;
hs is a positive integer less than n;
hr is a positive integer less than n;
Dαq is a discrete Gaussian distribution;
Dαqn is a product distribution of independent and identically distributed n random variables according to the distribution Dαq;
(Dαqn)d is a product distribution of independent and identically distributed d random variables according to the distribution Dαqn; and
custom characterWTn(hs)d and custom characterWTn(hr)d are distributions of randomly sampled d polynomials of degree (n−1), the coefficients of which are −1, 0, or +1, from custom characterWTn(hs) and
custom characterWTn(hr), respectively, wherein custom characterWTn(hs) and custom characterWTn(hr) are distributions of uniformly sampled vectors from {−1, 0, 1}n, under the condition that said vectors have hs and hr non-zero elements, respectively.