Public key encryption (secure against passive attacks) was the first application and main motivation to investigate the LWE problem.
On lattices, learning with errors, random linear codes, and cryptography
(Regev - J.ACM 2009 / STOC 2005)
Public-Key Cryptosystems from the Worst-Case Shortest Vector Problem
(Peikert, STOC 2009)
On Ideal Lattices and Learning with Errors over Rings
(Lyubashevsky, Peikert & Regev - J.ACM 2013 / Eurocrypt 2010)
Better Key Sizes (and Attacks) for LWE-Based Encryption
(Lindner & Peikert - CT-RSA 2011)
Efficient Public Key Encryption Based on Ideal Lattices
(Stehle, Steinfeld, Tanaka & Xagawa - Asiacrypt 2009)
Multi-bit Cryptosystems Based on Lattice Problems]
(Kawachi, Tanaka & Xagawa - PKC 2007)
Bi-Deniable Public-Key Encryption
(O’Neill, Peikert & Waters - Crypto 2011)
Fast Cryptographic Primitives and Circular-Secure Encryption Based on Hard Learning Problems
(Applebaum, Cash, Peikert & Sahai - Crypto 2009)
Lattice-based completely non-malleable public-key encryption in the standard model
(Sepahi, Steinfeld & Pieprzyk - DCC 2014)
Lattice-based certificateless public-key encryption in the standard model
(Sepahi, Steinfeld & Pieprzyk - IJIS 2014)
A Simple BGN-Type Cryptosystem from LWE
(Gentry, Halevi & Vaikuntanathan - Eurocrypt 2010)
One-Shot Verifiable Encryption from Lattices
(Lyubashevsky & Neven - EuroCrypt 2017)