Homomorphic encryption from codes

We propose a new homomorphic encryption scheme based on the hardness of decoding under independent random noise from certain affine families of codes. Unlike in previous latticebased homomorphic encryption schemes, where the message is hidden in the noisy part of the ciphertext, our scheme carries the message in the affine part of the transformation and applies noise only to achieve security. Our scheme can tolerate noise of arbitrary magnitude, as long as the noise vector has sufficiently small hamming weight (and its entries are independent). Our design achieves “proto-homomorphic” properties in an elementary manner: message addition and multiplication are emulated by pointwise addition and multiplication of the ciphertext vectors. Moreover, the extremely simple nature of our decryption makes the scheme easily amenable to bootstrapping. However, some complications are caused by the inherent presence of noticeable encryption error. Our main technical contribution is the developme...

• Type: Journal
• Year: 2011
• Where: IACR
• Authors: Andrej Bogdanov, Chin Ho Lee
• Keywords: Encryption Schemes, Homomorphic Encryption, IACR 2011, Simple Nature