Paper 2024/920
Leveraging Small Message Spaces for CCA1 Security in Additively Homomorphic and BGN-type Encryption
Abstract
We show that the smallness of message spaces can be used as a checksum allowing to hedge against CCA1 attacks in additively homomorphic encryption schemes. We first show that the additively homomorphic variant of Damgård's Elgamal provides IND-CCA1 security under the standard DDH assumption. Earlier proofs either required non-standard assumptions or only applied to hybrid versions of Damgård's Elgamal, which are not additively homomorphic. Our security proof builds on hash proof systems and exploits the fact that encrypted messages must be contained in a polynomial-size interval in order to enable decryption. With
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- A major revision of an IACR publication in EUROCRYPT 2025
- Keywords
- Additively homomorphic encryptionBGN encryptionCCA1 securitystandard assumptions
- Contact author(s)
- benoit libert @ zama ai
- History
- 2025-02-17: revised
- 2024-06-09: received
- See all versions
- Short URL
- https://ia.cr/2024/920
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2024/920, author = {Benoit Libert}, title = {Leveraging Small Message Spaces for {CCA1} Security in Additively Homomorphic and {BGN}-type Encryption}, howpublished = {Cryptology {ePrint} Archive, Paper 2024/920}, year = {2024}, url = {https://eprint.iacr.org/2024/920} }