Paper 2015/027 Original: eprint.iacr.org/2015/027 ↗
On the Regularity of Lossy RSA: Improved Bounds and Applications to Padding-Based Encryption
Abstract
We provide new bounds on how close to regular the map x |--> x^e is on arithmetic progressions in Z_N, assuming e | Phi(N) and N is composite. We use these bounds to analyze the security of natural cryptographic problems related to RSA, based on the well-studied Phi-Hiding assumption. For example, under this assumption, we show that RSA PKCS #1 v1.5 is secure against chosen-plaintext attacks for messages of length roughly (log N)/4 bits, whereas the previous analysis, due to Lewko et al (2013), applies only to messages of length less than (log N)/32. In addition to providing new bounds, we also show that a key lemma of Lewko et al. is incorrect. We prove a weaker version of the claim which is nonetheless sufficient for most, though not all, of their applications. Our technical results can be viewed as showing that exponentiation in Z_N is a deterministic extractor for every source that is uniform on an arithmetic progression. Previous work showed this type of statement only on average over a large class of sources, or for much longer progressions (that is, sources with much more entropy).
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2015-01-14: last updated
- 2015-01-14: published
- Short URL
- https://ia.cr/2015/027
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2015/027,
author = {Adam Smith and Ye Zhang},
title = {On the Regularity of Lossy RSA: Improved Bounds and Applications to Padding-Based Encryption},
howpublished = {Cryptology {ePrint} Archive, Paper 2015/027},
year = {2015},
url = {https://eprint.iacr.org/2015/027}
}