Cryptology ePrint Archive: Report 2015/027

On the Regularity of Lossy RSA: Improved Bounds and Applications to Padding-Based Encryption

Adam Smith and Ye Zhang

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).

Category / Keywords: public-key cryptography / PKCS, Phi-Hiding, Regularity

Original Publication (in the same form): IACR-TCC-2015

Date: received 12 Jan 2015

Contact author: yxz169 at cse psu edu

Available format(s): PDF | BibTeX Citation

Version: 20150114:164955 (All versions of this report)

Short URL: ia.cr/2015/027