TY - GEN

T1 - On the regularity of lossy RSA

T2 - 12th Theory of Cryptography Conference, TCC 2015

AU - Smith, Adam

AU - Zhang, Ye

PY - 2015/1/1

Y1 - 2015/1/1

N2 - We provide new bounds on how close to regular the map x ↦ xe is on arithmetic progressions in ℤN, assuming e|Φ(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 Φ-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 bits, whereas the previous analysis, due to [19], applies only to messages of length less than. In addition to providing new bounds, we also show that a key lemma of [19] 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 ℤN 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).

AB - We provide new bounds on how close to regular the map x ↦ xe is on arithmetic progressions in ℤN, assuming e|Φ(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 Φ-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 bits, whereas the previous analysis, due to [19], applies only to messages of length less than. In addition to providing new bounds, we also show that a key lemma of [19] 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 ℤN 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).

UR - http://www.scopus.com/inward/record.url?scp=84924675025&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84924675025&partnerID=8YFLogxK

U2 - 10.1007/978-3-662-46494-6_25

DO - 10.1007/978-3-662-46494-6_25

M3 - Conference contribution

AN - SCOPUS:84924675025

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 609

EP - 628

BT - Theory of Cryptography - 12th Theory of Cryptography Conference, TCC 2015, Proceedings

A2 - Dodis, Yevgeniy

A2 - Nielsen, Jesper Buus

PB - Springer Verlag

Y2 - 23 March 2015 through 25 March 2015

ER -