By Adi Shamir, Eran Tromer (auth.), Dan Boneh (eds.)
Crypto 2003, the twenty third Annual Crypto convention, was once backed through the Int- nationwide organization for Cryptologic study (IACR) in cooperation with the IEEE machine Society Technical Committee on safeguard and privateness and the pc technology division of the collage of California at Santa Barbara. The convention obtained 169 submissions, of which this system committee chosen 34 for presentation. those lawsuits include the revised types of the 34 submissions that have been provided on the convention. those revisions haven't been checked for correctness, and the authors undergo complete accountability for the contents in their papers. Submissions to the convention signify cutti- aspect learn within the cryptographic group world wide and canopy all components of cryptography. Many top of the range works couldn't be authorised. those works would definitely be released somewhere else. The convention application incorporated invited lectures. Moni Naor spoke on cryptographic assumptions and demanding situations. Hugo Krawczyk spoke at the ‘SI- and-MAc’approachtoauthenticatedDi?e-HellmananditsuseintheIKEpro- cols. The convention application additionally incorporated the normal rump consultation, chaired via Stuart Haber, that includes brief, casual talks on late-breaking examine information. Assembling the convention application calls for assistance from many many of us. To all those that pitched in, i'm endlessly on your debt. i need to ?rst thank the various researchers from around the world who submitted their paintings to this convention. with no them, Crypto couldn't exist. I thank Greg Rose, the final chair, for protecting me from innumerable logistical complications, and exhibiting nice generosity in aiding my e?orts.
Read or Download Advances in Cryptology - CRYPTO 2003: 23rd Annual International Cryptology Conference, Santa Barbara, California, USA, August 17-21, 2003. Proceedings PDF
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Additional resources for Advances in Cryptology - CRYPTO 2003: 23rd Annual International Cryptology Conference, Santa Barbara, California, USA, August 17-21, 2003. Proceedings
Lemma 10 Given N, α, and M as deﬁned in Theorem 9. Then for all but O(N α− ) choices of e in the interval [3, N α ] the following holds: Let X = 1 1 N 2 −α− and Y = 3N 2 +α . Then the lattice L contains two linearly independent vectors with norm less than √N3 . 40 J. Bl¨ omer and A. May Proof: In terms of lattice theory, we have to show that for most of the choices of e the second successive minima λ2 of L is strictly less than √N3 . By Minkowski’s second theorem we know that for any 3-dimensional lattice L and its successive minima λ1 , λ2 , λ3 λ1 λ2 λ3 ≤ 2 det(L).
The secret exponent d corresponding to (N, e) satisﬁes the equality ed = 1 mod φ(N ), where φ(N ) is the Euler totient function. We will often talk of known most or least signiﬁcant bits (MSBs/LSBs) of d, but we want to point out that this should only be understood as a helpful simpliﬁcation to explain our results in the context of side-channel attacks. To be more precise, when we talk of k known LSBs of d, then in fact we only need to know integers d0 , M such that d0 = d mod M , where M ≥ 2k .
In Figure 4, the upper half of the table states the results for known MSBs whereas the lower half is dedicated to the results for known LSBs. The attacks for known bits of dp are stated in the last lines of each half. α = logN (e) Fraction of bits that is needed Restriction/Comment BDF  [ 14 , 12 ] α e prime/known fact. BDF  [0, 12 ] 1−α Section 4 [ 12 , √ 6−1 ] 2 BDF  [0, 12 ] Section 2 [0, 14 ] BDF  O(logN log N ) Section 5 [0, 12 ] Section 6 [0, 78 ] 1 8 3 + 2α + √ 36α2 + 12α − 15 1 6 Section 2 O(logN log N ) +α 1 4 1 2 + 1 3 heuristic = Ω(1) bits of dp N = 3 mod 4 +α √ = Ω(1) d √ , |p−q| φ(N ) N 3 4 1 4 d φ(N ) 1 + 6α 1 4 all but O(N α− ) e’s heuristic bits of dp Fig.