Events Calendar

CS Colloquium

Speaker: Prof. Yevgeniy Dodis, NYU

Talk Title: Leftover Hash Lemma, Revisited

Abstract: The famous Leftover Hash Lemma (LHL) states that (almost) universal hash functions are good randomness extractors. Despite its numerous applications, LHL-based extractors suffer from the following two drawbacks:

(1) Large Entropy Loss: to extract v bits from distribution X of min-entropy m which are e-close to uniform, one must set v = 2*log(1/e).
(2) Large Seed Length: the seed length n of universal hash function required by the LHL must be linear in the length of the source.

Quite surprisingly, we show that both limitations of the LHL --- large entropy loss and large seed --- can often be overcome (or, at least,
mitigated) in various quite general scenarios. First, we show that entropy loss could be reduced to L=log(1/e) for the setting of deriving secret keys for a wide range of cryptographic applications, including *all* "unpredictability" applications (signatures, MACs, etc.) and also some prominent "indistinguishability" applications, including chosen plaintext (or ciphertext) attack secure (public- or symmetric-key) encryption schemes. Specifically, the security of these schemes gracefully degrades from e to at most e + sqrt(e * 2^{-L}).(Notice that, unlike standard LHL, this bound is meaningful even for negative entropy loss, when we extract more bits than the the min-entropy we have!)

Second, we study the soundness of the natural *expand-then-extract* approach, where one uses a pseudorandom generator (PRG) to expand a short "input seed" S into a longer "output seed" S', and then use the resulting S' as the seed required by the LHL (or, more generally, any randomness extractor). Unfortunately, we show that, in general, expand-then-extract approach is not sound if the Decisional Diffie-Hellman assumption is true. Despite that, we show that it is sound either: (1) when extracting a "small" (logarithmic in the security of the PRG) number of bits; or (2) in *minicrypt*.
Implication (2) suggests that the sample-then-extract approach is likely secure when used with "practical" PRGs, despite lacking a reductionist proof of security!
The paper can be found at http://eprint.iacr.org/2011/088

Biography: Yevgeniy Dodis is an Associate Professor of computer science at New York University, which he joined in 2001 after receiving his PhD at MIT in 2000 and being a post-doc at IBM T.J.Watson Research center.
He also spent 2007-2008 academic year visiting the CRCS center at Harvard University.

Dr. Dodis' research is primarily in cryptography and network security.
In particular, he worked in a variety of areas including leakage-resilient cryptography, cryptography under weak randomness, cryptography with biometrics and other noisy data, hash function and block cipher design, protocol composition and information-theoretic cryptography. Dr. Dodis has more than 90 scientific publications at various conferences, journals and other venues, has been on program committees of many international conferences (including FOCS, STOC, CRYPTO and Eurocrypt), and gave numerous invited lectures and courses at various venues. Dr. Dodis is the recipient of National Science Foundation CAREER Award, IBM Faculty Award, Google Faculty Award and Best Paper Award at 2005 Public Key Cryptography Conference. As an undergraduate student, he was also a winner of the US-Canada Putnam Mathematical Competition in 1995.

Host: Prof. David Kempe

Location: Grace Ford Salvatori Hall Of Letters, Arts & Sciences (GFS) - 118

Audiences: Everyone Is Invited

Contact: Kanak Agrawal