*12:00*[PhD][New] Karim Belabas

Name: Karim Belabas

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Name: Marc Stevens

Topic: Attacks on Hash Functions and Applications

Category: secret-key cryptography

Description: Cryptographic hash functions compute a small fixed-size hash value for any given message. A main application is in digital signatures which require that it must be hard to find collisions, i.e., two different messages that map to the same hash value. In this thesis we provide an analysis of the security of the cryptographic hash function standards MD5 and SHA-1 that have been broken since 2004 due to so called identical-prefix collision attacks. In particular, we present more efficient identical-prefix collision attacks on both MD5 and SHA-1 that improve upon the literature. Furthermore, we introduce a new more flexible attack on MD5 and SHA-1 called the chosen-prefix collision attack that allows significantly more control over the two colliding messages. Moreover, we have proven that our new attack on MD5 poses a realistic threat to the security of everyday applications with our construction of a rogue Certification Authority (CA). Our rogue CA could have enabled the total subversion of secure communications with any website -- if we had not purposely crippled it. Finally, we have introduced an efficient algorithm to detect whether a given message was generated using an identical-prefix or chosen-prefix collision attack on MD5 or SHA-1.[...]

Name: Eike Kiltz

Topic: Complexity Theoretic Lower Bounds on Cryptographic Functions

Category: foundations

Required:

• Senior hands-on engineer with broad experience in cryptography

• Experienced with designing and implementing cryptographic algorithms and key management systems

• Must be familiar with algorithms and protocols including AES-CBC, AES-GCM, SHA, EC-DH, EC-DSA, random number generation, PKI

• Knowledge of Suite B crypto, TLS, smartcards/CAC, X.509, soft certificates, PKCS11

• Experience developing crypto APIs for both internal and external use

• Must have strong skills with C/C++ and/or Java programming languages on multiple platforms

• Ability to work with and mentor a team of programmers

• Ability to obtain US security clearance.

Highly desired:

• Familiar with FIPS 140-2 process, VPNs, S/MIME, data at rest crypto, and other cryptographic products.

• Familiar with DoD and US Federal requirements and regulations related to cryptography for SBU/CUI and classified data.

• Familiar with secure voice protocols, such as SRTP, SIP/TLS, SSIP, zRTP, etc.

• Ability to create high-level software design documents.

• Experience writing device drivers, low-level APIs, or software development kits.

• Familiar with implementing crypto in hardware in ASIC or FPGA-based systems

• BA/BS, MS, Ph.D. degree in Cryptography, Mathematics, Computer Science, Software Engineering, Computer Engineering, Electrical Engineering or equivalent experience.

• CISSP, CSSLP, or SANS certifications

2012-11-01

There has been considerable recent interest in \"cloud storage\'\' wherein a user asks a server to store a large file. One issue is whether the user can verify that the server is actually storing the file, and typically a challenge-response protocol is employed to convince the user that the file is indeed being stored correctly. The security of these schemes is phrased in terms of an extractor which will recover or retrieve the file given any \"proving algorithm\'\' that has a sufficiently high success probability.

This paper treats proof-of-retrievability schemes in the model of unconditional security, where an adversary has unlimited computational power. In this case retrievability of the file can be modelled as error-correction in a certain code. We provide a general analytical framework for such schemes that yields exact (non-asymptotic) reductions that precisely quantify conditions for extraction to succeed as a function of the success probability of a proving algorithm, and we apply this analysis to several archetypal schemes. In addition, we provide a new methodology for the analysis of keyed POR schemes in an unconditionally secure setting, and use it to prove the security of a modified version of a scheme due to Shacham and Waters under a slightly restricted attack model, thus providing the first example of a keyed POR scheme with unconditional security. We also show how classical statistical techniques can be used to evaluate whether the responses of the prover are accurate enough to permit successful extraction. Finally, we prove a new lower bound on storage and communication complexity of POR schemes.

Time memory tradeoff algorithms are tools for inverting one-way functions, and they are often used to recover passwords from unsalted password hashes. There are many publicly known tradeoff algorithms, and the rainbow tradeoff is widely believed to be the best algorithm. This work provides an accurate complexity analysis of the fuzzy rainbow tradeoff algorithm, which has not yet received much attention. It is shown that when the pre-computation cost and the online efficiency are both taken into consideration, the fuzzy rainbow tradeoff is preferable to the original rainbow tradeoff.

The notion of indifferentiability was introduced in [MRH04] and in [CDMP05] it was tailored for security analysis of hash function constructions, making indifferentiability from a random oracle the desired property for any hash function design. However, the widely accepted view that a construction enjoying such a proof with an underlying ideal compression function can replace the random oracle in any application without compromising security is not justified in certain settings, as pointed out recently in [RSS11].

In this paper we argue that one general reason for such a failure is the inflexibility of the indifferentiability notion with respect to more complex restrictions on resources (such as memory, randomness) available to the attacker: Typically, the distinguisher and the simulator in an indifferentiability statement are only required to be PPT algorithms, implicitly posing a polynomial restriction also on the resources available to them. We argue that this is not sufficient in certain scenarios and explain why this is the problem underlying the security breakdown described in [RSS11]. We present a systematic treatment of such settings by proposing a more fine-grained notion of memory-aware reducibility that is necessary in contexts when memory is the resource that requires a more detailed quantification.

We employ this new formalism to prove a lower bound on the memory required by any simulator in a domain extension construction of a public random function. Our results imply that if we restrict to simulators without memory, even domain extension by a single bit becomes impossible. On the other hand, for the infinite extension from an ideal compression function to a random oracle, a memory roughly linear in the total sum of the lengths of all queries is required. This solves an open problem given in [RSS11].

Finally, it follows from our results that for any multi-party setting where one cannot assume the existence of a central adversary and hence it requires to be modeled using an independent local simulator for each party, it is impossible to securely construct a public random oracle from a public ideal compression function.

In this paper we prove an explicit formula for an arithmetic intersection number on the Siegel moduli space of abelian surfaces, generalizing the work of Bruinier-Yang and Yang.

These intersection numbers allow one to compute the denominators of Igusa class polynomials, which has important applications to the construction of genus 2 curves for use in cryptography.

Bruinier and Yang conjectured a formula for intersection numbers on an arithmetic Hilbert modular surface, and as a consequence obtained a conjectural formula for the intersection number relevant to denominators of Igusa class polynomials under strong assumptions on the ramification of the primitive quartic CM field K. Yang later proved this conjecture assuming that the ring of integers is freely generated by one element over the ring of integers of the real quadratic subfield. In this paper, we prove a formula for the intersection number for more general primitive quartic CM fields, and we use a different method of proof than Yang. We prove a tight bound on this intersection number which holds for all primitive quartic CM fields. As a consequence, we obtain a formula for a multiple of the denominators of the Igusa class polynomials for an arbitrary primitive quartic CM field. Our proof entails studying the Embedding Problem posed by Goren and Lauter and counting solutions using our previous article that generalized work of Gross-Zagier and Dorman to arbitrary discriminants.

We introduce the \\emph{linear centralizer method} for a passive adversary

to extract the shared key in group-theory based key exchange protocols (KEPs).

We apply this method to obtain a polynomial time cryptanalysis of the

\\emph{Commutator KEP}, introduced by Anshel--Anshel--Goldfeld in 1999 and considered

extensively ever since.

We also apply this method to the \\emph{Centralizer KEP}, introduced by Shpilrain--Ushakov in 2006.

Our method is proved to be of polynomial time using a technical lemma

about sampling invertible matrices from a linear space of matrices.