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2013-02-20
13:17 [Pub][ePrint] Path-PIR: Lower Worst-Case Bounds by Combining ORAM and PIR, by Travis Mayberry and Erik-Oliver Blass and Agnes Chan

  Recent research results on \"bucketed\" ORAM reduce com- munication of N-capacity storage with blocks of length l bits down to poly-logarithmic complexity O(l · log^3 N ). The individual buckets, how- ever, are constructed using traditional ORAMs which have worst-case communication complexity being linear in their size. PIR protocols are able to provide better worst-case bounds, but have traditionally been less practical than ORAM due to the fact that they require O(N) computa- tion complexity on the server. This paper presents Path-PIR, a hybrid construction between PIR and ORAM that overcomes the individual weaknesses of each. Path-PIR\'s main idea is to replace the individual buckets in the ORAM construction by Shi et al. [15] with buckets backed by PIR. We show that this leads to substantially smaller data transfer costs for many databases of practical size and lower worst-case costs, O(l · log^2 (N) + log^3 (N)), than the existing construction. Additionally, the typically high computational cost of PIR is offset by the small size of the individual buckets. We also show that Path-PIR has very low latency, i.e., a low amount of data is required before a user receives the result of his data request (less than 10 times the block size). Using Amazon EC2, we demonstrate that monetary cost induced by the server\'s PIR computation are far outweighed by the savings in data transfer.



13:17 [Pub][ePrint] Square Root Algorithm in F_q for q=2^s+1 (mod 2^(s+1)), by Namhun Koo and Gook Hwa Cho and Soonhak Kwon

  We present a square root algorithm in F_q which generalizes Atkins\'s square root algorithm for q=5(mod 8) and Kong et al.\'s algorithm for q=9(mod 16) Our algorithm precomputes a primitive 2^s-th root of unity where s is the largest positive integer satisfying 2^s| q-1, and is applicable for the cases when s is small. The proposed algorithm requires one exponentiation for square root computation and is favorably compared with the algorithms of Atkin, Muller and Kong et al.



10:17 [Pub][ePrint] Analysis and Improvement of the securing RFID systems conforming to EPC Class 1 Generation 2 standard, by Amin Mohammadali; Zahra Ahmadian; Mohammad Reza Aref

  Radio Frequency IDentification (RFID) technology is a wireless identification method in which security and privacy are important parameters for public acceptance and widespread use. In order to thwart such security and privacy problems, a wide variety of authentication protocols have been proposed in the literature. In 2010, Yeh et al\'s proposed a new RFID authentication protocol conforming to EPC Class 1 Generation 2 standard. They claimed that this protocol is secure against DoS attack, replay attack, DATA forgery attack, and provides untraceability and forward secrecy. In 2012, Yoon showed that this protocol does not provide forward secrecy and DATA integrity. He improved the protocol and tried to eliminate the weaknesses and claimd that the improved protocol does not have the weaknesses of the primary protocol. In this paper, we show that the improved protocol has some weaknesses including DoS attack, back-end server impersonation, tag impersonation and DATA forgery attack. We also show that it can not provide forward secrecy of the reader and untraceability. We improve the protocol, which offers a high level of security and provides mutual authentication, untraceability and forward secrecy as well as resistance to DATA forgery, replay and DoS attacks, while retaining a competitive communication cost.



10:17 [Pub][ePrint] Power Analysis of Hardware Implementations Protected with Secret Sharing, by Guido Bertoni and Joan Daemen and Nicolas Debande and Thanh-Ha Le and Michael Peeters and Gilles Van Assche

  We analyze the security of three-share hardware implementations against differential power analysis and advanced variants such as mutual information analysis. We present dedicated distinguishers that allow to recover secret key bits from any cryptographic primitive that is implemented as a sequence of quadratic functions. Starting from the analytical treatment of such distinguishers and information-theoretic arguments, we derive the success probability and required number of traces in the presence of algorithmic noise. We show that attacks on

three-share hardware implementation require a number of traces that scales in the third power of the algorithmic noise variance. Finally, we apply and test our model on Keccak in a keyed mode.



10:17 [Pub][ePrint] Why Proving HIBE Systems Secure is Difficult, by Allison Lewko and Brent Waters

  Proving security of Hierarchical Identity-Based Encryption (HIBE) and

Attribution Based Encryption scheme is a challenging problem. There are multiple well-known schemes in the literature where the best known (adaptive) security proofs degrade exponentially in the maximum

hierarchy depth. However, we do not have a rigorous understanding of

why better proofs are not known. (For ABE, the analog of hierarchy depth is the maximum number of attributes used in a ciphertext.)

In this work, we define a certain commonly found checkability property on ciphertexts and private keys. Roughly the property states that any two different private keys that are both ``supposed to\'\' decrypt a ciphertext will decrypt it to the same message. We show that any simple black box reduction to a non-interactive assumption for a HIBE or ABE system that contains this property will suffer an exponential degradation of security.



10:17 [Pub][ePrint] Hardness of SIS and LWE with Small Parameters, by Daniele Micciancio and Chris Peikert

  The Short Integer Solution (SIS) and Learning With Errors (LWE) problems are the foundations for countless applications in lattice-based cryptography, and are provably as hard as approximate lattice problems in the worst case. A important question from both a practical and theoretical perspective is how small their parameters can be made, while preserving their hardness.

We prove two main results on SIS and LWE with small parameters. For SIS, we show that the problem retains its hardness for moduli $q \\geq \\beta \\cdot n^{\\delta}$ for any constant $\\delta > 0$, where $\\beta$ is the bound on the Euclidean norm of the solution. This improves upon prior results which required $q \\geq \\beta \\cdot \\sqrt{n \\log n}$, and is essentially optimal since the problem is trivially easy for $q \\leq \\beta$. For LWE, we show that it remains hard even when the errors are small (e.g., uniformly random from $\\set{0,1}$), provided that the number of samples is small enough (e.g., linear in the dimension $n$ of the LWE secret). Prior results required the errors to have magnitude at least $\\sqrt{n}$ and to come from a Gaussian-like distribution.



10:17 [Pub][ePrint] Related-key Attacks Against Full Hummingbird-2, by Markku-Juhani O. Saarinen

  We present attacks on full Hummingbird-2 which are able to recover

the 128-bit secret keys of two black box cipher instances that have a certain type of low-weight XOR difference in their keys. We call these

highly correlated keys as they produce the same ciphertext with a

significant probability. The complexity of our main chosen-IV

key-recovery attack is $2^{64}$. The first 64 bits of the key can be independently recovered with only $2^{36}$ effort. This is the first sub-exhaustive attack on the full cipher under two related keys. Our attacks use some novel tricks and techniques which are made possible by Hummingbird-2\'s unique word-based structure. We have verified the correctness and complexity of our attacks by fully implementing them.

We also discuss enabling factors of these attacks and describe an alternative design for the WD16 nonlinear keyed function which is resistant to attacks of this type. The new experimental function replaces S-boxes with simple $\\chi$ functions.



10:17 [Pub][ePrint] Relation collection for the Function Field Sieve, by Jérémie Detrey and Pierrick Gaudry and Marion Videau

  In this paper, we focus on the relation collection step of the Function Field Sieve (FFS), which is to date the best algorithm known for computing discrete logarithms in small-characteristic finite fields of cryptographic sizes. Denoting such a finite field by GF(p^n), where p is much smaller than n, the main idea behind this step is to find polynomials of the form a(t)-b(t)x in GF(p)[t][x] which, when considered as principal ideals in carefully selected function fields, can be factored into products of low-degree prime ideals. Such polynomials are called \"relations\", and current record-sized discrete-logarithm computations need billions of those.

Collecting relations is therefore a crucial and extremely expensive step in FFS, and a practical implementation thereof requires heavy use of cache-aware sieving algorithms, along with efficient polynomial arithmetic over GF(p)[t]. This paper presents the algorithmic and arithmetic techniques which were put together as part of a new public implementation of FFS, aimed at medium- to record-sized computations.



10:17 [Pub][ePrint] The UC approach: an application view, by István Vajda

  What kind of guidelines can the UC approach provide for traditional designs and applications? The aim of this report is to bring this theoretically rooted, computer scientist technology closer to the community of practitioners in the field of protocol designs.



10:17 [Pub][ePrint] Zero-Knowledge Using Garbled Circuits: How To Prove Non-Algebraic Statements Efficiently, by Marek Jawurek and Florian Kerschbaum and Claudio Orlandi

  Zero-knowledge protocols are one of the fundamental concepts in modern cryptography and have countless applications. However, after more than 30 years from their introduction, there are only very few languages (essentially those with a group structure) for which we can construct zero-knowledge protocols that are efficient enough to be used in practice.

In this paper we address the problem of how to construct efficient zero-knowledge protocols for generic languages and we propose a protocol based on Yao\'s garbled circuit technique.

The motivation for our work is that in many cryptographic applications it is useful to be able to prove efficiently statements of the form e.g., ``I know x s.t. y=SHA-256(x)\'\' for a

common input y (or other ``unstructured\'\' languages), but no efficient protocols for this task are currently known.

It is clear that zero-knowledge is a subset of secure two-party computation (i.e., any protocol for generic secure computation can be used to do zero-knowledge). The main contribution of this paper is to construct an efficient protocol for the special case of secure two-party computation where only one party has input (like in the zero-knowledge case).

The protocol achieves active security and is essentially only twice as slow as Yao\'s garbled circuit protocol. This is a great improvement with respect to the cut-n-choose technique to make Yao\'s protocol actively secure, where the complexity grows linearly with the security parameter.



10:17 [Pub][ePrint] On the Function Field Sieve and the Impact of Higher Splitting Probabilities: Application to Discrete Logarithms in $\\F_{2^{1971}}$, by Faruk Gologlu and Robert Granger and Gary McGuire and Jens Zumb

  In this paper we propose a binary field variant of the Joux-Lercier medium-sized Function Field Sieve, which results not only in complexities as low as $L_{q^n}(1/3,2/3)$ for computing arbitrary logarithms, but also in an heuristic {\\em polynomial time} algorithm

for finding the discrete logarithms of degree one elements. To illustrate the efficiency of the method, we have successfully solved the DLP in the finite field with $2^{1971}$ elements.