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2013-02-20
10:17 [Pub][ePrint]

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]

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 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]

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.

10:17 [Pub][ePrint]

In 1996, Hoffstein, Pipher and Silverman introduced an efficient lattice based encryption scheme dubbed NTRUEncrypt. Unfortunately, this scheme lacks a proof of security. However, in 2011, Stehle and Steinfeld showed how to modify NTRUEncrypt to reduce security to standard problems in ideal lattices. At STOC 2012, Lopez-Alt, Tromer and Vaikuntanathan proposed a fully homomorphic scheme based on this modified system. However, to allow homomorphic operations and prove security, a non-standard assumption is required in their scheme. In this paper, we show how to remove this non-standard assumption via techniques introduced by Brakerski at CRYPTO 2012 and construct a new fully homomorphic encryption scheme from the Stehle and Steinfeld version based on standard lattice assumptions and a circular security assumption. The scheme is scale-invariant and therefore avoids modulus switching, it eliminates ciphertext expansion in homomorphic multiplication, and the size of ciphertexts is one ring element. Moreover, we present a practical variant of our scheme, which is secure under stronger assumptions, along with parameter recommendations and promising implementation results. Finally, we present a novel approach for encrypting larger input sizes by applying a CRT approach on the input space.

10:17 [Pub][ePrint]

Keeping user data private is a huge problem both in cloud computing and computation outsourcing. One paradigm to achieve data privacy in these settings is to use tamper-resistant processors. Users\' private data is decrypted and computed upon in a secure compartment from which that data will not be revealed to an untrusted party. Since program working sets seldom fit within the on-chip storage of today\'s processor solutions, a secure and efficient way of transporting and storing data off-chip is required. A simple solution to this problem is to encrypt all data that leaves the chip. However, the address sequence that goes off-chip may still leak information. ORAM (Oblivious RAM) has been previously proposed to hide the address leakage of the program. However, ORAM has mainly been explored in server/file settings which assume a vastly different computation model than secure processors (e.g., accesses are for files not processor cache blocks). Not surprisingly, naively applying ORAM to a secure processor setting incurs large performance overheads.

In this paper, we demonstrate techniques to make ORAM practical in a secure processor setting. A particular ORAM proposed recently, called Path ORAM, is studied. For the first time, we thoroughly explore the design space of Path ORAM, and introduce a novel throughput-driven design space exploration approach based on ORAM background eviction schemes and super blocks. With our ORAM optimizations, ORAM latency drops by 45%, and SPEC benchmark execution time improves by 39% in relation to a baseline configuration. We also propose an efficient integrity verification scheme for Path ORAM.

Our work can be used to improve the security level of previous secure processors.

10:17 [Pub][ePrint]

In this paper, we show the first UC-secure multi-session OT protocol using tamper-proof hardware tokens. The sender and the receiver exchange tokens only at the beginning. Then these tokens are reused in arbitrarily many sessions of OT. An instantiation of the proposed scheme is UC-secure against static adversaries under the DDH assumption and the RSA assumption in the random oracle model.

10:17 [Pub][ePrint]

We initiate the study of broadcast steganography (BS), an extension of steganography to the multi-recipient setting. BS enables a sender to communicate covertly with a dynamically designated set of receivers, so that the recipients recover the original content, while unauthorized users and outsiders remain \\emph{unaware} of the covert communication. One of our main technical contributions is the introduction of a new variant of anonymous broadcast steganography that we term \\emph{anonymous identity-based encryption with pseudorandom ciphertexts} (oABE$). Our oABE$ construction achieves sublinear ciphertext size and is secure in the standard model. Besides being of interest in its own right, oABE$enables an efficient construction of BS secure in the standard model against adaptive adversaries that also features sublinear ciphertexts. 10:17 [Pub][ePrint] In the setting of secure two-party computation, two parties wish to securely compute a joint function of their private inputs, while revealing only the output. One of the primary techniques for achieving efficient secure two-party computation is that of Yao\'s garbled circuits (FOCS 1986). In the semi-honest model, where just one garbled circuit is constructed and evaluated, Yao\'s protocol has proven itself to be very efficient. However, a malicious adversary who constructs the garbled circuit may construct a garbling of a different circuit computing a different function, and this cannot be detected (due to the garbling). In order to solve this problem, many circuits are sent and some of them are opened to check that they are correct while the others are evaluated. This methodology, called \\emph{cut-and-choose}, introduces significant overhead, both in computation and in communication, and is mainly due to the number of circuits that must be used in order to prevent cheating. In this paper, we present a cut-and-choose protocol for secure computation based on garbled circuits, with security in the presence of malicious adversaries, that vastly improves on all previous protocols of this type. Concretely, for a cheating probability of at most$2^{-40}$, the best previous works send between 125 and 128 circuits. In contrast, in our protocol 40 circuits alone suffice (with some additional overhead). Asymptotically, we achieve a cheating probability of$2^{-s}$where$s$is the number of garbled circuits, in contrast to the previous best of$2^{-0.32s}$. We achieve this by introducing a new cut-and-choose methodology with the property that in order to cheat, \\emph{all} of the evaluated circuits must be incorrect, and not just the \\emph{majority} as in previous works. 10:17 [Pub][ePrint] L\\\"ondahl and Johansson proposed last year a variant of the McEliece cryptosystem which replaces Goppa codes by convolutional codes. This modification is supposed to make structural attacks more difficult since the public generator matrix of this scheme contains large parts which are generated completely at random. They proposed two schemes of this kind, one of them consists in taking a Goppa code and extending it by adding a generator matrix of a time varying convolutional code. We show here that this scheme can be successfully attacked by looking for low-weight codewords in the public code of this scheme and using it to unravel the convolutional part. It remains to break the Goppa part of this scheme which can be done in less than a day of computation in the case at hand. 10:17 [Pub][ePrint] Beginning with the work of Lindell and Pinkas, researchers have proposed several protocols for secure two-party computation based on the cut-and-choose paradigm. In existing instantiations of this paradigm, one party generates$\\kappa$garbled circuits; some fraction of those are checked\'\' by the other party, and the remaining fraction are evaluated. We introduce here the idea of symmetric cut-and-choose protocols, in which each party generates$\\kappa$circuits to be checked by the other party. The main advantage of our technique is that the number$\\kappa\$ of garbled circuits can be reduced by a factor of 3 while attaining the same statistical security level as in prior work. Since the number of garbled circuits dominates the costs of the protocol, especially as larger circuits are evaluated, our protocol is expected to run up to 3 times faster than existing schemes. Preliminary experiments validate this claim.