*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]
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} algorithmfor 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]
Design Space Exploration and Optimization of Path Oblivious RAM in Secure Processors, by Ling Ren and Xiangyao Yu and Christopher Fletcher and Marten van Dijk and Srinivas Devadas
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]
Fast Cut-and-Choose Based Protocols for Malicious and Covert Adversaries, by Yehuda Lindell
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]
An efficient attack of a McEliece cryptosystem variant based on convolutional codes, by Grégory Landais and Jean-Pierre Tillich
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]
Efficient Secure Two-Party Computation Using Symmetric Cut-and-Choose, by Yan Huang and Jonathan Katz and Dave Evans
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.