We consider Initial Public Offering (IPO) on blockchains while preserving privacy using Secure Multiparty Computation (MPC), which allows participants to perform a computation on secret data. We provide “MPC as a service”, where users requiring a computation distributes shares of their data to MPC workers who run an MPC protocol on the shares and return the result. Previous work by Benhamouda et al. considered IPO over Hyperledger Fabric. We improve by providing a tighter and easier integration of MPC protocol in Fabric using the MPC library SCALE-MAMBA. We explain the obtained security benefits and experimental results are provided.

International audience

The most fundamental purpose of blockchain technology is to enable persistent, consistent, distributed storage of information. Increasingly common are authentication systems that leverage this property to allow users to carry their personal data on a device while a hash of this data is signed by a trusted authority and then put on a blockchain to be compared against. For instance, in 2015, MIT introduced a schema for the publication of their academic certificates based on this principle. In this work, we propose a way for users to obtain assured identities based on face-to-face proofing that can then be validated against a record on a blockchain. Moreover, in order to provide anonymity, instead of storing a hash, we make use of a scheme of Brands to store a commitment against which one can perform zero-knowledge proofs of identity. We also enforce the confidentiality of the underlying data by letting users control a secret of their own.We show how our schema can be implemented on Bitcoin's blockchain and how to save bandwidth by grouping commitments using Merkle trees to minimize the number of Bitcoin transactions that need to be sent. Finally, we describe a system in which users can gain access to services thanks to the identity records of our proposal.

We here provide a method for systematic encoding of the Multiplicity codes introduced by Kopparty, Saraf and Yekhanin in 2011. The construction is built on an idea of Kopparty. We properly define information sets for these codes and give detailed proofs of the validity of Kopparty's construction, that use generating functions. We also give a complexity estimate of the associated encoding algorithm.

This article presents a new algorithm to find MDS matrices that are well suited for use as a diffusion layer in lightweight block ciphers. Using an recursive construction, it is possible to obtain matrices with a very compact description. Classical field multiplications can also be replaced by simple F2-linear transformations (combinations of XORs and shifts) which are much lighter. Using this algorithm, it was possible to design a 16×16 matrix on a 5-bit alphabet, yielding an efficient 80-bit diffusion layer with maximal branch number.

We transpose the theory of rank metric and Gabidulin codes to the case of fields of characteristic zero. The Frobenius automorphism is then replaced by any element of the Galois group. We derive some conditions on the automorphism to be able to easily transpose the results obtained by Gabidulin as well and a classical polynomial-time decoding algorithm. We also provide various definitions for the rank-metric.

We study the list-decoding problem of alternant codes (which includes obviously that of classical Goppa codes). The major consideration here is to take into account the (small) size of the alphabet. This amounts to comparing the generic Johnson bound to the q-ary Johnson bound. The most favourable case is q = 2, for which the decoding radius is greatly improved. Even though the announced result, which is the list-decoding radius of binary Goppa codes, is new, we acknowledge that it can be made up from separate previous sources, which may be a little bit unknown, and where the binary Goppa codes has apparently not been thought at. Only D. J. Bernstein has treated the case of binary Goppa codes in a preprint. References are given in the introduction. We propose an autonomous and simplified treatment and also a complexity analysis of the studied algorithm, which is quadratic in the blocklength n, when decoding e-away of the relative maximum decoding radius.

The key step of syndrome-based decoding of Reed-Solomon codes up to half the minimum distance is to solve the so-called Key Equation. List decoding algorithms, capable of decoding beyond half the minimum distance, are based on interpolation and factorization of multivariate polynomials. This article provides a link between syndrome-based decoding approaches based on Key Equations and the interpolation-based list decoding algorithms of Guruswami and Sudan for Reed-Solomon codes. The original interpolation conditions of Guruswami and Sudan for Reed-Solomon codes are reformulated in terms of a set of Key Equations. These equations provide a structured homogeneous linear system of equations of Block-Hankel form, that can be solved by an adaption of the Fundamental Iterative Algorithm. For an (n,k) Reed-Solomon code, a multiplicitysand a list sizel, our algorithm has time complexityO(ls4n2).

In 2000 Roth and Ruckenstein proposed an extended key equation for solving the interpolation step in the Sudan decoding algorithm. Generalizing their idea, a sequence of key equations for the Guruswami-Sudan (GS) algorithm, which is able to list decode a Reed-Solomon code with arbitrary rate, is derived. This extension allows a reduction of the number of equations and therefore a reduction of the algorithmpsilas complexity. Furthermore, we indicate how to adapt the fundamental iterative algorithm for block Hankel matrices and thus solving the GS-interpolation step efficiently.

We address the problem of the algebraic decoding of any cyclic code up to the true minimum distance. For this, we use the classical formulation of the problem, which is to find the error locator polynomial in terms of the syndromes of the received word. This is usually done with the Berlekamp-Massey algorithm in the case of BCH codes and related codes, but for the general case, there is no generic algorithm to decode cyclic codes. Even in the case of the quadratic residue codes, which are good codes with a very strong algebraic structure, there is no available general decoding algorithm. For this particular case of quadratic residue codes, several authors have worked out, by hand, formulas for the coefficients of the locator polynomial in terms of the syndromes, using the Newton identities. This work has to be done for each particular quadratic residue code, and is more and more difficult as the length is growing. Furthermore, it is error-prone. We propose to automate these computations, using elimination theory and Grobner bases. We prove that, by computing appropriate Grobner bases, one automatically recovers formulas for the coefficients of the locator polynomial, in terms of the syndromes.

A group key agreement (GKA) protocol is a mechanism to establish a cryptographic key for a group of participants, based on each one's contribution, over a public network. The key, thus derived, can be used to establish a secure channel between the participants. When the group composition changes (or otherwise), one can employ supplementary GKA protocols to derive a new key. Thus, they are well-suited to the key establishment needs of dynamic peer-to-peer networks as in ad hoc networks. While many of the proposed GKA protocols are too expensive to be employed by the constrained devices often present in ad hoc networks, others lack a formal security analysis. We present a simple, secure and efficient GKA protocol well suited to dynamic ad hoc networks. We also present results of our implementation of the protocol in a prototype application.

This article presents an algorithmic improvement to Sudan's (see J. Complexity, vol.13, p.180-93, 1997) list-decoding algorithm for Reed-Solomon codes and its generalization to algebraic-geometric codes from Shokrollahi and Wasserman (see ibid., vol.45, p.432-37, 1999). Instead of completely factoring the interpolation polynomial over the function field of the curve, we compute sufficiently many coefficients of a Hensel development to reconstruct the functions that correspond to codewords. We prove that these Hensel developments can be found efficiently using Newton's method. We also describe the algorithm in the special case of Reed-Solomon codes.

We present architectures for the secure delivery of images over open networks, such as the Internet or broadcast networks. Those systems integrate access control mechanisms and tracking procedures, once the pictorial material has been accessed. We show how these architectures have been tested in the context of the connection of cultural databases to the Internet (AQUARELLE system) and in the context of broadcasting of high-value TV programs (OCTALIS system used during the football World Cup). This work shows the interest for a global integrated design of delivery systems in which watermarking, monitoring, and public key infrastructures based on trusted third parties are designed according to coherent functional models.

We consider primitive cyclic codes of length p/sup m/-1 over F/sub p/. The codes of interest here are duals of BCH codes. For these codes, a lower bound on their minimum distance can be found via the adaptation of the Weil bound to cyclic codes. However, this bound is of no significance for roughly half of these codes. We shall fill this gap by giving, in the first part of the correspondence, a lower bound for an infinite class of duals of BCH codes. Since this family is a filtration of the duals of BCH codes, the bound obtained for it induces a bound for all duals. In the second part we present a lower bound obtained by implementing an algorithmic method due to Massey and Schaub (1988)-the rank-bounding algorithm. The numerical results are surprisingly higher than all previously known bounds.

Using a characterization of the idempotents of a narrow-sense primitive binary BCH code, the authors are able to give classes of such codes whose minimum distance does not exceed the BCH bound. Their results are compiled in a table.>

Primitive binary cyclic codes of length n=2/sup m/ are considered. A BCH code with designed distance delta is denoted B(n, delta ). A BCH code is always a narrow-sense BCH code. A codeword is identified with its locator polynomial, whose coefficients are the symmetric functions of the locators. The definition of the code by its zeros-set involves some properties for the power sums of the locators. Moreover, the symmetric functions and the power sums of the locators are related to Newton's identities. An algebraic point of view is presented in order to prove or disprove the existence of words of a given weight in a code. The principal result is the true minimum distance of some BCH codes of length 255 and 511. which were not known. The minimum weight codewords of the codes B(n2/sup h/-1) are studied. It is proved that the set of the minimum weight codewords of the BCH code B(n,2/sup m-2/-1) equals the set of the minimum weight codewords of the punctured Reed-Muller code of length n and order 2, for any m.>