Daniel Augot

Daniel Augot, Hervé Chabanne, Olivier Clémot et al.

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.

Daniel Augot, Hervé Chabanne, Thomas Chenevier et al.

We present an identity management scheme built into the Bitcoin blockchain, allowing for identities that are as indelible as the blockchain itself. Moreover, we take advantage of Bitcoin's decentralized nature to facilitate a shared control between users and identity providers, allowing users to directly manage their own identities, fluidly coordinating identities from different providers, even as identity providers can revoke identities and impose controls.

Daniel Augot, Françoise Levy-Dit-Vehel, Man Cuong Ngô

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 Kop-party. 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.

Daniel Augot, Françoise Levy-Dit-Vehel, Abdullatif Shikfa

Since the concept of locally decodable codes was introduced by Katz and Trevisan in 2000, it is well-known that information the-oretically secure private information retrieval schemes can be built using locally decodable codes. In this paper, we construct a Byzantine ro-bust PIR scheme using the multiplicity codes introduced by Kopparty et al. Our main contributions are on the one hand to avoid full replica-tion of the database on each server; this significantly reduces the global redundancy. On the other hand, to have a much lower locality in the PIR context than in the LDC context. This shows that there exists two different notions: LDC-locality and PIR-locality. This is made possible by exploiting geometric properties of multiplicity codes.

Daniel Augot, Matthieu Finiasz

MDS matrices allow to build optimal linear diffusion layers in block ciphers. However, MDS matrices cannot be sparse and usually have a large description, inducing costly software/hardware implementations. Recursive MDS matrices allow to solve this problem by focusing on MDS matrices that can be computed as a power of a simple companion matrix, thus having a compact description suitable even for constrained environ- ments. However, up to now, finding recursive MDS matrices required to perform an exhaustive search on families of companion matrices, thus limiting the size of MDS matrices one could look for. In this article we propose a new direct construction based on shortened BCH codes, al- lowing to efficiently construct such matrices for whatever parameters. Unfortunately, not all recursive MDS matrices can be obtained from BCH codes, and our algorithm is not always guaranteed to find the best matrices for a given set of parameters.

Daniel Augot, Matthieu Finiasz

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 16x16 matrix on a 5-bit alphabet, yielding an efficient 80-bit diffusion layer with maximal branch number.