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On certain types of code-based signatures

Abstract : Digital signatures were first introduced in the work of DIFFIE and HELLMAN, dated back in 1976. It is a scientific art replacing the traditional way of written signatures. Each signer has a \personal knowledge," or a signing key, to produce signatures. And as the same as handwritten signatures, anyone seeing this signature would be convinced that it belong to a certain person (and no one else). In order to produce such a signature, the signing key is indispensable, and the secret of this entity is usually protected by the hardness assumption of some computational problems. In the earliest stage, these are number theoretic problems such as factoring large integer numbers or computing the discrete logarithm of an element with respect to some prime modulus. However, with the rapid development of technology, these problems will be solved efficiently when the era of quantum computer arrives. Then comes the next stage in the progressing course of digital signatures when most of the attention is given to the decoding problem (and many of its variants), of which the hardness resists even the quantum computer. This problem, however, takes part in two important branches of cryptography, namely, lattice-based cryptography and code-based cryptography due to the main object it is related to. This thesis mainly concerns with signatures in the latter branch, i.e., the code-based cryptography. It proposes two main contributions. The first of which is a signature scheme in the HAMMING metric context. The scheme is achieved as an application of a chameleon hash function, which is constructed entirely from classical code-based hardness assumptions. The most notable feature of this scheme is that it is proved to be secure in the standard model. While security of code-based schemes in the random oracle model is still unclear, such property is highly desirable. The second contribution is a group signature scheme in the rank metric context. In general, the construction of the scheme follow the frame devised for the HAMMING metric. At the core, this frame uses two permutations which are designed from a random vector. Though quite efficient for the binary case, that is, the base field is F2; this method shows its disadvantages when the base field is changed. A natural question arises out of this situation: How can we construct schemes in another fields ? We answer this question by proposing a different method of permuting. Our method has the advantage that it can be applied regardless the metric being in consideration.
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Dang Truong Mac. On certain types of code-based signatures. Cryptography and Security [cs.CR]. Université de Limoges, 2021. English. ⟨NNT : 2021LIMO0088⟩. ⟨tel-03542019⟩

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