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Quantum-Resistant Forward-Secure Digital Signature Scheme Based on q-ary Lattices

Jurkiewicz Mariusz

Journal of Telecommunications and Information Technology

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2024

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nr 2

90--103

EN

In this paper, we design and consider a new digital signature scheme with an evolving secret key, using random q-ary lattices as its domain. It is proved that, in addition to offering classic eu-cma security, the scheme is existentially forward unforgeable under an adaptive chosen message attack (fu-cma). We also prove that the secret keys are updated without revealing anything about any of the keys from the prior periods. Therefore, we design a polynomial-time reduction and use it to show that the ability to create a forgery leads to a feasible method of solving the well-known small integer solution (SIS) problem. Since the security of the scheme is based on computational hardness of a SIS problem, it turns out to be resistant to both classic and quantum methods. In addition, the scheme is based on the "Fiat-Shamir with aborts" approach that foils a transcript attack. As for the key-updating mechanism, it is based on selected properties of binary trees, with the number of leaves being the same as the number of time periods in the scheme. Forward security is gained under the assumption that one out of two hash functions is modeled as a random oracle.

2

Binary Tree Based Forward Secure Signature Scheme in the Random Oracle Model

Jurkiewicz Mariusz

International Journal of Electronics and Telecommunications

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2021

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Vol. 67, No. 4

717--726

EN

In this paper we construct and consider a new group-based digital signature scheme with evolving secret key, which is built using a bilinear map. This map is an asymmetric pairing of Type 3, and although, for the reason of this paper, it is treated in a completely abstract fashion it ought to be viewed as being actually defined over E(Fqn )[p] × E(Fqnk )[p] → Fqnk [p]. The crucial element of the scheme is the key updater algorithm. With the adoption of pairings and binary trees where a number of leaves is the same as a number of time periods, we are assured that an updated secret key can not be used to recover any of its predecessors. This, in consequence, means that the scheme is forward-secure. To formally justify this assertion, we conduct analysis in fu-cma security model by reducing the security of the scheme to the computational hardness of solving the Weak ℓ-th Bilinear Diffie-Hellman Inversion problem type. We define this problem and explain why it can be treated as a source of security for cryptographic schemes. As for the reduction itself, in general case, it could be possible to make only in the random oracle model.

3

Improving Security of Existentially Unforgeable Signature Schemes

Jurkiewicz Mariusz

International Journal of Electronics and Telecommunications

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2020

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Vol. 66, No. 3

473--480

EN

In this paper we present a family of transforms that map existentially unforgeable signature schemes to signature schemes being strongly unforgeable. In spite of rising security, the transforms let us make a signature on a union of messages at once. The number of elements in this union depends on the signing algorithm of a scheme being transformed. In addition to that we define an existentially unforgeable signature scheme based on pairings, which satisfies all assumptions of the first part and is able to be subjected to transformation.