New MRA Schemes Based on the CRT for Polynomial Rings

At present, existing multi-receiver authentication (MRA) schemes can only handle situations where the capacities of all receivers in the schemes are the same. However, in reality, different receivers may need to have different storage capacities. In this paper, inspired by the secret sharing scheme based on the Chinese Remainder Theorem (CRT) for polynomial rings where each participant holds the share with different sizes, we propose three new constructions of unconditionally secure MRA schemes for multiple messages using the CRT for polynomial rings, including a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(k,n)$ </tex-math></inline-formula>-threshold MRA scheme, a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(k,n,\omega)$ </tex-math></inline-formula>-weighted threshold MRA scheme, and a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(\mathcal {Q},\mathcal {F})$ </tex-math></inline-formula>-general MRA scheme. As far as we know, our proposed MRA schemes are the first MRA schemes with different storage capacities for different receivers and the first ones based on the CRT for polynomial rings. Moreover, the proposed schemes can be seen as extensions of the MRA scheme in Safavi-Naini and Wang. In particular, as for our <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(\mathcal {Q},\mathcal {F})$ </tex-math></inline-formula>-general MRA scheme, it has generally more communication complexity and much less computation complexity than the existing <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(\mathcal {Q},\mathcal {F})$ </tex-math></inline-formula>-general MRA scheme.