Abstract—Many types of digital signature schemes have been researched and published in recent years. In this paper, we propose two new types of collective signature schemes, namely i) the collective signature for several signing groups and ii) the collective signature for several individual signings and several signing groups. And then we used two difficult problems factoring and discrete logarithm to construct these schemes. To create a combination of these two difficult problems we use the prime module p with a special structure: p = Nn + 1 with n = rq, N is an even number, r and q are prime numbers of at least 512 bit. Schnorr’s digital signature scheme and the RSA key generation algorithm are used to construct related basic schemes such as the single signature scheme, the collective signature scheme, and the group signature scheme. The proposed collective signature schemes are built from these basic schemes. The correctness, security level and performance of the proposed schemes have also been presented in this paper. 
 

Keywords—Schnorr’s signature, collective signature, group signature, signing group, individual signings 

Cite: Tuan Nguyen Kim, Duy Ho Ngoc, Nin Ho Le Viet, and Nikolay A. Moldovyan, "The New Collective Signature Schemes Based on Two Hard Problems Using Schnorr's Signature Standard," Journal of Advances in Information Technology, Vol. 14, No. 1, pp. 77-84, February 2023.

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