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We propose a new certificate-based signature scheme and an identity-based ring signature scheme based on quintic residues in order to improve the efficiency of computation. The schemes do not need any bilinear pairing computation which is known to be difficult to computation. The schemes are secure against existential forgery on the adaptive chosen message and identity attacks assuming the hardness of factoring. Introduction Many signature schemes require pairing operations. The pairing computation is considered as expensive comparing with normal operations such as modular exponentiations in finite fields.Liu et al. [1] first proposed a certificated-based signature scheme without pairings. However, Zhang [2] showed that the scheme without pairings was insecure and gave an improved scheme with pairings. Ming and Wang [3] proposed a certificate-based signature scheme without pairings. Li et al. [4] showed that the scheme is subject to universal forgery for a Type II adversary and constructed a new certificate-based signature scheme. Under the discrete logarithm assumption, the scheme is existentially unforgeable against adaptive chosen message and identity attacks in the random oracle model. Rong et al. [5] proposed a certificate-based signature scheme. The scheme does not need any bilinear pairing computation, just needs compute Jacobi symbol, quadratic residue and power exponentiation. Dong et al. [6] proposed a certificate-based signature scheme based on cubic residues. If one selects proper parameters, the computational efficiency of constructing a cubic residue is better than constructing a quadratic residue. On the other hand, a ring signature can be regarded as a simplified group signature with no manager, no group setup procedure, and no revocation mechanism against signer’s anonymity. In a ring signature scheme, the information of all possible signers serves as a part of the ring signature for the signed message. A valid ring signature will convince the verifier that the signature is generated from one of the ring members, without revealing any information about which ring member is the actual signer. In [7], an identity-based ring signature scheme was proposed based on quadratic residues. The proposed signature scheme is more efficient than those which are constructed from bilinear pairings. Dong et al. [8] proposed an identity-based ring signature scheme based on cubic residues. The schemes in [6] and [8] are only suitable for primes p and q , where 2(mod3) p ≡ and 4(mod9) q ≡ or 7(mod9) q ≡ .In [9], we proposed a novel method to compute a quintic root of a quintic residue and then gave a new identity based signature scheme by the method. The scheme is the first identity based signature scheme based on quintic residues. The scheme is suitable for primes p and q , where 1(mod 5) p ≠ , 1(mod5) q ≡ and 1(mod 25) q ≠ . In this paper we propose a new certificate-based signature scheme and an identity-based ring signature scheme based on quintic residues in order to improve the efficiency of computation. The rest of the paper is organized as follows. In Section 2, we give some preliminaries. In Section 3, a certificate-based signature scheme is proposed based on quintic residues. In Section 4, we give an identity-based ring signature scheme. 481 5th International Conference on Frontiers of Manufacturing Science and Measuring Technology (FMSMT 2017) Advances in Engineering Research (AER), volume 130

Two Signature Schemes Based on Quintic Residues