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The security of the signature scheme is destroyed because its secret information of the signature system is leaked due to the side channel attack. Ring signature has good application value, which can provide more flexibility and complete anonymity. It can be used in some systems such as anonymous authentication in ad hoc networks, electronic voting and crypto coin based on blockchain. Because of the side channel attack, the private key of the ring signature system may be exposed, which may cause insecurity. We present a ring signature system against continuous side channel attack. Because of the symmetry of the ring, the user’s identity has good privacy protection. The proposed scheme is completely secure without a random oracle model and the private key disclosure rate is close to 1/3. Through the dual system technique, the existential unforgeability and unconditional anonymity of the scheme are proved in the composite order group based on the subgroup decision assumption.