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In this article, a secure and verifiable vector space secret sharing scheme without a dealer is proposed in detail. It's security is based on the security of elliptic curve cryptography. This scheme has the following characteristics: There is no dealer, thus the cost can be saved and it makes the scheme more security. A verifiable infrastructure based on elliptic curve cryptography is provided, which can be used to detect the cheaters from participants and outside attackers. Meanwhile, the length of key of elliptic curve cryptography is much less than that of RSA cryptography, so the current scheme is valuable in applications with limited memory and communication bandwidth. Results indicate that the security and information rate of this scheme is very high. Analysis shows that this scheme is perfect.