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| In view of the fact that the existing forward secure digital signature scheme can not guarantee safety,and it has some problem such as forgery attacks,this paper presented a kind of strong forward secure digital signature scheme based on elliptic curves cryptosystems .Such scheme prevent attackers from forging the signer¡¯s valid signature of both time point by introducing dual key technology even if they get the signer¡¯s two keys of a certain period to aquire ¡°two-way security¡±.The security and computational complexity analysis of the scheme showed that it was not only correct,valid and highly safety,but with smaller computational complexity,higher efficiency,etc.,and has important theoretical and practical value. |

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