Conventional shadow image connection based(

t

s

k

n

) sharing is prone to different size shadow images and Birkhoff interpolation based(

t

s

k

n

) sharing leads to low recovery efficiency

while in double authentications based self-recovery image sharing

the recovery capabilities of secret image and backup image are very limited.To address these problems

random participation values were used to construct master key based(

t

s

k

n

) sharing by means of(

k

s

) and(

k-t

n-s

) schemes and MD5 values s

tored in the third party were used to prevent cheating.The proposed scheme scrambled

LL

subband of secret image by master key and formed multi-version backup images with different scrambling degrees where more backups for more significant bits.Restricted double authentication strategy can embed as many backup bits as possible while maintaining authentication accuracy by(

k

n

) sharing over GF(2^8) field to form stego carriers.Theoretical and experimental results show

master key based(

t

s

k

n

) scheme can be solved efficiently.Random participation values avoid the disclosure of participant numbers and prevent tampering distributed information or guessing authentication bits.Multi-version backup strategy can restore backup images with high confidence while authentication capability of restricted double authentication strategy is no less than that of double authentications based self-recovery image sharing scheme.