Abstract
After any distribution of secret sharing shadows in a threshold changeable secret sharing scheme, the threshold may need to be adjusted to deal with changes in the security policy and adversary structure. For example, when employees leave the organization, it is not realistic to expect departing employees to ensure the security of their secret shadows. Therefore, in 2012, Zhang et al. proposed (t → t′, n) and ({t1, t2,⋯, tN}, n) threshold changeable secret sharing schemes. However, their schemes suffer from a number of limitations such as strict limit on the threshold values, large storage space requirement for secret shadows, and significant computation for constructing and recovering polynomials. To address these limitations, we propose two improved dealer-free threshold changeable secret sharing schemes. In our schemes, we construct polynomials to update secret shadows, and use two-variable one-way function to resist collusion attacks and secure the information stored by the combiner. We then demonstrate our schemes can adjust the threshold safely.
Highlights
Rapid advances in Internet technologies have resulted in significant changes in our society, but there are associated security and privacy risks
The threshold changeable secret sharing (TCSS)-B scheme was the first scheme that could resist collusion attacks launched by participants who have historical secret shadows
We propose two improved dealer-free threshold changeable secret sharing schemes
Summary
Rapid advances in Internet technologies have resulted in significant changes in our society (e.g. digitalization of our society), but there are associated security and privacy risks. In Zhang et al.’s schemes, since the dealer needs to adjust the threshold and deal with the enrollment and disenrollment of the participant, he/she holds the secret and all secret shadows in the running phase until the secret is recovered. In the TCSS schemes of [21, 24, 28] based on the advance secret shadow technique, participants have both historical and current secret shadows after changing the threshold Such schemes cannot resist attacks carried out by t − 1 colluding participants. Zhang et al [16] proposed the first scheme (i.e. TCSS-B) designed to resist such collusion attack, by encrypting secret shadows and validating the new threshold with the corresponding key. Our schemes can resist attacks carried out by tj − 1 colluding participants who have both current and historical shadows
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