Compact sequences of co-primes and their applications to the security of CRT-based threshold schemes

CRT-based threshold secret sharing schemes use sequences of pairwise co-prime positive integers in their construction. If these sequences are not “compact”, then the CRT-based threshold secret sharing schemes may have a weak security in the sense of a massive loss of entropy or an arbitrarily large information rate. In this paper, compact sequences of co-primes are introduced, and their applications to the security of CRT-based threshold secret sharing schemes is throughout investigated. It is shown that all the results regarding the security of CRT-based threshold secret sharing schemes that use sequences of consecutive primes also hold for threshold secret sharing schemes that use compact sequences of co-primes. Moreover, compact sequences of co-primes may be significantly denser than sequences of consecutive primes of the same length, and their use in the construction of CRT-based threshold secret sharing schemes may lead to better security properties.