Considerate ramp secret sharing

Abstract In this work we revisit the fundamental findings by Chen et al. (in: Advances in Cryptology—EUROCRYPT 2007. Lecture Notes in Computer Science, Springer, Berlin, 2007) on general information transfer in linear ramp secret sharing schemes to conclude that their method not only gives a way to establish worst case leakage (Chen et al. 2007; Kurihara et al. in IEICE Trans Fundam E95-A(11):2067–2075, 2012) and best case recovery (Chen et al. 2007; Geil et al. in IEEE Trans Inf Theory 60(10):5938–5949, 2014) , but can also lead to additional insight on non-qualifying sets for any prescribed amount of information. We then apply this insight to schemes defined from monomial-Cartesian codes and by doing so we demonstrate that the good schemes from (Galindo et al. in IEEE Trans Inf Theory 64(4, part 1):2444–2459, 2018, Sec. IV) have a second layer of security. Elaborating further, when given designed partial recovery numbers, in a new construction the focus is entirely on ensuring that the access structure possesses desirable second layer security, rather on what is the worst case information leakage in terms of number of participants. The particular structure of largest possible sets being not able to determine any amount of information suggests that we coin the concept of considerate ramp secret sharing schemes of which the proposed new construction is a well-structured example.