A  -restricted key agreement scheme

On τ-time secure key agreement

“…In the KAS model of Blundo et al [15], an eavesdropped conference is uncorrupted. We show that if it can contain a corrupted user, the revised model will be strictly stronger than the original one.…”

“…For τ > 1, every previous τ -time KAS needs a global counter to maintain the number of conferences executed so far. This assumption has been assumed in [12,15]. Practically, this could be hard to realize even if Ref.…”

“…Practically, this could be hard to realize even if Ref. [15] has a scheme that is more efficient than τ -independent 1-time secure KAS. We show that polynomially synthesizing d-independent certain KPS gives a new d-time secure KAS without a global counter.…”

“…KPS is a special case of a ∞-time key agreement under their model as b P is empty. This condition is added later by Blundo et al [15]. However, in their model, H(ck Pτ |K F , b P1 , .…”

“…Blundo et al [14] considered the ratio (called information rate) of user key size to the number of keys generated in one execution and constructed a 1-time scheme more efficient than Beimel-Chor [12]. Blundo et al [15] proposed a τ -time KAS that is more efficient than the trivial scheme of τ -independent 1-time KAS by extending [14]. However, the drawback of their scheme is that they assume a global counter for recording the number of conference executed so far.…”