Efficient Generic Forward-Secure Signatures with an Unbounded Number of Time Periods

Abstract

Abstract.We construct the first efficient forward-secure digital signature scheme where the total number of time periods for which the public key is used does not have to be fixed in advance. The number of time periods for which our scheme can be used is bounded only by an exponential function of the security parameter (given this much time, any scheme can be broken by exhaustive search), and its performance depends (minimally) only on the time elapsed so far. Our scheme achieves excellent performance overall, is very competitive with previous schemes with respect to all parameters, and outperforms each of the previous schemes in at least one parameter. Moreover, the scheme can be based on any underlying digital signature scheme, and does not rely on specific assumptions. Its forward security is proven in the standard model, without using a random oracle. As an intermediate step in designing our scheme, we propose and study two general composition operations that can be used to combine any existing signature schemes (whether standard or forward-secure) into new forward-secure signature schemes.

Yet Another Forward Secure Signature from Bilinear Pairings

“…In Table 1, T is total number of time periods and in Table 2, l is a security parameter of conventional cryptographic operation as explained in [20].…”

“…Although this scheme is efficient in signing and verifying, it increases the size of key and signature. Malkin et al [20] proposed a new construction of a forward secure signature scheme based on a product and sum composition method. Utilizing this method, one can construct a new forward signature scheme with more time periods from any two forward digital signature schemes.…”

“…Utilizing this method, one can construct a new forward signature scheme with more time periods from any two forward digital signature schemes. The combining of the sum and product compositions leads to a MMM [20] tree construction of a forward secure signature scheme. The advantage of MMM tree construction is that the maximal number of time periods needs not to be fixed in advance.…”

Forward Secure Ring Signature without Random Oracles

“…In particular the size of the secret key, public key and signature should not be dependent on the number of time period during the lifetime of the public key. Several schemes [2,13,1,12,15] have been proposed by traditional signatures and threshold signatures that satisfy this efficiency property. In addition, a forward secure group signature scheme and a forward secure identity-based signature scheme are proposed in [21] and [24] respectively.…”

Exposure-resilience for free: the hierarchical ID-based encryption case

“…The approach of key evolution [2] assumes that the timeline is divided into different periods, and a different secret key is used from one period to the next. This somewhat recent approach has already led to many useful notions, including those of forward-secure [3,24,1,20,26,8], keyinsulated [11,12,4] and intrusion-resilient [21,13] cryptosystems. While very powerful, the disadvantage of this approach is the need to introduce "global time" and the issue of what to do with documents produced outside of the "current" period.…”