Hybrid secret key escrow mechanisms as counters

Many of the cryptographic primitives can be used in several ways. One interesting application of the Shamir´s secret sharing scheme in the context of privacy aware traffic monitoring is to escrow a secret key after m suspicious events have been observed [1]. In the proposed system, a so-called front-end component encrypts the monitored data traffic, which is then stored at the back-end. At the same time, the front-end analyzes the traffic, and if suspicious packets are observed, this is indicated to the back-end by revealing one share of the corresponding encryption key. Once m suspicious events have been detected, the back-end can disclose the secret key, decrypt the particular traffic flow, and carry out further investigations. In this paper we study the secret sharing scheme as a counter at the limit when the threshold m is relatively large. We first analyze how the scheme behaves as m approaches the maximum possible value of p - 1, where p is a prime number (design parameter). Then, we also analyze a probabilistic version developed to overcome the limited counting range, or excessive reporting overhead, by revealing shares only with a certain probability after each event, and provide expressions describing the resulting inaccuracy from the introduced randomness. Finally, we also propose a hybrid solution to mitigate the otherwise detoriating performance by using a forward error correction scheme similar to LT codes to encode the shared secret revealing process.