Cheating prevention in linear secret sharing

Cheating detection in linear secret sharing is considered. The model of cheating extends the Tompa-Woll attack and includes cheating during multiple (unsuccessful) recovery of the secret. It is shown that shares in most linear schemes can be split into subshares. Subshares can be used by participants to trade perfectness of the scheme with cheating prevention. Evaluation of cheating prevention is given in the context of different strategies applied by cheaters.

Cheating prevention in secret sharing over GF(pt)

The work investigates cheating prevention in secret sharing. It is argued that cheating is immune against cheating if the cheaters gain no advantage over honest participants by submitting invalid shares to the combiner. This work addresses the case when shares and the secret are taken from GF(pt). Two models are considered. The first one examines the case when cheaters consistently submit always invalid shares. The second modeldeal s with cheaters who submit a mixture of valid and invalid shares. For these two models, cheating immunity is defined, properties of cheating immune secret sharing are investigated and their constructions are given.

Constructions of cheating immune secret sharing

The work addresses the problem of cheating prevention in secret sharing. Two cheating scenarios are considered. In the first one, the cheaters always submit invalid shares to the combiner. In the second one, the cheaters collectively decide which shares are to be modified so the combiner gets a mixture of valid and invalid shares from the cheaters. The secret scheme is said to be k-cheating immune if any group of k cheaters has no advantage over honest participants. The paper investigates cryptographic properties of the defining function of secret sharing so the scheme is k-cheating immune. Constructions of secret sharing immune against k cheaters are given.

Ideal threshold schemes from MDS codes

We observe that MDS codes have interesting properties that can be used to construct ideal threshold schemes. These schemes permit the combiner to detect cheating, identify cheaters and recover the correct secret. The construction is later generalised so the resulting secret sharing is resistant against the Tompa-Woll cheating.

Ideal threshold schemes from orthogonal arrays

The work investigates the design of ideal threshold secret sharing in the context of cheating prevention. We showed that each orthogonal array is exactly a defining matrix of an ideal threshold scheme. To prevent cheating, defining matrices should be nonlinear so both the cheaters and honest participants have the same chance of guessing of the valid secret. The last part of the work shows how to construct nonlinear secret sharing based on orthogonal arrays.