4.1. Copyright Offense by Colluding with Miners: Game Theoretical Dangerous
According to YODA’s design, an adversary needs to calculate the ES of each round of execution before submitting an illegal request and force a significant number of miners in each ES to perform the wrong calculation. If this fails, the request is rejected, and the miner will be isolated at a cost considered to be
. The MIRACLE and RICE algorithms ensure that the processing of a request is repeated for multiple rounds by multiple random ES, and the calculation process cannot be forged. The feasibility and security of YODA were respectively proved [
22], so we can assume that the probability of attack failure
is close to 1. The value of the publication is denoted as
v, the number of miners in ES is denoted as
n, and the cost of controlling a miner is expressed as
c. Then the profit expectation of this process is
If copyright payment is regarded as value exchange, we can assume that the user’s profit in this process is 0. The user’s profit matrix can be obtained:
Non-infringement | Infringement |
0 | |
Obviously, in this single-player static game, non-infringement decision forms dominance. Therefore, performing copyright infringement via collusion with miners is almost impossible, such an attempt is also extremely costly.
4.2. Copyright Offense via Sharing Publication Copy: Game Theoretical Dangerous
One common way to circumvent Y-DWMS and other DRM schemes is to share copies outside the jurisdiction of the platform. Assuming that the infringer has already obtained and divulged copies through screen recording or I/O listening, the following subgame is introduced.
In the game presented in
Figure 5, the player set contains all users and the copyright holder, i.e., N = {holder, C
, C
, …, C
}. For each user C
, the action set is A = s ∧ r, ¬ s ∧ r, s ∧¬ r, ¬ s ∧¬ r, in which selling copies is denoted as
s, and reporting is denoted as
r. To simplify the analysis, we firstly assume that each user is allowed to perform selling copies only once, and the copyright holder’s profit will not be discussed in figures (we will discuss these respectively). We denote the profit function of C
as u
.
Next, we perform the analysis of this game. According to the contract design of Y-DWMS, this game adopts the following rules:
If C launches s, then the profit of C increases by v, and the profit of C increases by –v. v is the price for selling divulged copies.
If C launches r, then the profit of C increases by b, the profit of C increases by –b–v, and the profit of the copyright holder increases by v. b is the reward for C, and v is original price of the publication.
If N is an infinite set, i.e., the number of users is large enough, the deposit the infringer transferred to the contract is sufficient, and b > v−v, then the whole game will form a unique sequential dominance. For C, C, …, C, the choice of s∧r will always bring the highest profit, and the dominance sequence will always be the leftmost route of the game tree. This game ideally will not terminate since N is an infinite set.
Formally, we have the followings:
If N is an infinite set, the balance of the user’s account is sufficient and b > v
−v
, then the subgame in the figure will perform a unique sequential equilibrium
where
Under this equilibrium, the profit of C1 is
when the profit of copyright holder is
Obviously, the cost of C is incredible, while the copyright holder suffered no loss.
Based on this subgame, the benefit of the infringer divulging the key is easy to calculate: instead of generating additional positive profit for C
, it adds negative revenue –c–p, where c is the property loss C
needs to suffer, and p is the losses generated by other users stealing C
’s identity. Based on the previous profit analysis of various attack means, we could perform the full game in
Figure 6:
In the full game, the player set contains all users and the copyright holder, i.e., N = {holder, C, C, …, C}. The action set of C is A = {Atk, CP, PK, NAN}, where Atk is a direct attack on Y-DWMS, CP is the divulged copy, PK is divulged public key of C, NAN is nothing to do. The action set of C is A’ = {t ∧ v, ¬ t ∧ v, t ∧¬ v, ¬ t ∧¬ v}, where t is stealing C’s balance, and v is stealing C’s identity. To simplify the analysis, we only discuss the profit of the copyright holder and C, and the matching profit function is u, u. According to the design of contracts, the full game adopts new rules on the basis of a subgame:
If C launches t, then the profit of C increases by –c, profit of C increases by c.
If C launches v, then profit of C increases by –p.
According to our game analysis of the infringer launching an attack on Y-DWMS, the profit of C launching Atk is . No matter whether C launches CP or PK, the subgame will be triggered. More importantly, launching PK generates additional negative profit. It is obvious that we have the following:
If the full game satisfies the conditions satisfied by the subgame, then a unique sequential equilibrium will form, where
Under this equilibrium, the profit of C is 0 when the profit of the copyright holder is still .
4.3. Countering Punishment via Smart Contract: Impossible
There is a fatal weakness in traditional smart contract schemes that an infringer could adopt to eliminate punishment, by forcing users to sign a smart contract before purchasing copies from the infringer. We denote this as Contract_Countermeasure. If the copies are submitted to the platform and the infringer’s watermark is detected, this contract is triggered to transfer a huge amount of compensation to the infringer, which is denoted as . Thus, if the infringement is reported, the informer will suffer heavy losses. The contract’s logic is simply presented as Algorithm 3.
Algorithm 3 Contract_Contermeasure |
- 1:
Var: - 2:
{account, infringer, informer:Address;} - 3:
- 4:
Func_Contermeasure(): - 5:
if exists transaction{Contract_Report->informer, amount=deposit} then - 6:
account.transfer(infringer, deposit) - 7:
else - 8:
reject and fallback - 9:
end if - 10:
- 11:
Func~: - 12:
destroy
|
Under a contract like this, the subgame mentioned above will be changed as in
Figure 7.
However, in Y-DWMS, informers can counter it simply. As an informer reward request is a secret parameter that the infringer will never correctly predict, this contract cannot know the exact loss the infringer will suffer. The compensation to the infringer must be settled when Contract_Countermeasure is signed, so the informer could simply increase the reward request, making sure that . As a result, the domain decision will switch to , maintaining the original subgame and full game.