Taktikos PoS
A blockchain’s consensus algorithm plays a crucial role in any blockchain’s overall design. Directly, the consensus algorithm is the set of rules to which block producing nodes must adhere. Indirectly, a blockchain’s choice of consensus algorithm will determine its energy footprint, influence transaction speed, throughput, and finality, and limit or extend its level of decentralization.
The centrality of blockchain consensus leads protocol designers to look to closely balance solid fundamentals with promising advances. This is exactly what Topl’s team sought to (and has) achieved with the creation of Taktikos, the first regularized Nakamoto consensus protocol


Taktikos is built from the foundation first established by IOHK in Ouroboros Praos and as such inherits a number of key advantages as compared to other approaches:
    As a pure Nakamoto-style protocol, Taktikos consensus remains robust and can continue to produce blocks with only >1/2 honest stake. This is in contrast with BFT protocols that can remain in consensus only if more than 2/3 of the network’s stake is honest.
    Taktikos can make use of a dynamically available and fully permissionless set of stakers with no fundamental maximum on the set of active block producers (as is the case for EOS) or even minimum thresholds for stake ownership (like we find in Ethereum’s Casper design).
    Among Praos’s key advantages is a provably secure consensus model that does not rely on any trusted execution environments or other hardware related assumptions. Leveraging a cryptographic construction known as verifiable random functions (VRFs), Praos and later algorithms such as Taktikos do not need to be concerned with hardware advancements that may render them insecure as is the case with algorithms (such as Ethereum’s Casper and Proof of Time used by Chia) that rely on the alternative construction of verifiable delay functions (VDFs).
    Praos, along with the larger family of Ouroboros consensus algorithms, have been formulated, studied, and verified under the cryptography framework of universal composability (UC). Not only does such a formulation deliver an unsurpassed standard of rigor to security assumptions, but it also ensures that the base protocol can be composed with additional protocols to extend functionality or interoperate.

Long-tails and slot-based consensus

One of the key drawbacks of Nakamoto consensus has historically been the high level of variability in the timing of block production. While the average block time for Bitcoin is set at 10 minutes, this is only an average and there exists a longtail where a new block may not arrive for hours.
Probability Density Function (PDF) of block time intervals in the Bitcoin network, showing an exponential profile characteristic of the statistical independence of valid proofs discovered in the mining process. Reference: C. Decker and R. Wattenhofer, "Information propagation in the Bitcoin network," IEEE P2P 2013 Proceedings, 2013, pp. 1-10, doi: 10.1109/P2P.2013.6688704.
This exponential distribution can be found across blockchains leveraging Nakamoto consensus as the process of block creation relies on applying a (near) constant probability from one block to another that a new block is produced in any single moment. Not only does this introduce the obvious problem that the blockchain network will occasionally stall, failing to confirm new transactions for an extended period, but it can also incentivize centralization where block producers can benefit from grouping themselves geographically. This was exactly the behavior that was realized with the so-call slot battles in Cardano (reference).
To solve this problem, Topl developed Taktikos. The motivating innovation of Taktikos is centered around the introduction of what we have dubbed, local dynamic difficulty. Like other proof-of-stake consensus protocols, Taktikos is round based, meaning that blocks are created and added in set rounds, with forgers each having a stake dependent probability of producing a valid block to extend the chain in each slot. However, Taktikos is unique in that the probability of block creation is not constant and uses slots to act as a clock to evolve the difficulty of producing a block over time. The goal of this perturbation is to regularize the production of new blocks so that blockchain stalls are minimized.
While many potential difficulty curves were considered and simulated, one curve in particular stands out for the chain growth and security properties it produces, the descriptively named snowplow curve (pictured below).
The time between blocks is shown on the x-axis, the y-axis corresponds to the value of the active slot coefficient, or difficulty, at a given slot interval δ.
The snowplow curve allows for blocks to be produced across two distinct periods, the Forging Window and the Recovery Phase. The effect of this curve with a a notable discontinuity between the two periods (the Cutoff), is to transform the distribution of new block production from the exponential distribution found in other protocols to a tight bell curve (-like) distribution, named the Taktikkos distribution, centered around the average block time.
A sample distribution function produced by Taktikos. The distribution goes to zero as δ approaches zero producing significantly fewer asynchronous extensions, or network stalls. The difficulty curve parameters in this example are γ = 40, Ψ = 0, fA = 0.4 fB = 0.05.
Beyond providing for more predictable block production, the introduction of Taktikos yields improved chain growth properties that in turn provide faster transaction finality, increased transaction throughput, and reduced adversarial influence. The complete methods by which these benefits are achieved will be detailed in future work, we will describe them briefly.
With regard to the faster transaction finality, this advantage is realized directly through the novel block distribution shown above. Simply put, because the vast majority of blocks are produced within a tight window of time immediately centered on the average block time, the probability that a transaction has been included on anything other than the canonical chain is substantially less than would be the case if blocks were produced according to the more standard exponential distribution. In the case of a exponential distribution describing block production, a transaction will often be included in either a block that is produced too quickly as to fall below the average network delay and thus have a higher probability of being reorged out or be relegated into a block that does not get added for an expended period.
Turning to the matter of throughput, the consideration becomes efficiency. Namely, the Taktikos distribution for block production enables blocks to be filled more efficiently. Put most simply, since block production according to a Taktikos distribution results in fewer block reorgs (for a given block time), transactions on average are included in fewer blocks. As transactions are included in fewer blocks, there is comparatively more space available for non-redundant transactions, thus increasing overall throughput.
Finally, and perhaps most interestingly, the introduction of local dynamic difficulty according to the snowplow curve has the effect of reducing the power of adversarial actors in the system. Returning to the snowplow curve and Taktikos distribution, we observe that the period shortly following the production of a block, also known as the forging window, is responsible for the vast majority of block production given the lower difficulty at the beginning of that window. Another way to think about this is to recognize that “blocks beget blocks”.
The result of blocks begetting blocks is to see that any adversary attempting to subvert the canonical chain by only extending on their own tine (ignoring blocks produced by other nodes) will have a distinct disadvantage in creating blocks even for slots where they would otherwise be eligible to extend the chain because they will probabilistically never be eligible to forge while still in the Forging Window from their previously minted block. The effect of this is that with proper parameterizations, Taktikos will diminish the power of any adversary (with less than 50% of active stake) to equal to less than the influence they would have if they were to behave honestly.
In this plot we see that the power of a network adversary can be tuned based on the fB, or the difficulty of block production during the Recovery Period.
In summary and while we believe there to exist several lines of potential further exploration for Taktikos we believe that parametrizations already obtained and currently being implemented into the Topl Blockchain offer notable improvements in terms of transaction finality, network throughput, and security compared with other POS protocols, all while retaining the strong fundamentals provided by Ouroboros Praos.
    The term Nakamoto consensus describes an incentive driven, probabilistic consensus algorithm where chain extension eligibility is determined via a race condition, originally presented in the Bitcoin whitepaper.
Last modified 9d ago