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start your week off with something sweet. we'll be taking a look at the latest politics, news, culture & tech predictions on @Polymarket:
https://t.co/tkhfXMo1au
And now it is time for America to reach far greater heights by sending astronauts to Mars!
Ultimately, anyone who wants to be a space traveler and help build a new civilization on Mars should be able to do so.
That is an inspiring future!
A deep, no-math dive into Polygon Plonky3:
Polygon Plonky3 is a ZK proving system toolkit for building use-case specific zkVMs and zkEVMs. It’s the next generation of Plonky2, widely adopted and known for its innovative use of the Goldilocks Field.
But where Plonky2 was opinionated in its choice of a single finite field and single hash function, Polygon Plonky3 is agnostic. Polygon Plonky3 can be configured with multiple finite fields and multiple hash functions, resulting in a proving system that can be optimized across a range of dimensions, including for target hardware, high-speed proof-generation, and proof size.
One of the finite fields available in Polygon Plonky3 is Mersenne31 (M31), a prime field known for its exceptionally simple structure: p = 2^31 - 1. On standard CPU architectures, M31 is considered the fastest prime on earth. But making M31 practical for proof-generation in a blockchain context required a research collaboration with @StarkWareLtd.
First, some context:
Regular STARKs encode execution trace data into polynomials. Why polynomials? Because they possess a quality called the local to global inference principle, which makes it possible to test that a polynomial is zero everywhere by checking its value locally at a single random point.
This simple observation (“Schwartz-Zippel lemma”) is the core argument of any polynomial interactive oracle proof (PIOP), the information-theoretic model behind STARKs and modern SNARKs.
The execution trace of a processor is arranged in a rectangular layout, which records the state of the processor over time, row by row. Once the columns are encoded into polynomials, valid state transitions of the processor are expressed by algebraic constraints imposed on the polynomials.
In practice, an FFT (Fast Fourier Transform) is needed for encoding data into polynomials efficiently. Because if you can’t encode fast, proving time increases to impractical length. The problem for M31 is that it is a non-FFT friendly field, meaning that its multiplicative group is not “smooth,” preventing the regular encoding approach.
So how is efficient encoding accomplished for M31? The solution combines StarkWare’s ECFFT with Polygon Labs’ prior work on Reed-Solomon codes over the circle group.
The ECFFT widened the scope for efficient encoding by imagining a non-linear underlying space for the polynomials: an elliptic curve. It is a groundbreaking construction of an FFT-like algorithm over *any* finite field, including M31.
However, the construction of the algorithm is complex and requires deep knowledge in the theory of elliptic curves; a chamber of secrets for ordinary humans.
The Circle FFT greatly simplifies the ECFFT by taking the unit circle as its underlying space. The circle curve preserves the capacity to perform an FFT that is in the spirit of the ECFFT but with a core construction that is simpler, making it possible for devs to build virtual machines that leverage the performance of the fastest prime on earth.
GitHub: https://t.co/D1CZMp2zWd
Sources: https://t.co/WuOnIYbBop; https://t.co/WXILPylHLX
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