What’s Next in Programmable Cryptography?

💡Key Ideas:

• Two ideas

  • Secure Multi-Party Computation(MPC) is a protocol that allows multiple entities to jointly compute a function without revealing their individual inputs.
  • Fully Homomorphic Encryption (FHE) is a technology that allows computation over encrypted data, where only the owner of the key can decrypt the result of the computation.

• MPC would enable for example: figuring out a potential disease risk in a population by aggregating completely encrypted data, finding out the optimal buy/sell price of a property without parties agreeing or showing them beforehand, collaborating in cross-regional entities for military or humanitarian assistance without revealing it beforehand.

FHE would enable for example:

• Running a private AI model into encrypted data that you've sent over a server (for example to detect a disease without revealing your health data)

• Encrypted searchers on the internet

• Data Protection Policy Compliance by companies operating over data without ever seeing it

🔗 Links:

Introduction of Programmable Cryptography by Brian Gu (Gubsheep)

Beyond Zero-Knowledge: What’s Next in Programmable Cryptography?

PSE Core Program Frontier

• MPC
• FHE
• TLSNotary
• ZKEmail

FHE (Fully Homomorphic Encryption) and friends

🔗Links:

Homomorphic encryption for IQ < 200 by Lauri Peltonen

🛠️ Build and Practice:

Try out Fhenix, an Ethereum L2 built using FHE.

MPC (Secure Multi-Party Computation)

🔗Links:

Secure Multi-Party Computation by PSE 🛠️ Build and Practice:

Try to follow Circom-2-arithc, a Circom to MPC framework in development.

Fiat-Shamir transformation

💡 Key Ideas:

• The Fiat-Shamir transformation, or heuristic, is a way to make interactive protocols non-interactive.
• This means that, instead of having to verify many times that something is true (probabilistic approach), we can verify it with a single check.
• This is a key element part of constructing proving systems.
• More to read: Fiat Shamir Secret Sharing

🔗 Links:

• Fiat-Shamir transformation for IQ < 200 by Lauri Peltonen

🛠️ Build and Practice:

• Run by hand (and calculator) the example of Fiat Shamir heuristic

Create a new wallet and extract the private key. Now split the key using Fiat Shamir Secret Sharing and then try to reconstruct it using a base code implementation like privy-io/shamir-secret-sharing. Try to implement your own.

[WIP] Schwartz–Zippel lemma

💡Key Ideas:

• The Schwartz-Zippel lemma allows us to compare two polynomials and check if they are identical by just comparing a single point, with a minuscule chance of failure.
• The more coefficients the harder to cheat.
• As a probabilistic tool, this is key element when constructing proving systems.

🔗Links:

• Schwartz–Zippel lemma for IQ < 200 by Lauri Peltonen