When do we need cryptography in blockchain space?

Cryptography
1

I want to check when will we need cryptography in blockchain field.I list all I know here:

  1. Consensus algorithm
    2.Signing transaction (including different kinds on digital signature )
    3.Layer2’s verification on Layer1
    4.Verifying the cross chain tx
    5.Rollup with different digital signature
    6.Cross-shard

Is there anything I miss ?

2

Consensus-layer:

  • Hashes for Merkle trees
  • Signatures for transactions
  • Signatures for blocks in PoS
  • Possibly, polynomial commitments as a replacement for Merkle trees
  • ZK-SNARKs/STARKs to enable more efficient client-side verification
  • Private information retrieval for privacy-preserving light clients

Application-layer

  • ZK-SNARKs for scaling (eg. ZK rollup)
  • ZK-SNARKs for privacy (eg. Tornado Cash)
  • Other forms of cryptography for privacy (confidential transactions, bulletproofs, ring signatures…)
  • Group homomorphisms for stealth addresses and deterministic wallets
  • Multi-party computation for privacy (in some situations ZK-SNARKs are not sufficient, particularly when you want to maintain state that no one can decrypt)
  • In the future, obfuscation: How obfuscation can help Ethereum
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3

Thanks Vitalik
it seems that the most cryptography in Consensus layer is hard code. Could Ewasm help ?
And could application layer get more flexibility for programming ? For example,zk rollup is hard to interact with general smart contract on Eth so they need to invent new lang like Zinc.

4

Ewasm could certainly be used to write cryptography more efficiently, though in many cases it’s not needed; rather, what’s needed is for EVM to get better support for big-integer operations, as that’s where the bulk of the cost of a lot of cryptographic operations comes in.

For example,zk rollup is hard to interact with general smart contract on Eth so they need to invent new lang like Zinc.

Yeah, this is a problem. The EVM is not very friendly to living inside of cryptographic systems like ZK-SNARKs (or STARKs, or MPC, or FHE). Ewasm is a little better, but the best would be a VM specifically designed for ZK-friendliness.

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5

Gotcha,thanks. What is the big-integer operations? I would take more study about that .

A VM especially for Zk is a solution but it is possible that a VM could read different kinds of cryptography in specific code format ?

6

Basically arithmetic (add, multiply, modulo, divide) with very big numbers, usually 80-2000 digits.

A VM especially for Zk is a solution but it is possible that a VM could read different kinds of cryptography in specific code format ?

VMs that specifically support certain cryptographic operations are definitely possible.

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