If SNARKs generally work in finite fields, how are non integer values handled - say fixed point decimal numbers?

user93353

2/8/24, 11:34 AM

In Vitalik Buterin's write-up on SNARKs Quadratic Arithmetic Programs: from Zero to Hero, he writes

Note that the above is a simplification; “in the real world”, the addition, multiplication, subtraction, and division will happen not with regular numbers, but rather with finite field elements

I assume SNARKs are used in blockchains to hide & also verify the transactions. However, blockchain transactions may involve non-integer amounts (the sender is sending a fractional amount), so how are the private (witness) & public inputs which involve non-integer numbers represented in finite fields?

UPDATE from one of the answers:

Since a Satoshi is 0.00000001 BTC every send/receive transaction can probably be an integer value.

Is there any other stuff on a blockchain which are shielded by zkSNARKs and can have non integer values or everything for which zkSNARKs are used on a blockchain is integer values?

1 + 4

finite-field

zero-knowledge-proofs

DannyNiu

2/8/24, 12:00 PM

I didn't realize blockchain transaction values are floating points. I always thought financial data would use fixed-point numbers for accuracy.

user93353

2/8/24, 12:10 PM

@DannyNiu - I have updated the question - I actually wanted to ask about any non-integer values

kodlu

2/9/24, 11:34 PM

Your question has been answered. In practice under finite precision all values are rational, and can be boosted up to integers by multiplying with the denominator.

user93353

2/10/24, 1:10 AM

@kodlu - I also want to know if there are any kinds of SNARK shielded transactions/computations on a blockchain which need this type of boosting

Score:4

Crypto

kodlu

2/8/24, 11:59 AM

If necessary, this can be done by sending all $n$ digits of the fraction (it has to be finite length to be represented digitally) and an encoding (in $\log_2(n+1)$ bits) of the position of the decimal point. However it may not be needed, one can simply express the transaction as an integer multiple of a minimum allowed amount in fractional satoshis.

Edit:

zk-snarks are used to shield cryptocurrency transactions and according to the bitcoin setup we have:

"A UTXO (unspent transaction output) can have an arbitrary value denominated as a multiple of satoshis." Reference is Mastering Bitcoin, Chapter 5

+ 2

user93353

2/8/24, 12:11 PM

Is it how it's actually done in real world blockchains which use SNARKs?

user93353

2/8/24, 12:53 PM

`A UTXO (unspent transaction output) can have an arbitrary value denominated as a multiple of satoshis` - Since a satoshi is 0.00000001 BTC every transaction is an integer value, right? So there is no chance a SNARK will involve non-integers on a blockchain?

Elon Musk

I sit in a Tesla and translated this thread with Ai:

EN: If SNARKs generally work in finite fields, how are non integer values handled - say fixed point decimal numbers?

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