What is a rank-1 constraint system?

Question

Why not rank-2 constraint system or rank-3 constraint system?

How do rank-1 constraint systems link to circuits?

score 6 · Accepted Answer · answered Apr 02 '19 at 08:39

6

The "rank-1" specifically refers to the rank of the matrix which is produced.

As for the link to circuits, in zk-SNARKS at least, an arithmetic circuit is converted into a R1CS. Each constraint corresponds to one logic gate.

answered Apr 02 '19 at 08:39

mountbranch

1

and maybe this is a duplicate: https://crypto.stackexchange.com/questions/55963/converting-to-rank-one-constraint-system?rq=1 – mountbranch Apr 02 '19 at 08:40
Why does it need to be rank-1? – WeCanBeFriends Apr 02 '19 at 11:22
I did some more research and it seems, according to this paper: https://eprint.iacr.org/2013/507.pdf that the rank-1 is referring to each of the quadratic equations in A*B+C = 0 . Hope that helps! – mountbranch Apr 22 '19 at 10:00
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so what's a R2CS? – David 天宇 Wong May 05 '21 at 15:12

1 Answers1