Add Blog for safety-of-methods-for-numeric-primitive-types - 2024-12-02

[rajathkotyal]

Towards : model-checking/verify-rust-std#59

Description : This blog post talks about verifying the safety of unsafe methods which use Rust's numeric primitive data types.

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[tautschnig]

Thank you!

[Yenyun035]

@tautschnig @celinval @zhassan-aws @feliperodri We have finished the draft. Appreciate any feedback :)

[celinval]

I really liked the blog post. My main suggestion is to improve a little bit the explanation about the need for range partitioning into the checks that involved multiplication.

I think it's good to clarify that the problem here is the complexity of the SAT formula generated for multiplications. For example, the input space for addition and multiplication are the same, but only the multiplication requires partitioning.

@tautschnig do you know any good reference that we can use so we don't have to give too much details on why multiplications are hard for sat solvers?

[tautschnig]

I really liked the blog post. My main suggestion is to improve a little bit the explanation about the need for range partitioning into the checks that involved multiplication.

I think it's good to clarify that the problem here is the complexity of the SAT formula generated for multiplications. For example, the input space for addition and multiplication are the same, but only the multiplication requires partitioning.

@tautschnig do you know any good reference that we can use so we don't have to give too much details on why multiplications are hard for sat solvers?

From Randy E Bryant's "Graph-Based Algorithms for Boolean Function Manipulation" (1986) we know that the Boolean function representing all outputs of a multiplier as a BDD is exponential in the size of the operands. We can do a more compact representation in CNF, but it will still be quadratic in the size of the operands. And those turn out to be hard to solve for SAT solvers, which in some ways is good news, as otherwise we could rather efficiently do factorisation of numbers (and thereby, in practice, break some of today's cryptographic algorithms).

[tautschnig]

Thank you!

[carolynzech]

This is a great post! Awesome job. My main comments are about some technical points in section 2--request my re-review once addressed and I'll approve.

[carolynzech]

Thanks!