How deeply does Real-World Cryptography cover homomorphic commitment?

Defines equality, addition, and public scaling, then adds pairings for one multiplication without detailing implementation.

Homomorphic commitment

As explained in Real-World Cryptography

A homomorphic commitment is a cryptographic commitment that supports operations on committed values while preserving corresponding algebraic relationships.

A homomorphic commitment hides a value while allowing a verifier to perform selected operations on the hidden value. In zk-SNARKs, it helps check polynomial relationships without revealing the polynomial itself. section 15.3.1 section 15.3.2

Typical commitment checks include:

Equality: ga = gb implies a = b. section 15.3.2
Addition: ga = gbgc implies a = b + c. section 15.3.2
Scaling: ga = (gb)c implies a = bc when c is public. section 15.3.2
Multiplication requires an additional mechanism, such as a bilinear pairing; the result is not fully homomorphic. section 15.3.2 section 15.3.3

Polynomial divisibility check

A prover commits to f(x) and h(x), while the verifier computes a commitment to the agreed constraint t(x). The verifier checks com(f(x)) = com(t(x))com(h(x)), corresponding to f(x) = t(x)h(x), without receiving the polynomials openly. section 15.3.2

How Real-World Cryptography covers it

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Related concepts

bilinear pairinguses · A bilinear pairing is a map from two groups into a third group that preserves the group operation in each argument separately.
hash functioncontrasts with · A hash function deterministically maps input data to a value in a bounded output range, commonly for indexing, lookup, comparison, or integrity checking.
zk-SNARKused by · A zk-SNARK is a zero-knowledge, succinct, non-interactive argument of knowledge that enables efficient verification of a prover’s knowledge of a computation’s secret witness without revealing it.
exponenthas part · An exponent is a number specifying the power to which a base or radix is raised, determining the scale of the resulting value.

This explainer was generated by Manning's knowledge graph from the text of Real-World Cryptography. The section links point to the parts of the book it draws on.