Any language in the classes PZK (perfect zero-knowledge), SZK (statistical zero-knowledge) or CZK (computational zero-knowledge) have interactive protocols that are zero knowledge and don't require a CRS. Some of the interesting non-trivial languages in these classes are listed below. (I'd also recommend this beautiful survey by Vadhan)

• PZK: Quadratic residuosity, graph isomorphism
• SZK: Quadratic non-residuosity, graph non-isomorphism, lattice problems like CVP
• CZK: Graph coloring

However, Oren [O] showed that only languages in BPP have NIZK proofs without CRS. You can find a proof sketch here (Lemma 1).

[O]: Oren. On the cunning power of cheating verifiers: Some observations about zero knowledge proofs (behind a paywall unfortunately).

Any language in the classes PZK (perfect zero-knowledge), SZK (statistical zero-knowledge) or CZK (computational zero-knowledge) have interactive protocols that are zero knowledge and don't require a CRS. Some of the interesting non-trivial languages in these classes are listed below. (I'd also recommend this beautiful survey by Vadhan)

• PZK: Quadratic residuosity, graph isomorphism
• SZK: Quadratic non-residuosity, graph non-isomorphism, lattice problems like CVP
• CZK: Graph coloring (and in fact as Geoffroy points out any language in IP)

However, Oren [O] showed that only languages in BPP have NIZK proofs without CRS. You can find a proof sketch here (Lemma 1).

[O]: Oren. On the cunning power of cheating verifiers: Some observations about zero knowledge proofs (behind a paywall unfortunately).

Any language in the classes PZK (perfect zero-knowledge), SZK (statistical zero-knowledge) or CZK (computational zero-knowledge) have interactive protocols that are zero knowledge and don't require a CRS. Some of the interesting non-trivial languages in these classes are listed below. (I'd also recommend this beautiful survey by Vadhan)

• PZK: Quadratic residuosity, graph isomorphism
• SZK: Quadratic non-residuosity, graph non-isomorphism, lattice problems like CVP
• CZK: Graph coloring

However, Oren [O] showed that only languages in BPP have NIZK proofs without CRS. You can find a proof sketch here (Lemma 1).

[O]: Oren. On the cunning power of cheating verifiers: Some observations about zero knowledge proofs (behind a paywall unfortunately).

Any language in the classes PZK (perfect zero-knowledge), SZK (statistical zero-knowledge) or CZK (computational zero-knowledge) have interactive protocols that are zero knowledge and don't require a CRS. Some of the interesting non-trivial languages in these classes are listed below. (I'd also recommend this beautiful survey by Vadhan)

• PZK: Quadratic residuosity, graph isomorphism
• SZK: Quadratic non-residuosity, graph non-isomorphism, lattice problems like CVP
• CZK: Graph coloring

However, Oren [O] showed that only languages in BPP have NIZK proofs without CRS. You can find a proof sketch here (Lemma 1).

[O]: Oren. On the cunning power of cheating verifiers: Some observations about zero knowledge proofs (behind a paywall unfortunately).