Lattice-Based Key-Value Commitment Scheme

A blockchain is an important component in the design of secure distributed file systems, such as cryptocurrencies. One of the key components of the blockchain is the key-value commitment scheme, which constructs a commitment value from two inputs: a key and a value. In a conventional commitment scheme, a single user constructs a commitment value from an input value, whereas in a key-value commitment scheme, multiple users construct a commitment value from their keys and values. Both conventional and key-value commitment schemes must satisfy binding and hiding properties. The key-binding and key-hiding properties guarantee that neither the sender nor the verifier can act maliciously. The concept of a key-value commitment scheme was first proposed by Agrawal et al. in 2020 using a strong RSA assumption. Their scheme satisfies the key-binding but not key-hiding properties. In this paper, we propose two lattice-based key-value commitment schemes, ${\mathsf { Insert}}\text {-}{\mathsf { KVC}}_{m/2,n,q,\beta }$ and ${\mathsf {\text {KVC}}}_{m,n,q,\beta }$ , that satisfy both the key-binding and the key-hiding properties. The key-binding property of both ${\mathsf { Insert}}\text {-}{\mathsf { KVC}}_{m/2,n,q,\beta }$ and ${\mathsf {\text {KVC}}}_{m,n,q,\beta }$ are proven under the short integer solution ( ${\mathsf {\text {SIS}}}^{\infty } _{n,m,q,\beta }$ ) problem. The key-hiding property of both ${\mathsf { Insert}}\text {-}{\mathsf { KVC}}_{m/2,n,q,\beta }$ and ${\mathsf {\text {KVC}}}_{m,n,q,\beta }$ are proven under the Decisional- ${\mathsf {\text {SIS}}}^{\infty } _{n,m,q,\beta }$ -form problem, which is newly defined in this paper. We demonstrate the difficulty of the Decisional- ${\mathsf {\text {SIS}}}^{\infty } _{n,m,q,\beta }$ -form problem by showing that the Decisional- ${\mathsf {\text {SIS}}}^{\infty } _{n,m,q,\beta }$ -form problem is secure when the ${\mathsf {\text {SIS}}}^{\infty } _{n,m,q,\beta }$ problem is secure. Finally, we analyze the computational costs of ${\mathsf { Insert}}\text {-}{\mathsf { KVC}}_{m/2,n,q,\beta }$ and ${\mathsf {\text {KVC}}}_{m,n,q,\beta }$ . Our method is the first lattice-based key-value commitment scheme with proven the key-binding and the key-hiding properties.