Cryptographic Proofs

Proof Types in Decentralized Systems

emRA.ls leverages multiple cryptographic proof systems to achieve trustless verification and privacy-by-design. These include:

SNARKs

Succinct Non-Interactive Arguments of Knowledge enable proofs of computation without revealing input data.

Verifiable Encryption

Allows mathematical verification that an encrypted value satisfies a given relation.

Proof of Presence

Cryptographic confirmation of node participation without revealing identity or location.

Zero-Knowledge Proofs (ZKPs)

Zero-knowledge proofs allow one party (the prover) to prove to another party (the verifier) that a given statement is true, without conveying any information beyond the truth of that statement.

ZKP System Requirements:

Completeness: Verifier accepts valid proofs
Soundness: Prover cannot trick verifier with false proofs
Zero-knowledge: Proof reveals nothing beyond validity
Succinctness: Verification time is bounded by proof length

Example: ZKP in emRA.ls Identity System


// Prove knowledge without revealing secret\n
π = zkprove(K, T(φ), w) // φ = circuit, w = witness\n
verify(π, T(φ)) == true

Allows users to prove they control a cryptographic identity (K) without revealing the private key.

zk-SNARKs Implementation

Our implementation uses libsnark for efficient circuit generation and verification. All arithmetic circuits are written in R1CS (Rank-1 Constraint Systems).

Circuit Constraint Example

a * b = c

Constraint: a • [a b c] = 1 • [a b c] • [0 0 1]

w^3 + x^2y = z

Constraint: w • [w² x² z] = 1

Real-World Applications

Private Authentication

Users prove ownership of a decentralized identity without exposing private keys or recovery phrases.

Content Access Control

Content creators can verify user credentials and subscription status without exposing sensitive payment data.

Auditable Moderation

Moderators can prove they followed established policies without reviewing content directly.