PRIVATE.ME / XorIDA vs Shamir's Secret Sharing
Same information-theoretic security guarantee. Fundamentally different performance, practicality, and deployment profile.
Both XorIDA and Shamir's Secret Sharing provide information-theoretic security — the strongest form of security in cryptography. This means:
| Property | Shamir's Secret Sharing | XorIDA (Ours) |
|---|---|---|
| Mathematical field | GF(p) — prime Galois field, large prime | GF(2) — binary Galois field, native XOR |
| Core operation | Polynomial interpolation (Lagrange) | XOR only |
| Speed (1 MB) | 500 – 2,000 ms | ~33 ms |
| Speed (typical API payload) | Milliseconds of overhead | Sub-millisecond |
| 8-bit embedded hardware | Impractical — requires big-integer arithmetic | Native — bit-level XOR operations |
| Key management | Required — polynomial coefficients | None — shares ARE the security |
| Share size | Same as secret | Same as secret |
| Security model | Information-theoretic | Information-theoretic |
| Quantum-proof | Theoretically yes | Unconditionally yes |
| Patent status | Public domain | Patent-pending (US 11,972,000 B2) |
| Production deployments | Limited — performance constraints | Production — AI agents, healthcare, financial, government |
Shamir's Secret Sharing operates over a prime field GF(p). This requires big-integer arithmetic — polynomial evaluation and Lagrange interpolation over integers modulo a large prime. On a 1 MB payload, this takes 500ms to 2 seconds. On 8-bit microcontrollers, it's practically impossible.
XorIDA operates over the binary field GF(2). Over GF(2), addition is XOR — a single CPU instruction available on every processor ever made, including 8-bit embedded chips. Splitting a 1 MB payload takes ~33ms. A typical API payload (64B–1KB) completes in sub-millisecond time.
The performance difference is not engineering — it's mathematics. XOR over GF(2) is inherently faster than polynomial arithmetic over GF(p). The security guarantee is identical.
XorIDA adds HMAC-SHA256 verification before reconstruction. Every share must pass HMAC verification before the data is assembled. This is non-negotiable and cannot be bypassed. A tampered share is rejected before reconstruction begins — the original data is never assembled from corrupted input.
This is the most important security invariant in the system.
Use Shamir's Secret Sharing when: you need a well-understood public-domain algorithm and performance is not a constraint (e.g., one-time key ceremonies, offline operations).
Use XorIDA when: you need real-time threshold sharing in production systems, AI agent messaging, embedded hardware, or any scenario where sub-millisecond performance matters.