VRIL-KEM

Vortex Resonance Implosion Lattice — Key Encapsulation Mechanism

A Schauberger centripetal-physics-inspired lattice-based KEM achieving Level 5+ post-quantum security.

Specification · Quick Start · Parameter Sets · Security Analysis · Release Artifacts · Integration

What is VRIL-KEM?

VRIL-KEM is a post-quantum Key Encapsulation Mechanism (KEM) built on Module Learning With Errors (M-LWE). It provides a drop-in replacement for classical key exchange in any TLS, SSH, or application-layer protocol — protecting encrypted communications against both classical and quantum adversaries.

VRIL-KEM introduces three novel cryptographic constructions absent from all existing post-quantum KEMs:

Construction	Purpose
HI-Gaussian Sampler	7-layer Fibonacci-weighted noise that resists Kannan-embedding and BKZ lattice reduction attacks
CVKDF (Centripetal Vortex KDF)	Schauberger-inspired one-way spiral compression of the secret key; 2⁻¹²⁸ estimated inversion probability
Outer Harmonic Commitment (OHC)	Post-decapsulation integrity token preventing ciphertext component-substitution attacks under adaptive chosen-ciphertext attack

Parameter Sets

Three stable parameter sets ship in v1.0, covering NIST Levels 3 through 5+:

Designator	N	k	Security	Public Key	Secret Key	Ciphertext	Suite ID
VRIL-KEM-1024-3	1024	4	~192-bit PQ (Level 3)	7,200 B	14,432 B	6,304 B	`0x0100`
VRIL-KEM-2048-5	2048	5	~256-bit PQ (Level 5)	17,952 B	35,936 B	15,392 B	`0x0101`
VRIL-KEM-4096-7	4096	7	~384-bit PQ (Level 5+)	50,208 B	100,448 B	42,016 B	`0x0102`

All three variants share the same ring algebra (R_q = Z_q[X]/(X^N + 1), q = 12289), arithmetic primitives, and API surface — selecting a parameter set is purely a compile-time flag.

Hybrid Suites (PQ + Classical)

For deployment environments requiring defense-in-depth against both quantum and classical adversaries:

Suite ID	Name	Composition	Security
`0x0030`	VRIL-HYBRID-1	VRIL-KEM-1024-3 + X25519	Level 3 ≥ AES-192
`0x0031`	VRIL-HYBRID-2	VRIL-KEM-2048-5 + X25519	Level 5 ≥ AES-256
`0x0032`	VRIL-HYBRID-3	VRIL-KEM-4096-7 + X25519	Level 5+

Quick Start

Prerequisites

C99-compliant compiler (GCC 11+, Clang 13+, MSVC 2022+)
GNU Make 4.0+
Linux, macOS, or Windows (WSL2)

Building from source

git clone https://github.com/VRIL-LABS/vril-kem.git
cd vril-kem

# Reference implementation (recommended starting point)
cd ref
make                          # builds libvril_ref_4096.a + test binary
./test/test_vril4096          # runs full test suite

# Select a parameter set (default is 4096-7)
make VRIL_MODE=1024           # VRIL-KEM-1024-3
make VRIL_MODE=2048           # VRIL-KEM-2048-5
make VRIL_MODE=4096           # VRIL-KEM-4096-7  (default)

Building optimized variants

# AVX2-accelerated (Linux x64 only, ~6-7× faster)
cd avx2 && make

# Constant-time masked (side-channel hardened)
cd ct && make

# Memory-optimized (< 32 KB stack — IoT/embedded)
cd mem && make

Integration

C API

#include "ref/api.h"

// ── KeyGen (recipient) ────────────────────────────────────────────────────────
uint8_t pk[VRIL_PUBLICKEYBYTES];   // publish this
uint8_t sk[VRIL_SECRETKEYBYTES];   // keep secret
crypto_kem_keypair(pk, sk);

// ── Encapsulate (sender) ──────────────────────────────────────────────────────
uint8_t ct[VRIL_CIPHERTEXTBYTES];
uint8_t ss_enc[VRIL_SSBYTES];      // 32-byte shared secret
crypto_kem_enc(ct, ss_enc, pk);    // send ct to recipient

// ── Decapsulate (recipient) ───────────────────────────────────────────────────
uint8_t ss_dec[VRIL_SSBYTES];
crypto_kem_dec(ss_dec, ct, sk);    // ss_dec == ss_enc iff ct is authentic

The API is NIST PQC competition-compatible. Any library using crypto_kem_keypair / crypto_kem_enc / crypto_kem_dec can be adapted to use VRIL-KEM with no protocol changes.

Go (Hybrid/Adaptive)

import "github.com/VRIL-LABS/vril-kem/vril-mesh/pkg/hybrid"

// Hybrid PQ+Classical key exchange (VRIL-KEM-4096-7 + X25519)
ctx, _ := hybrid.NewContext(hybrid.ProfileHybrid3)
pk, sk, _ := ctx.KeyGen()
ct, ssEnc, _ := ctx.Encapsulate(pk)
ssDec, _ := ctx.Decapsulate(sk, ct)
// ssEnc == ssDec — 32-byte shared secret

Release Artifacts

Every release ships pre-built static libraries for Linux x64, Linux ARM64, and macOS:

v1.0-rc1 — Available Now

Naming convention: vril-kem-<variant>-<backend>-<os>-<version>.tar.gz

Artifact	Variant	Backend	Platforms
`vril-kem-1024-3-ref-*`	VRIL-KEM-1024-3	Reference C99	Linux x64, Linux ARM64, macOS
`vril-kem-1024-3-avx2-*`	VRIL-KEM-1024-3	AVX2 SIMD	Linux x64
`vril-kem-1024-3-ct-*`	VRIL-KEM-1024-3	Constant-time	Linux x64, Linux ARM64, macOS
`vril-kem-1024-3-mem-*`	VRIL-KEM-1024-3	Memory-optimized	Linux x64, Linux ARM64, macOS
`vril-kem-2048-5-ref-*`	VRIL-KEM-2048-5	Reference C99	Linux x64, Linux ARM64, macOS
`vril-kem-2048-5-avx2-*`	VRIL-KEM-2048-5	AVX2 SIMD	Linux x64
`vril-kem-2048-5-ct-*`	VRIL-KEM-2048-5	Constant-time	Linux x64, Linux ARM64, macOS
`vril-kem-2048-5-mem-*`	VRIL-KEM-2048-5	Memory-optimized	Linux x64, Linux ARM64, macOS
`vril-kem-4096-7-ref-*`	VRIL-KEM-4096-7	Reference C99	Linux x64, Linux ARM64, macOS
`vril-kem-4096-7-avx2-*`	VRIL-KEM-4096-7	AVX2 SIMD	Linux x64
`vril-kem-4096-7-ct-*`	VRIL-KEM-4096-7	Constant-time	Linux x64, Linux ARM64, macOS
`vril-kem-4096-7-mem-*`	VRIL-KEM-4096-7	Memory-optimized	Linux x64, Linux ARM64, macOS
`vril-hybrid-{1,2,3}-*`	Hybrid suites 1-3	Go source	All (source)
`vril-adaptive-1-*`	Adaptive selector	Go source	All (source)

Each bundle contains: static library (.a), all public headers, LICENSE, and (where available) NIST KAT response files.

Download → github.com/VRIL-LABS/vril-kem/releases
Checksums → See MANIFEST.md attached to each release.

Security Analysis

Security Assumptions

IND-CCA2 security reduces to the hardness of Module-LWE with:

Ring R_q = Z_q[X]/(X^N + 1), q = 12,289 (NTT-friendly prime)
Module rank k ∈ {4, 5, 7} for the three stable variants
Error distribution: HI-Gaussian (Fibonacci-weighted, 7 layers, η₁=3)

The Fujisaki-Okamoto transform provides IND-CCA2 security in the random oracle model. The Outer Harmonic Commitment provides an additional binding layer preventing ciphertext-component substitution.

Estimated Security Levels

Attack Model	VRIL-KEM-1024-3	VRIL-KEM-2048-5	VRIL-KEM-4096-7
Classical (BKZ)	~215-bit	~260-bit	~350-bit
Quantum (QBKZ)	~195-bit	~260-bit	~350-bit
Grover (shared secret)	128-bit	128-bit	128-bit
NIST Level	3	5	5+

What is "Level 5+"?

NIST Level 5 targets ~256-bit quantum security, equivalent to AES-256. VRIL-KEM-4096-7 substantially exceeds this with an estimated ~350-bit quantum Core-SVP cost — the highest security margin of any publicly available lattice-based KEM.

Honest Disclosures

No formal EasyCrypt security proofs yet (planned for v2.0)
Constant-time behavior is compiler-dependent on some targets; use the ct/ backend for side-channel-hardened deployments
Large key and ciphertext sizes — evaluate whether your protocol can accommodate them
Not yet peer-reviewed; not recommended for production use without independent review
Research prototype — audit the code before deploying in security-critical systems

Implementations

Backend	Description	When to Use
`ref/`	Reference C99, portable	Default, all platforms
`avx2/`	AVX2 SIMD (~6-7× faster)	Linux x64 with AVX2 CPU
`ct/`	Constant-time masked (ISW 2-share)	Side-channel sensitive environments
`mem/`	Streaming, < 32 KB stack	IoT, embedded MCUs

Repository Structure

vril-kem/
├── ref/                    Reference implementation (C99)
│   ├── api.h               Public KEM API (NIST PQC compatible)
│   ├── kem.c/h             IND-CCA2 KEM: KeyGen / Encaps / Decaps + OHC
│   ├── indcpa.c/h          IND-CPA encryption layer + CVKDF
│   ├── hi_sample.c/h       HI-Gaussian noise sampler ★
│   ├── cvkdf.c/h           Centripetal Vortex KDF ★
│   ├── poly.c/h            Polynomial arithmetic in R_q
│   ├── ntt.c/h             N-point NTT over Z_12289
│   └── Makefile
├── avx2/                   AVX2 SIMD-optimized implementation
├── ct/                     Constant-time masked implementation
├── mem/                    Memory-optimized variant
├── vril-mesh/              Go bindings (hybrid/adaptive suites)
├── dist/                   Distribution assets and validation reports
├── docs/                   Specification, whitepaper, parameter family
├── CHANGELOG.md
└── LICENSE                 MIT

★ VRIL-novel constructions absent from all existing post-quantum KEMs.

Comparison with NIST PQC Candidates

Property	VRIL-KEM-4096-7	ML-KEM-1024 (KYBER)	FrodoKEM-1344	Classic McEliece
Security level	Level 5+ (~384-bit Q)	Level 5 (~256-bit Q)	Level 5	Level 5
Quantum hardness assumption	M-LWE	M-LWE	LWE	Code-based
Public key size	50,208 B	1,568 B	21,520 B	>1 MB
Ciphertext size	42,016 B	1,568 B	21,536 B	128 B
Outer Harmonic Commitment	✅	❌	❌	❌
HI-Gaussian noise	✅	❌	❌	N/A
CVKDF secret hardening	✅	❌	❌	❌
`no_std` / embedded	✅ (`mem/`)	✅	❌	✅
NIST standardized	Research	FIPS 203	Draft	FIPS 205

VRIL-KEM trades key/ciphertext size for a significantly higher security margin and novel algorithmic defenses. For bandwidth-constrained protocols, VRIL-KEM-1024-3 offers a competitive profile against ML-KEM-768.

Documentation

Document	Description
VRIL-KEM-Complete-Specification.md	Full technical specification (algorithms, parameters, security proofs)
VRIL-KEM-Parameter-Family.md	Detailed parameter set rationale and arithmetic scaffolding
VRIL-KEM-Whitepaper.pdf	Academic whitepaper
CHANGELOG.md	Version history
docs/future-work/	Research roadmap (EasyCrypt proofs, TLS 1.3, FPGA/ASIC)

Contributing

Issues, security reports, and pull requests are welcome at github.com/VRIL-LABS/vril-kem.

Security disclosures: Please report vulnerabilities privately via GitHub Security Advisories before public disclosure.

License

MIT License — see LICENSE.

VRIL LABS

Vortex Resonance Implosion Lattice — Where energy concentrates inward, secrets remain protected.

github.com/VRIL-LABS/vril-kem

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VRIL-KEM

What is VRIL-KEM?

Parameter Sets

Hybrid Suites (PQ + Classical)

Quick Start

Prerequisites

Building from source

Building optimized variants

Integration

C API

Go (Hybrid/Adaptive)

Release Artifacts

v1.0-rc1 — Available Now

Security Analysis

Security Assumptions

Estimated Security Levels

What is "Level 5+"?

Honest Disclosures

Implementations

Repository Structure

Comparison with NIST PQC Candidates

Documentation

Contributing

License

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