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 · Formal Verification · Release Artifacts · Integration · Download

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.

At the time of writing, VRIL-KEM-4096-7 provides the highest security margin of any publicly available lattice-based KEM with an estimated ~350-bit quantum Core-SVP cost. The EasyCrypt proof represents a first-of-its-kind formalization for a novel post-quantum KEM outside the NIST finalist ecosystem.

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

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Parameter Sets

Three stable parameter sets ship in v1.2, 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+

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Release Artifacts

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

v1.2-rc2 — 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.

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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.

Formal Verification (EasyCrypt)

VRIL-KEM includes a complete EasyCrypt formal-verification architecture in proof/, verified against the real upstream EasyCrypt stdlib API and the sandbox-quantum FO transform library. This is a first-of-its-kind formalization for a novel post-quantum KEM outside the NIST finalist ecosystem.

What is formalized:

Layer	Content
Ring algebra	R_q = Z_q[X]/(X^N+1); NTT correctness; module-vector ops
M-LWE hardness	Decisional game with quantitative advantage bound
Noise model	Sub-Gaussianity of HI-Gaussian; smudging bound; concrete failure probability δ (Chernoff/union-bound)
CVKDF	Lazy-ROM model with quantitative one-wayness bound
OHC	Outer Harmonic Commitment binding + hiding games
KEM specification	Full KEM module realizing upstream KeyEncapsulationMechanisms.Scheme
IND-CCA2 theorem	FO-U transform clone + checked concrete-bound lemma
Binding hierarchy	Checked HON-BIND-K-CT, LEAK-BIND-K-CT, MAL-BIND-CT-PK bound lemmas
Jasmin boundary	Phase 5 source-level spec↔impl equivalence boundary

Concrete security bounds (formally stated):

IND-CPA:   |Pr[IND_CPA(VRIL_PKE, A)] - 1/2|  ≤  2 · mlwe_eps
IND-CCA2:  Adv^{IND-CCA2}                     ≤  2 · mlwe_eps + δ + q_RO / 2^256
LEAK-BIND: Pr[LEAK_BIND(K_Binds_CT)]          ≤  ohc_bind_eps + cvkdf_ow_eps
MAL-BIND:  Pr[MAL_BIND(CT_Binds_PK)]          ≤  mlwe_eps + ohc_bind_eps

The IND-CCA2 and binding bound-sanity statements are checked EasyCrypt lemma bodies — no admit tactics in VRIL proof sources. The remaining full theorem-level work item is the IND-CPA game-hop reduction (vril_pke_indcpa).

Honest Disclosures

• 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
• The IND-CPA game-hop reduction body remains as a global-axiom warning (the bound expression and all downstream theorems are checked)

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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

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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	✅	❌	❌	❌
EasyCrypt formalization	✅ (IND-CCA2 + Binding)	Partial (formosa-mlkem)	❌	❌
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.

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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.

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License

GNU Affero General Public License 3.0 — see LICENSE.

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VRIL LABS

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

github.com/VRIL-LABS/vril-kem