ENTROPIS

Initializing Quantum Lattice

τ(n) = Σ τ(n)q^nζ(s) = Π 1/(1-p^-s)η(τ) = e^(πiτ/12)G(χ,p) = Σ χ(a)e^(2πia/p)E₄(q) = 1 + 240Σσ₃(n)q^nφ(n) = n·Π(1-1/p)
FIPS 203 + FIPS 204 Compliant

Post-QuantumCryptographyReimagined

ML-KEM-768 lattice encryption hardened through a 40-stage mathematical key derivation pipeline spanning Ramanujan, Gauss, Riemann, and Dedekind. No single compromise point exists.

ML-KEM-768|ML-DSA-65|AES-256-GCM|SHA-3|RE-KDF-v1
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Security Architecture

Three layers. Zero compromise.

01

Lattice-Based Security

ML-KEM-768 operates in dimension 768 over polynomial rings. No known quantum algorithm reduces the Module-LWE problem in polynomial time.

(A·s + e) mod qNIST Level 3 — 192-bit classical, 128-bit post-quantum
02

40-Stage Key Derivation

Every shared secret traverses 40 independent mathematical transformations. Each stage is a one-way SHA-3 compression seeded by a distinct number-theoretic function.

K_{i+1} = SHA3-256(K_i ‖ f_i(K_i))Ramanujan · Gauss · Riemann · Dedekind · Eisenstein
03

Ring Signatures

ML-DSA-65 signs over the polynomial ring Z_q[X]/(X^256+1). Shor's algorithm finds no period to exploit — there is no abelian group structure.

Z_q[X]/(X^256+1)FIPS 204 — Noether polynomial ring signatures
Cryptographic Primitives

Built on proven mathematics

{ }FIPS 203

ML-KEM-768

Module-Lattice Key Encapsulation at NIST Security Level 3. 1184-byte public keys, 1088-byte ciphertexts.

LatticeKEM192-bit
[ ]FIPS 204

ML-DSA-65

Digital signatures over polynomial rings. 3293-byte signatures that resist both Shor and Grover algorithms.

RingDSANoether
< >Post-Grover 128-bit

AES-256-GCM

Authenticated encryption with 256-bit keys. Grover reduces effective security to 128-bit — still computationally infeasible.

AEADShannon128-bit PQ
// 40-Stage Pipeline

RE-KDF v1

40 independent mathematical transformations through SHA-3. Ramanujan tau, Gauss sums, Riemann zeta, and 37 more.

KDFSHA-3One-Way
::Oracle Resistance

Constant-Time

All decrypt and verify operations padded to fixed duration. Timing side-channels are eliminated by design.

Side-Channel50ms PadGCM-Safe
##Stateless Transforms

Zero Retention

Private keys never persist server-side. All intermediates are zeroed after each operation. Pure cryptographic transforms.

EphemeralZero-CopyStateless
Standing on the Shoulders of Giants

Three centuries of number theory

Every stage of the RE-KDF pipeline is rooted in a proven mathematical result. These aren't abstractions — they're exact implementations of published theorems.

Ramanujan

1916

Tau function, partition congruences, Rogers-Ramanujan identities

STAGES 1-6

Euler

1763

Totient, Mobius inversion, continued fractions, Carmichael

STAGES 7-10

Gauss

1801

Legendre/Jacobi/Kronecker symbols, quadratic Gauss sums

STAGES 11-15

Bernoulli

1713

Bernoulli numbers, polynomial evaluations

STAGES 16-17

Riemann

1859

Zeta function, Euler product formula

STAGES 18-19

Dirichlet

1837

L-functions, multiplicative series mixing

STAGES 20-21

Jacobi

1829

Theta functions, triple product identity

STAGES 22-24

Eisenstein

1847

Modular forms E₄, E₆, divisor sums

STAGES 25-26

Dedekind

1877

Eta function, Dedekind sums, reciprocity

STAGES 27-28

Kloosterman

1926

Exponential sums with Weil bound

STAGES 29-30

Hardy

1920

Circle method, singular series

STAGES 31

Chebyshev

1854

Orthogonal polynomials T_n, U_n

STAGES 32-33
Ready for the Post-Quantum Era

Your data deserves
quantum-grade protection

Entropis combines NIST-standardized post-quantum algorithms with centuries of number theory. No shortcuts. No compromises.

FIPS 203|FIPS 204|NIST Level 3|40-Stage KDF