Quantum R&D — Post-Quantum Cryptography Research

What we're doing

Most of the cryptography the internet runs on — RSA, Diffie-Hellman, elliptic curves — rests on number-theoretic problems (factoring, discrete logarithms) that a large quantum computer running Shor's algorithm would break outright. Our R&D focuses on the schemes that do not depend on those problems, so they survive that transition.

The work is primarily theoretical and mathematical: we implement each candidate as an exact, reference-faithful model — real lattice arithmetic, real hash chains, real information-theoretic constructions — and measure their genuine properties (entropy, avalanche, security-bit levels, statistical randomness) rather than simulating or fabricating numbers. That gives us an honest, reproducible baseline before anything is ever proposed for production.

The two quantum threats we design against

Shor's algorithm — efficiently factors integers and solves discrete logs, breaking RSA/ECC entirely. Our answer: schemes based on problems Shor doesn't touch (lattices, hash preimages, information theory).
Grover's algorithm — gives a quadratic speedup on brute-force search, effectively halving symmetric-key and hash-preimage security. Our answer: quantify the loss precisely and restore margin by doubling key/digest sizes.

The mathematical models

Post-quantum security comes from choosing a hard problem that a quantum computer gains little or no advantage on. We work across four families.

Hash-based cryptography

Security rests only on the preimage resistance of a hash function — nothing number-theoretic for Shor to attack. Only Grover applies, and that's neutralised by using a large enough digest. This family gives us signatures and integrity structures that are quantum-safe by construction.

Models: Lamport & Winternitz one-time signatures, Merkle trees, S/KEY hash chains.

Lattice-based cryptography

Built on the Learning-With-Errors (LWE) problem: recovering a secret from noisy linear equations over a modulus is believed hard even for quantum computers. This is the family behind the NIST-selected standards (Kyber/Dilithium) and the most promising route to full public-key replacement.

Model: a real LWE instance with discrete-Gaussian error sampling.

Information-theoretic security

The one-time pad is unconditionally secure — proven by Shannon to leak zero information regardless of an attacker's computing power, quantum or otherwise. It's the theoretical gold standard we benchmark everything else against, key-management constraints and all.

Model: XOR one-time pad with a measured proof of perfect secrecy.

Quantum-adjusted symmetric analysis

Symmetric primitives (hashes, MACs, KDFs, RNGs) survive the quantum era if sized correctly. We compute the exact post-quantum margin from complexity theory: Grover halves preimage security, Brassard-Høyer-Tapp reduces collision security to a third — no guesswork.

Models: Grover/BHT bit-level analysis, memory-hard KDFs, HMAC, NIST SP 800-22 randomness testing.

The tools that implement them

Twelve real tools — every calculation is genuine (real hash chains, real modular lattice arithmetic, real CSPRNG output), never simulated. Here's what each one is and why it's usable.

Hash-based signatures & structures

Lamport Signature Tool

Generates a one-time Lamport keypair, signs a message's hash digest and verifies it. Post-quantum-secure because its security rests only on hash preimage resistance — the canonical proof that quantum-safe signatures are possible.

Winternitz OTS Tool

A Winternitz one-time signature using hash chains plus a checksum against forgery-by-shortening. More space-efficient than plain Lamport, still resting purely on hash preimage resistance — the building block of modern schemes like SPHINCS+.

Merkle Tree Generator

Builds a Merkle tree, generates an audit proof for every leaf and verifies it against the root. The structure that lets one-time signatures scale to many messages, and the same construction behind certificate transparency and blockchains.

Hash Chain Generator

An S/KEY-style iterative hash chain (hₙ = hash(hₙ₋₁)) demonstrating the one-time-password property: a presented value authenticates without ever revealing the next one. Simple, hash-only, quantum-safe authentication.

Lattice & information-theoretic

Lattice Crypto Simulator

Generates a real Learning-With-Errors instance: a uniform random matrix A, a discrete-Gaussian error vector (genuine Box-Muller sampling) and b = As + e (mod q) via real modular arithmetic. It reports the naive exhaustive-search bound as an honest lower bound — real lattice-reduction (BKZ) is faster, so we never overstate it. This is the hands-on model of the problem that underpins tomorrow's public-key crypto.

Quantum-Safe OTP

A real one-time pad: a message-length key from a CSPRNG, XOR encryption/decryption and a measured demonstration of perfect secrecy via the ciphertext's Shannon entropy. Unconditionally secure against any adversary — the theoretical ceiling we compare every practical scheme to.

Quantum-adjusted symmetric & randomness

Hash Algorithm Quantum-Resistance Analyzer

Measures a hash's real avalanche, entropy and throughput, then reports its quantum-security bits from complexity theory: Grover halves preimage security, Brassard-Høyer-Tapp reduces collision security to a third.

Quantum-Resistant MAC Tool

Computes an HMAC, verifies it in constant time and reports classical key-search, Grover-adjusted quantum key-search and birthday-bound forgery resistance — the exact margin a MAC keeps after quantum.

Post-Quantum KDF Tool

Derives a key with standardized hashlib.scrypt / pbkdf2_hmac — genuine memory-hard / iteration-hard KDFs, parameterized to OWASP's current recommendations, with a fresh random salt each run.

Password Hasher

Hashes with real scrypt (OWASP memory-hard parameters, fresh salt), verifies the round-trip in constant time and reports charset-entropy strength analysis and substring weakness detection.

Password Generator

Bias-free random passwords via secrets.choice, with real Grover-adjusted quantum brute-force bits, a NIST SP 800-22 self-check of the CSPRNG and an optional scrypt storage hash. Never stored — shown once.

RNG Statistical Analyzer

Runs four real NIST SP 800-22 randomness tests (monobit, block frequency, runs, longest-run) on your data or on fresh CSPRNG bytes, using the exact NIST formulas — good randomness is the foundation every key rests on.

Why these can be used

Each family sidesteps the specific weakness a quantum computer exploits:

Hash-based schemes rely on preimage resistance, which only Grover attacks — quadratically — so a large digest fully restores the security margin. They're provably quantum-safe today and need no new hardness assumption.
Lattice problems (LWE, shortest-vector) have no known efficient quantum algorithm, which is exactly why NIST standardised lattice schemes as the general-purpose replacement for RSA/ECC.
Information-theoretic security (the OTP) is unconditional: no amount of computing power, classical or quantum, can break it.
Sized symmetric primitives stay strong once we double keys/digests to absorb Grover's quadratic speedup — which is why we measure the exact post-quantum bit level rather than assume it.

Next steps

Our models are validated on classical hardware today. The roadmap is to take them further:

Harden the theoretical models — move from reference LWE instances toward the parameter sets of the ratified NIST standards (ML-KEM / ML-DSA) and add stateful hash-based signatures (XMSS/SPHINCS+).
Prepare the models to run natively on the first available quantum operating systems and quantum computers — expressing them for emerging quantum runtimes so they can be validated on real quantum hardware, not just simulated.
Benchmark real quantum attacks (Grover/Shor circuits) against our own constructions on that hardware to confirm the security margins we calculate here hold in practice.
Fold the proven models back into SecurAppt's tooling, so customers get a migration path to post-quantum crypto as the hardware matures.

This is forward-looking R&D: the tools here are working, honest models of the mathematics — the quantum-hardware step is the direction we're building toward.