Secure computation,
from the research end.

Qubits, briefly

A classical bit is 0 or 1. A qubit can be in a superposition of both, described by two amplitudes; measuring it gives 0 or 1 with probabilities set by those amplitudes, and the superposition is gone. Several qubits can be entangled, so their measurement outcomes are correlated in ways no classical system reproduces.

A quantum algorithm arranges for the amplitudes of wrong answers to cancel and those of right answers to reinforce. For most problems this gives no meaningful advantage. For a few, with a specific mathematical structure, it changes everything, and some of those problems are the ones cryptography relies on.

Why it matters for cryptography

Shor's algorithm, on a large, fault-tolerant quantum computer, factors integers and computes discrete logarithms efficiently. That would break:

• RSA, used for signatures and key exchange.
• Diffie–Hellman and elliptic-curve cryptography, including ECDSA and EdDSA signatures, which secure most wallets and TLS connections.
• Pairing-based assumptions, which underpin proof systems such as Groth16 and KZG-based PLONK.

Grover's algorithm speeds up brute-force search quadratically. It weakens symmetric keys and hash functions rather than breaking them, and the answer is larger parameters, such as 256-bit keys.

The machines that could run Shor's algorithm at this scale do not exist today. The reason to care now is that data encrypted today can be recorded today and decrypted later. Secrets that must stay secret for years are already exposed to that risk.

Post-quantum assumptions

Post-quantum cryptography is classical cryptography, running on ordinary computers, built on problems with no known efficient quantum attack.

• Lattice problems, such as learning with errors, underpin ML-KEM for key establishment and ML-DSA for signatures, standardised by NIST in 2024 as FIPS 203 and FIPS 204.
• Hash functions underpin SLH-DSA (FIPS 205), a signature scheme whose security rests only on the hash.

For proof systems the picture is mixed. Hash-based STARKs are generally considered plausibly post-quantum. Pairing-based systems are not, though the distinction matters: a quantum adversary threatens their soundness, the ability to forge new proofs, while what a perfectly zero-knowledge proof such as Groth16 hid stays hidden.

Quantum protocols, not only quantum attacks

Quantum computers are not only a threat. Parties who have them can run protocols that use quantum effects directly, and the theory of what those protocols can achieve has its own landmarks.

In 1997 Hoi-Kwong Lo showed that unconditionally secure two-party quantum computation is impossible when one party is malicious. Under computational assumptions, such as a one-way permutation secure against quantum adversaries, secure quantum bit commitment becomes possible. Complete fairness, where both parties get the output or neither does, remained open, and for quantum protocols an impossibility result by Ben-Or and co-authors (FOCS 2006) stood against it.

The paper: ePrint 2026/883

Secure Two-Party Quantum Computation with Complete Fairness without Trusted Third Party, by Arpita Maitra, Goutam Paul, Asim K. Pal, Asmita Samanta and Hridam Basu, shows for the first time that some functions admit secure two-party quantum computation with complete fairness and no trusted third party, in sharp contrast with that impossibility result.

It is open access on the IACR Cryptology ePrint Archive, under CC BY. Secure computation and the quantum question explains the background in plain terms.

How Rump Labs works in quantum

Our quantum work is research: published work on secure two-party quantum computation with complete fairness, fairness protocols, and quantum-safe assumptions, released open access so anyone can read and check it.

For teams shipping cryptography today, it gives us a working view of what quantum adversaries mean in practice: which of your assumptions are exposed, which data is worth protecting first, and what migrating looks like. That question is a good fit for a Technical Brief: a written answer, with the reasoning, in three business days.

Where it shows up

No domain we work in runs on quantum hardware. Quantum shows up in the assumptions under the cryptography, most of all where keys and signatures carry the weight.

Where to start

Further reading