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# Quantum-Safe Cryptography

**Quantum computers**are ...

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**Quantum computing**is a model of computing based on the quantum physics, which works differently than classical computers and can do things that classical computers can’t, such as breaking RSA and ECC efficiently.

**Quantum computers**are not "faster computers" and they are not all-powerful and cannot do any computing job faster. Quantum computers are very efficient for certain problems and quite weak for others.

It is well known in computer science that

**quantum computers will break some cryptographic algorithms**, especially the public-key cryptosystems like**RSA**,**ECC**and**ECDSA**that rely on the**IFP**(integer factorization problem), the**DLP**(discrete logarithms problem) and the**ECDLP**(elliptic-curve discrete logarithm problem). Quantum algorithms will not be the end of cryptography, because:- Only some cryptosystems are
**quantum-unsafe**(like RSA, DHKE, ECC, ECDSA and ECDH). - Some cryptosystems are
**quantum-safe**and will be only slightly affected (like cryptographic hashes, MAC algorithms and symmetric key ciphers).

Let's discuss this in details.

Most cryptographic

**hashes**(like SHA2, SHA3, BLAKE2),**MAC**algorithms (like HMAC and CMAK),**key-derivation functions**(bcrypt, Scrypt, Argon2) are basically**quantum-safe**(only slightly affected by quantum computing).- Use 384-bits or more to be quantum-safe (256-bits should be enough for long time)

**Symmetric ciphers**(like AES-256, Twofish-256) are

**quantum-safe**.

- Use 256-bits or more as key length (don't use 128-bit AES)

Most popular

**public-key cryptosystems**(like RSA, DSA, ECDSA, EdDSA, DHKE, ECDH, ElGamal) are**quantum-broken**!- Most
**digital signature**algorithms (like RSA, ECDSA, EdDSA) are**quantum-broken**! **Quantum-safe signature**algorithms and public-key cryptosystems are already developed (e.g. lattice-based or hash-based signatures), but are not massively used, because of longer keys and longer signatures than ECC.

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Quantum-Resistant Crypto Algorithms

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A

**k**-bit number can be factored in time of order**O(k^3)**using a quantum computer of**5k+1 qubits**(using Shor's algorithm).256-bit number (e.g. Bitcoin public key) can be factorized using 1281 qubits in 72*256^3 quantum operations.

- ~ 1.2 billion operations == ~ less than 1 second using good machine

ECDSA, DSA, RSA, ElGamal, DHKE, ECDH cryptosystems are all quantum-broken

Conclusion: publishing the signed transactions (like Ethereum does) is not quantum safe -> avoid revealing the ECC public key

Cryptographic

**hashes**(like SHA2, SHA3, BLAKE2) are considered**quantum-safe**:- On traditional computer, finding a collision for 256-bit hash takes √2^256 steps (using the
**birthday attack**) -> SHA256 has 2^128 crypto-strength - Quantum computers might find hash collisions in ∛2^256 operations (see the BHT algorithm), but this is disputed (see [Bernstein 2009] - http://cr.yp.to/hash/collisioncost-20090823.pdf
- On theory it might take 2^85 quantum operations to find SHA256 / SHA3-256 collision, but in practice it may cost significantly more.

Conclusion: SHA256 / SHA3-256 are most probably quantum-safe

- SHA384, SHA512 and SHA3-384, SHA3-512 are quantum-safe

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Most symmetric ciphers (like AES and ChaCha20) are quantum-safe:

- [Grover's algorithm]([[[[[[https://en.wikipedia.org/wiki/Grover's_algorithm](https://en.wikipedia.org/wiki/Grover's_algorithm)](https://en.wikipedia.org/wiki/Grover's_algorithm](https://en.wikipedia.org/wiki/Grover's_algorithm))](https://en.wikipedia.org/wiki/Grover's_algorithm](https://en.wikipedia.org/wiki/Grover's_algorithm)](https://en.wikipedia.org/wiki/Grover's_algorithm](https://en.wikipedia.org/wiki/Grover's_algorithm)))](https://en.wikipedia.org/wiki/Grover's_algorithm](https://en.wikipedia.org/wiki/Grover's_algorithm)](https://en.wikipedia.org/wiki/Grover's_algorithm](https://en.wikipedia.org/wiki/Grover's_algorithm))](https://en.wikipedia.org/wiki/Grover's_algorithm](https://en.wikipedia.org/wiki/Grover's_algorithm)](https://en.wikipedia.org/wiki/Grover's_algorithm](https://en.wikipedia.org/wiki/Grover's_algorithm))))](https://en.wikipedia.org/wiki/Grover's_algorithm](https://en.wikipedia.org/wiki/Grover's_algorithm)](https://en.wikipedia.org/wiki/Grover's_algorithm](https://en.wikipedia.org/wiki/Grover's_algorithm))](https://en.wikipedia.org/wiki/Grover's_algorithm](https://en.wikipedia.org/wiki/Grover's_algorithm)](https://en.wikipedia.org/wiki/Grover's_algorithm](https://en.wikipedia.org/wiki/Grover's_algorithm)))](https://en.wikipedia.org/wiki/Grover's_algorithm](https://en.wikipedia.org/wiki/Grover's_algorithm)](https://en.wikipedia.org/wiki/Grover's_algorithm](https://en.wikipedia.org/wiki/Grover's_algorithm))](https://en.wikipedia.org/wiki/Grover's_algorithm](https://en.wikipedia.org/wiki/Grover's_algorithm)](https://en.wikipedia.org/wiki/Grover's_algorithm](https://en.wikipedia.org/wiki/Grover's_algorithm)))))](https://en.wikipedia.org/wiki/Grover's_algorithm]%28https://en.wikipedia.org/wiki/Grover's_algorithm%29]%28https://en.wikipedia.org/wiki/Grover's_algorithm]%28https://en.wikipedia.org/wiki/Grover's_algorithm%29%29]%28https://en.wikipedia.org/wiki/Grover's_algorithm]%28https://en.wikipedia.org/wiki/Grover's_algorithm%29]%28https://en.wikipedia.org/wiki/Grover's_algorithm]%28https://en.wikipedia.org/wiki/Grover's_algorithm%29%29%29]%28https://en.wikipedia.org/wiki/Grover's_algorithm]%28https://en.wikipedia.org/wiki/Grover's_algorithm%29]%28https://en.wikipedia.org/wiki/Grover's_algorithm]%28https://en.wikipedia.org/wiki/Grover's_algorithm%29%29]%28https://en.wikipedia.org/wiki/Grover's_algorithm]%28https://en.wikipedia.org/wiki/Grover's_algorithm%29]%28https://en.wikipedia.org/wiki/Grover's_algorithm]%28https://en.wikipedia.org/wiki/Grover's_algorithm%29%29%29%29]%28https://en.wikipedia.org/wiki/Grover's_algorithm]%28https://en.wikipedia.org/wiki/Grover's_algorithm%29]%28https://en.wikipedia.org/wiki/Grover's_algorithm]%28https://en.wikipedia.org/wiki/Grover's_algorithm%29%29]%28https://en.wikipedia.org/wiki/Grover's_algorithm]%28https://en.wikipedia.org/wiki/Grover's_algorithm%29]%28https://en.wikipedia.org/wiki/Grover's_algorithm]%28https://en.wikipedia.org/wiki/Grover's_algorithm%29%29%29]%28https://en.wikipedia.org/wiki/Grover's_algorithm]%28https://en.wikipedia.org/wiki/Grover's_algorithm%29]%28https://en.wikipedia.org/wiki/Grover's_algorithm]%28https://en.wikipedia.org/wiki/Grover's_algorithm%29%29]%28https://en.wikipedia.org/wiki/Grover's_algorithm]%28https://en.wikipedia.org/wiki/Grover's_algorithm%29]%28https://en.wikipedia.org/wiki/Grover's_algorithm]%28https://en.wikipedia.org/wiki/Grover's_algorithm%29%29%29%29%29)) finds AES secret key using √𝑁 quantum operations
- Quantum era will
**double the key size**of the symmetric ciphers, see [http://cr.yp.to/codes/grovercode-20100303.pdf](http://cr.yp.to/codes/grovercode-20100303.pdf%29%29)

AES-256 in the post-quantum era is like AES-128 before

- 128-bits or less symmetric ciphers are quantum-attackable

Conclusion: 256-bit symmetric ciphers are generally quantum safe

- AES-256, ChaCha20-256, Twofish-256, Camellia-256 are considered quantum-safe

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Post-quantum signature scheme XMSS:

- Post-quantum key agreement schemes McEliece and NewHope

Post-quantum signatures and key agreements (XMSS, McEliece, NewHope):
https://github.com/randombit/botan

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**GLYPH**signatures (lattice-based Ring-LWE Lattice, Ring-LWE, Ring Learning with Errors)

**NewHope**

**XMSS**

**NTRU**: NTRUEncrypt and NTRUSign

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The quantum-safe cryptography is still emerging, not mature, and still not widely supported by the most crypto-libraries and tools like Web browsers, OpenSSL, OpenSSH, etc. This is a list of well developed quantum crypto algorithm libraries:

Last modified 2yr ago