Category
14 articles in this category.
BIKE is a post-quantum key encapsulation scheme built on codes with a sparse parity-check matrix. Learn how its keys hide a sparse code in a dense one, how the Black-Gray-Flip decoder removes the error, why one flipped bit is rejected, and why NIST chose HQC instead.
30 min read
GeMSS is a post-quantum signature scheme whose signatures have only a few hundred bits and whose public key is a system of quadratic equations. Learn how a hidden polynomial over GF(2^n) becomes a signature, how the signer finds roots, and why NIST dropped the scheme after a key-recovery attack.
41 min read
Picnic is a post-quantum signature scheme built only from a block cipher and a hash function. Learn how a zero-knowledge proof about a secret LowMC key becomes a signature, how three simulated parties hide the key, why 219 repetitions are needed, and why NIST did not select it.
36 min read
XMSS and LMS sign with nothing but a hash function, so quantum computers do not break them. Learn how Winternitz chains and Merkle trees work, why a signer must never reuse a one-time key, and how a reused key lets an attacker forge a message.
34 min read
NIST's primary post-quantum signature standard works by signing, checking your own signature against a size limit, and throwing it away and starting over if it's too big. Learn how 'Fiat-Shamir with Aborts' turns a leaky lattice proof into a secure signature.
14 min read
Falcon produces the smallest signatures of any NIST post-quantum standard. It does that by solving a problem that broke the leading lattice signature schemes of the late 1990s/early 2000s. Learn the hash-and-sign paradigm, and why the naive version of it is fatally insecure.
13 min read
FrodoKEM deliberately throws away the algebraic structure that makes lattice cryptography fast. It trades performance for a security proof that rests on plain, 'vanilla' Learning With Errors. Learn how it works and why some cryptographers prefer that trade.
10 min read
In March 2025, NIST picked a second code-based algorithm to back up Kyber. This one hides its noise completely differently from McEliece. Learn how HQC masks a public, unscrambled code with pure algebraic randomness instead.
10 min read
The key encapsulation mechanism NIST chose to replace RSA and ECDH for general-purpose use. Learn how Kyber hides a noisy linear system inside a polynomial ring to get both lattice-hard security and real-world speed.
9 min read
Before Kyber, before LWE was even named, NTRU showed that ordinary polynomial multiplication in the right ring could resist quantum attacks. Learn how NTRU hides a fast decryption trick behind a public convolution product.
11 min read
Rainbow signed messages using polynomial equations so tangled that solving them looks impossible. Then, in 2022, someone found a shortcut and broke it in a weekend on a laptop. Learn how it worked, and how it fell.
12 min read
SABER reached the final round of NIST's post-quantum competition with a trick Kyber doesn't use: instead of adding random noise, it rounds numbers down and lets the rounding error itself do the job. Learn how Learning With Rounding works.
10 min read
Every other post-quantum signature scheme bets on a new hard math problem holding up. SPHINCS+ makes almost no new bet at all: its security rests on nothing but hash functions. Learn how a tree of one-time signatures becomes a full signature scheme.
11 min read
McEliece has survived over 45 years of cryptanalysis without ever being broken. It's one of NIST's chosen post-quantum standards. Learn how hiding an error-correcting code behind scrambling matrices creates a public-key system quantum computers can't crack.
10 min read
