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Kyber

Kyber

2024-02-22 02:09:16

CRYSTALS-Kyber

Introduction


Kyber is an IND-CCA2-secure key encapsulation mechanism (KEM), whose safety relies
on the hardness of fixing the learning-with-errors (LWE) downside over module lattices.
Kyber is among the finalists within the
NIST post-quantum cryptography project.
The submission lists three totally different parameter units aiming at totally different safety ranges.
Particularly, Kyber-512 goals at safety roughly equal to AES-128,
Kyber-768 goals at safety roughly equal to AES-192, and
Kyber-1024 goals at safety roughly equal to AES-256.


For customers who’re serious about utilizing Kyber, we suggest the next:


  • Use Kyber in a so-called hybrid mode together with established
    “pre-quantum” safety; for instance together with elliptic-curve Diffie-Hellman.

  • We suggest utilizing the Kyber-768 parameter set,
    which—in accordance with a really conservative evaluation—achieves
    greater than 128 bits of safety towards all recognized classical and quantum assaults.

Scientific Background


The design of Kyber has its roots within the seminal
LWE-based encryption scheme of Regev.
Since Regev’s unique work, the sensible effectivity of LWE encryption schemes has been improved
by observing that the key in LWE can come from the
same distribution
because the noise and likewise noticing that “LWE-like” schemes
might be constructed by utilizing a sq. (slightly than an oblong) matrix as the general public key.
One other enchancment was making use of an concept initially used within the
NTRU cryptosystem
to outline the Ring-LWE and Module-LWE
issues that used polynomial rings slightly than integers.
The CCA-secure KEM Kyber is constructed on prime of a CPA-secure cryptosystem that’s primarily based on the hardness of Module-LWE.

Customers of Kyber


Kyber is already being built-in into libraries and programs by business. For instance,

Efficiency Overview


The tables beneath offers a sign of the efficiency of Kyber.
All benchmarks had been obtained on one core of an Intel Core-i7 4770K (Haswell) CPU.
We report benchmarks of two totally different implementations: a C reference
implementation and an optimized implementation utilizing AVX2 vector directions.
For benchmarks on an ARM Cortex-M4 microcontroller, see the
benchmarks reported by the pqm4 project.



















Kyber-512
Sizes (in bytes) Haswell cycles (ref) Haswell cycles (avx2)
sk: 1632 gen: 122684 gen: 33856
pk: 800 enc: 154524 enc: 45200
ct: 768 dec: 187960 dec: 34572
Kyber-768
Sizes (in bytes) Haswell cycles (ref) Haswell cycles (avx2)
sk: 2400 gen: 199408 gen: 52732
pk: 1184 enc: 235260 enc: 67624
ct: 1088 dec: 274900 dec: 53156
Kyber-1024
Sizes (in bytes) Haswell cycles (ref) Haswell cycles (avx2)
sk: 3168 gen: 307148 gen: 73544
pk: 1568 enc: 346648 enc: 97324
ct: 1568 dec: 396584 dec: 79128


As an replace for spherical 2 of the NIST undertaking we additionally proposed a variant of Kyber that’s meant to showcase
the efficiency of Kyber when {hardware} help for the symmetric primitives is accessible.
This variant, referred to as Kyber-90s, makes use of AES-256 in counter mode and SHA2 as an alternative of SHAKE.



See Also

















Kyber-512-90s
Haswell cycles (ref) Haswell cycles (avx2)
gen: 213156 gen: 21880
enc: 213156 enc: 28592
dec: 277612 dec: 20980
Kyber-768-90s
Haswell cycles (ref) Haswell cycles (avx2)
gen: 389760 gen: 30460
enc: 432764 enc: 40140
dec: 473984 dec: 30108
Kyber-1024-90s
Haswell cycles (ref) Haswell cycles (avx2)
gen: 636380 gen: 43212
enc: 672644 enc: 56556
dec: 724144 dec: 44328

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