# Questions tagged [lattice-crypto]

Lattice-cryptography is the study and use of lattice problems applied to cryptography.

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### Key-Privacy in Postquantum Public-key Encryption

is there any post-quantum public-key encryption that achieves "key-privacy" (IK-CPA, IK-CCA) as described in this paper? I saw one code-based public-key encryption construction, but I wonder if ...
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### Hash chain based secret revealing using homorphic princples?

I have recently been looking into Homomorphic encryption and I am looking for a specific hash-based encryption/decryption scheme. I don't need a full implementation but I am not sure if what I want ...
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### How are the constants found in the AVX2 implementation of CRYSTALS-KYBER round 2 generated?

The post-quantum lattice-based cryptosystem CRYSTALS-KYBER which has made it to the second round of NIST PQC includes two implementations: 1) a baseline reference implementation in C and 2) an ...
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### Forging a new secret key in RLWE

In a RLWE setting where you are given a secret key $s$ and an associated public key $pk = (p_0,p_1) = (-(p_1s+e),p_1)$, is it possible/easy to forge a new secret key $s'$ such that $p_0+p_1s'$ has a ...
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### Hardware Gaussian random numbers for lattice-based cryptography

I have been recently reading about lattice-based cryptography. I read that a key aspect of such protocols rely on added Gaussian noise on lattices, and which therefore require highly efficient and ...
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### SVP=SIVP in ring lattice (ideal lattice)

SVP (shortest vector problem) is equivalent to SIVP (shortest independent vectors problem) in ring lattice (ideal lattice). How to prove this? Could someone explain it to me? Thanks!
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### Coppersmith's method for small public exponent

Can Coppersmith's method be used to break RSA when we only have access to public key and one ciphertext? For e.g. suppose we have N and ciphertext c both are 1024-bit numbers and the public exponent e ...
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### average-case SIS and average-case BDD

In lattice based cryptography, we say the average-case SIS (short integer solution) problem because it is such kind problem " $A \stackrel{\$}{\leftarrow} \mathbb{Z}^{n\times m}_{...
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### Is the “decapsulate” function from lattice based cryptography homomorphic?

Observing the code example from pqcrypto-kyber, is the decapsulate function $d$ homomorphic? If $d(ct, sk_i) = ss_i$, is it true that $d(ct, \sum_i sk_i) = \sum_i ss_i$ ?
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### Decision to Search LWE when modulus $q=p^e$

I am reading Applebaum et al.. In Lemma 1. (page 7), Applebaum et al. proved the decision to search reduction when the modulus $q=p^e$ for prime $p$. In the proof, they define the hybrid ...
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### How to have a bound (upper or lower) of Gaussion distribution over lattice based crypto>

In lattice-based crypto, we always need to sample 'noise' from Gaussian distribution, but how to measure the bound the noise? For example, if the Gaussian distribution is D_{u,\sigma}, where u is the ...
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### security parameter in lattice cryptography

In paper Lattice Signatures Without Trapdoors(Lyubashevsky2012), $n$ is the security parameter, why the authors set $n$ as 512 but not 80/100/112 to get 80-bit security/100-bit/112-bit security?
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### Most influential/illuminating papers/books/courses on lattice based cryptography?

I'm interested in some sort of "compendium" on lattice-based crypto. There are a bunch of maths behind FALCON and other stuff. A lot of articles are devoted to lattice crypto, but not of them are of ...
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### set of integers modulo an integer q in lattice

Some literature about lattices set $\mathbb{Z}_{q}$ in $[-\frac{q}{2}, \frac{q}{2})\cap \mathbb{Z}$ but not $[0,q-1]$ such as "lattice signatures without trapdoors" and "lattice based blind ...
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### Learning with rounding (LWR)

This may be a naive question: LWR assumption states that for ${A} \stackrel{$}{\leftarrow} \mathbb{Z}^{m \times n}_q, s \stackrel{$}{\leftarrow} \mathbb{Z}^n_q$, given $(A, \lfloor A\cdot s \rfloor_p$...
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### Block size of BKZ algorithm and related security of CRYSTALS-Kyber

Security of lattice-based schemes in the NIST Posto-Quantum Project often relies on the complexity of dual attack. Complexity of this attack depends on the running time of lattice basis reduction ...