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# Questions tagged [lattice-crypto]

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

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### Error Correcting Codes Post Quantum Finalists

I have been looking into error-correcting codes in lattice, I am specifically hoping to find some information on hardware implementations for the NIST PQ PKE/KEM finalists (Saber, CRYSTALS-Kyber, NTRU)...
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### Coppersmith attack on NTRU and non-commutativity

In this paper, Coppersmith and Shamir used lattice reduction to attack NTRU. At the very end of the paper, they note that developing non-commutative variants of NTRU would be wise, in light of their ...
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3 answers
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### Why do Problems for Post-Quantum algorithms have to be NP-Hard?

The mathematical problems used for Post-Quantum Cryptography problems I came across, are NP-complete, e.g. Solving quadratic equations over finite fields short lattice vectors and close lattice ...
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### Why is the proof on the commitment correct?

In the paper "Efficient Zero-Knowledge Proofs for Commitments from Learning with Errors over Rings", they gave a commitment from Ring-LWE: to commit to a polynomial $m$ in $Rq(Zq[x]/(x^n+1))$...
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### GSW and homomorphic addition on integers

Is it possible to use the GSW scheme (Gentry, Sahai, Waters) also on integer values and not just single bits? If not, are there any schemes that support integer arithmetic with the same nice property ...
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### GSW13 scheme and integer arithmetic

I'm new to lattice-based cryptography and have trouble understanding if the GSW13 (Gentry, Sahai, Waters) scheme works only on single bits. But is it also possible to encrypt integers with this scheme ...
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1 vote
1 answer
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### Algebraic Variants of NTRU

There are a large number of algebraic NTRU variants: for example, in some (such as ETRU), the underlying ring has been changed to the ring of integers of a certain number field; there is GR-NTRU, ...
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2 votes
1 answer
202 views

### Significance of parameter q in NTRU lattice attack

In NTRU (N,p,q,d), N is usually chosen to be prime and q be a power of 2. Why is it that if I increase the parameter q, the probability of finding a key or spurious key that can decrypt the message is ...
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1 vote
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### Attacks on LWE when q is a power of 2

I am working on an LWE instance where q is a power of 2 and I'm wondering if there is any literature about attacks in this context, especially if there are any attacks which work significantly better. ...
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0 votes
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### Short Integer Solution Problem with ||z||<=B

Why following constraints on $||z||$ are required $||z||<=B, B<q$
1 vote
3 answers
828 views

### I need a pathway for studying Lattice-Based Cryptography

I realize that I need a study pathway for post-quantum cryptography. I started to study post-quantum crypto by reading NIST PQC 3rd-round submissions of the lattice-based schemes (let's start with the ...
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