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Results tagged with lattice-crypto
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user 87135
Lattice-cryptography is the study and use of lattice problems applied to cryptography.
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Software package to create a basis of the q-ary lattice $\Lambda_q(A)$
Consider a matrix $A \in \mathbb{Z}_q^{m \times n}$ and its respective lattice
$$\Lambda_q(A) = \{x \in \mathbb{Z}^m : \exists z \in \mathbb{Z}_q^n, x = Az \mod q\}$$
The basis for such a lattice is d …
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Lattice based cryptography: How do negative coefficients in $Z_q[x]/(X^n+1)$ work? [duplicate]
I saw that in lattice-based cryptography schemes, for example Dilithium, coefficients in $Z_q$ are allowed to be negative. For example, in Dilithium the secret key is $s_1 \in R_q^{k \times l}$, where …
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How can CPA-secure LWE cryptosystem be broken by an active attacker?
The LWE-cryptosystem is only CPA-secure as for example stated in A Decade of Lattice-Based Cryptography. Consider the following system described there (Section 5.2)
The secret key is a uniform LWE se …
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Paper "How to Meet Ternary LWE Keys": Why can Odlyzko's hash function not be used to constru...
In Alexander May's Paper "How to Meet Ternary LWE Keys", Alexander May writes the following about combining representation techniques with Odlyzko's locality sensitive hash function (Page 12):
Intui …
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NTL: Solve the closest vector problem for non-square matrix using LLL/Nearest Plane Algorithm
Assume I have a matrix $A \in \mathbb{Z}^{m \times n}$, $m > n$, which forms a basis of a lattice. Given a vector target vector $t = Ax + e$, $t,e \in \mathbb{Z}^m$,$x \in \mathbb{Z}^n$, I want to fin …
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Performance of elliptic curve Diffie-Hellman vs NIST-PQC finalist KEMS
I am looking for performance measurements in cycle counts for an implementation of the elliptic curve Diffie-Hellman for curve, ed25519. Ideally, the cycle counts should be for the M4, so that they ar …
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