Suppose we are using an LWE based cryptosystem with LWE samples of the form As + e. The result of running the key generation algorithm produces the matrix A, and vectors s, e and t. The public key is _____ and the private key is _____.

Question

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We are given an LWE-based cryptosystem where samples have the form A s + e, and the key generation outputs A, s, e, and t. In LWE-based schemes, the public key is typically the matrix A together with the evaluated LWE sample t = A s + e, while the private key is the secret vector s.
Option a: (A, t), s. This matches the standard public-key form where the public key is the pair (A, t) and the private key is s, since t encodes A s + e and retains the relation to s through the equation t = A s + e.
Option b: s, (A, t). This reverses the roles, listing the private key first and the public key second; in standard LWE schemes, the public key must reveal A and t, not just s, so this is inconsistent.
Option c: s, (t, e). Here the private key would be s, but the public key would be (t, e). The pair (t, e) does not reveal A in a way that matches the typical public-key output, and e is a noise term, not part of the public key in the usual formulation.
Option d: (t, e), s. This suggests the public key consists of (t, e), which omits A entirely and incorrectly places e into the public key; e is a noise vector not meant to be publicly exposed as part of the public key.
In summary, the correct construction requires the public key to reveal A and the resulting t, where t = A s + e, while the private key remains s. The other options misplace the roles or misidentify which components constitute the public versus private keys, leading to inconsistencies with the standard LWE key generation structure.

Suppose we are using an LWE based cryptosystem with LWE samples of the form As + e. The result of running the key generation algorithm produces the matrix A, and vectors s, e and t. The public key is _ and the private key is _.单项选择题

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Suppose we are using an LWE based cryptosystem with LWE samples of the form As + e. The result of running the key generation algorithm produces the matrix A, and vectors s, e and t. The public key is _____ and the private key is _____.单项选择题