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I came across this paper about aggregate lattice-based signatures, however, I'm not able to fully understand it. Specifically, I'm wondering if someone could help answer the following questions:

  1. In part III. System model of Aggregate Signature, the authors state there is a KeyExtract algorithm where "Given parameters $n$ and $PP$, the KGC provides public/secret key pairs ($pk$; $sk$) for all single signers." - is this to be understood as all key pairs must be generated by some trusted authority?
  2. What are the sizes of public keys, signatures, and aggregated signatures (in bytes)? On the second to last page there are two tables that address this, but I'm not sure how to translate this info into bytes (at ~128 bit security level).
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  1. "Given parameters $n$ and $PP$, the KGC provides public/secret key pairs $(pk; sk)$ for all single signers."

Yes, the key generation center (KGC) generate the key pairs $(pk; sk)$ and distributes them. It is also clear from figure 3 of the article.

  1. What are the sizes of public keys, signatures, and aggregated signatures (in bytes)?

The parameters are used in $TrapGen(n,q,m)$, which actually generates for SIS parameters. You can find example secure paremeters from here or similar work.

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