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TRON [TRX] Is Now Available To 4.5M Users Of Crypto APIs

TRON Mainnet is now integrated into the Crypto APIs blockchain infrastructure product suite granting access to the latter’s 4.5 million clients, the announcement post read. On the latest addition, it said, “To address the growing demand for operating and building on TRON, we have incorporated it into several of our products. Crypto APIs customers can now interact […]

Precise heuristic for size of a uniform sample in $(mathbb{Z} / N mathbb{Z})^times$

I’m primarily a mathematicians dipping my toes into cryptography, and I have often seen/heard cryptographers use the heuristic that a uniformly random sample $a$ from $(mathbb{Z} / N mathbb{Z})^times$ will be "large", or that $a approx N$, without referring to a specific result. I want to make sure I understand the precise heuristic here. Is ::Listen

I’m primarily a mathematicians dipping my toes into cryptography, and I have often seen/heard cryptographers use the heuristic that a uniformly random sample $a$ from $(mathbb{Z} / N mathbb{Z})^times$ will be "large", or that $a approx N$, without referring to a specific result.

I want to make sure I understand the precise heuristic here. Is the precise statement that the expected value of a uniformly random sample from $(mathbb{Z} / N mathbb{Z})^times$ will be $N / 2$, and therefore linear in $N$. Thus for parameter selection (as an example), if we can choose $N$ and security relies on a uniformly random sample being sufficiently large, we can make $N$ large enough that with high probability we get a sample of sufficient size?