The Securities and Exchange Commission is cracking down on suspicious cryptocurrencies and that will only continue, according to a former chairman of the regulatory body.

"We're in line for some serious regulatory responses to all of this and that will be forthcoming after the first of the year," Harvey Pitt said Thursday on CNBC's "Fast Money."

The SEC has already issued warnings — with the Financial Industry Regulatory Authority adding cautions as well — and Pitt says there is "activity on the horizon" for further regulation.

"Everyone else is investing in it, and the price seems to be going up," Pitt said. "That's a real problem because there's a lack of education and knowledge on the part of many of the people who are actually doing the investing."

The SEC on Tuesday temporarily suspended trading in shares of ., whose stock has surged more than 2,700 percent this month. The commission said in a release that questions have "arisen concerning potentially manipulative transactions in the company's stock in November 2017."

Pitt identified many cryptocurrency offerings as "offerings of securities," which therefore fit under the SEC's legal authority. For him, that means insider trading is a very real possibility.

"There absolutely can be insider trading," Pitt added. "When people have advanced knowledge of the offerings of these interests and take advantage of the offering long before it occurs."