AUSTIN, Texas—Cody Wilson rattled lawmakers and law-enforcement agencies with a plastic gun created from a 3-D printer, home computer and blueprints he posted online for anyone to download.

Now, the 25-year-old law-school dropout is about to launch software aimed at covering the tracks of financial transactions made with bitcoin, the virtual currency that has exploded in popularity among spenders and speculators—and raised concerns among regulators that it might be used for illegal activity.

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