veil of (something)

That which serves to conceal or obscure the truth (of something). Despite many calls by activists to lift the veil of secrecy surrounding the government's plan, officials once again declined to make any details public. There has long been a veil of silence within the organization meant to protect those in charge. You've kept a veil of deceit drawn over our marriage for years, Tom. I want the truth about where you've been spending all our money!

web of deceit

An intricate contrivance of misdirection, omission, or deception that ultimately serves to ensnare or entangle oneself or others. It turned out that she had been embezzling money for years, but the CEO's web of deceit finally caught up with her after federal investigators started poking around the company's accounts. You had a happy life with her, but you decided to throw it all away for a fling with some secretary. You spun a web of deceit to hide it all, but now you've been caught in it.