The basic mathematical tools required to create a stealth aircraft were first described by the Soviet mathematician Petr Ufimtsev. The Soviets themselves apparently never did much work in this area, but after a scientific paper describing his work was published internationally engineers at Lockheed quickly realized the significance of what they were looking at and went on to create the F-117.
What I've always heard is that the Soviet censors weren't technically sophisticated enough to realize the importance of this paper, but Ufimtsev himself was certainly smart enough to understand what he was writing about so why did he choose to publish it where it could be read by the Americans?
I once wrote a short article about the origins of the F-117 (it's available here, but it's in Polish). I based it mainly on the memoirs of Ben Rich, Director of Skunk Works in the 1970s and 80s. The quotations below will also be taken from Rich's book; if you're interested in the F-117, I highly recommend it. The title is, appropriately, 'Skunk Works.'
Now, on to the topic at hand.
Denys Overholser, one of the fathers of the F-117, called Ufimtsev's article, Method of Edge Waves in the Physical Theory of Diffraction, 'so obtuse and impenetrable that only a nerd's nerd would have waded through it all.' This lends credence to the theory that Soviet censors really were unaware what gem they were dealing with.
After Ufimtsev himself emigrated to the USA, he said, 'Senior Soviet designers were absolutely uninterested in my theories.' Now, this is speculation on my part, but I believ this might be the key reason why Ufimtsev released his findings worldwide. He simply got frustrated and decided, 'Fine, if you don't want my discoveries, maybe someone else will find them useful.' The Soviet system, even though it craved new, advanced weaponry, was plagued by immense bureaucratic inertia coupled with cronyism and corruption. These are paralyzing circumstances for introducing innovation.
Since, as mentioned above, Ufimtsev emigrated to America, he might have already been thinking about it in the 1960s. While there's nothing to support this hypothesis, it's not entirely unlikely that he wanted 'Method of Edge Waves...' to be his calling card in the Western world. However, I believe that ultimately his reason was frustration. This is a normal, human reaction. If you feel you've achieved something momentous, you want at least some praise and some acknowledgement of your success.