Russian hackers able to reliably break anonymity network Tor will have the chance to earn 3.9 million roubles (£65,000) in a new contract put up for tender by the government.
Applicants must pay 195,000 roubles (£3,250) to enter, with those from outside the federation are barred for security reasons.
Andrei Soldatov, editor of security services news site Agentura.Ru, told the Guardian: "It's not important if the Russian government is able to block Tor or not."
"The importance is that they're sending signals that they are watching this. People will start to be more cautious."
Tor protects its users privacy by routing their connections through numerous servers, making it difficult for users to be tracked.
Earlier this month German broadcaster ARD claimed that the US National Security Agency (NSA) was snooping on two Tor servers in Germany.
However last November a leak from Edward Snowden suggested that American and British surveillance agencies were still struggling to break the service, which is partly funded by the US government.
One document said: "We will never be able to de-anonymise all Tor users all the time. With manual analysis we can de-anonymise a very small fraction of Tor users."