(credit: BalticServers.com)

For years, privacy advocates have pushed developers of websites, virtual private network apps, and other cryptographic software to adopt the Diffie-Hellman cryptographic key exchange as a defense against surveillance from the US National Security Agency and other state-sponsored spies. Now, researchers are renewing their warning that a serious flaw in the way the key exchange is implemented is allowing the NSA to break and eavesdrop on trillions of encrypted connections.

The cost for adversaries is by no means modest. For commonly used 1024-bit keys, it would take about a year and cost a “few hundred million dollars” to crack just one of the extremely large prime numbers that form the starting point of a Diffie-Hellman negotiation. But it turns out that only a few primes are commonly used, putting the price well within the NSA’s $11 billion-per-year budget dedicated to “groundbreaking cryptanalytic capabilities.”

“Since a handful of primes are so widely reused, the payoff, in terms of connections they could decrypt, would be enormous,” researchers Alex Halderman and Nadia Heninger wrote in a blog post published Wednesday. “Breaking a single, common 1024-bit prime would allow NSA to passively decrypt connections to two-thirds of VPNs and a quarter of all SSH servers globally. Breaking a second 1024-bit prime would allow passive eavesdropping on connections to nearly 20% of the top million HTTPS websites. In other words, a one-time investment in massive computation would make it possible to eavesdrop on trillions of encrypted connections.”

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How the NSA can break trillions of encrypted Web and VPN connections