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"Since a handful of primes are so widely reused, the payoff, in terms of connections they could decrypt, would be enormous," said Alex Halderman and Nadia Heninger in a blog post published Wednesday.
"Breaking a single, 1024-bit prime would allow the 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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