The computer attacks, apparently originating in Russia, first hit the Web site of Estonia’s prime minister on April 27, the day the country was mired in protest and violence. The president’s site went down, too, and soon so did those of several departments in a wired country that touts its paperless government and likes to call itself E-stonia. Then the attacks, coming in waves, began to strike newspapers and television stations, then schools and finally banks, raising fears that what was initially a nuisance could have economic consequences. The attacks have peaked and tapered off since then, but they have...