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Recent breakthrough results by Brakerski et al and Dodis et al have shown that signature schemes can be made secure even if the adversary continually obtains information leakage from the secret key of the scheme. However, the schemes currently do not allow leakage on the secret key and randomness during signing, except in the random oracle model. Further, the random oracle based schemes require updates to the secret key in order to maintain security, even when no leakage during computation is present.
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