<P> In their foundational paper, Goldwasser, Micali, and Rivest lay out a hierarchy of attack models against digital signatures: </P> <Ol> <Li> In a key - only attack, the attacker is only given the public verification key . </Li> <Li> In a known message attack, the attacker is given valid signatures for a variety of messages known by the attacker but not chosen by the attacker . </Li> <Li> In an adaptive chosen message attack, the attacker first learns signatures on arbitrary messages of the attacker's choice . </Li> </Ol> <Li> In a key - only attack, the attacker is only given the public verification key . </Li> <Li> In a known message attack, the attacker is given valid signatures for a variety of messages known by the attacker but not chosen by the attacker . </Li>

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