Original temporary secret key

Furthermore, it suffices to define test for the same values pk e PK All as verify. Similarly, a value skjemp can only be an original temporary secret key (as in the requirement on SKJTemp in Definition 7.1) if there exist parameters par = ( 1 , 1 ) as above, a prekey prek e Allj g, and a value mk such that... 

Let/ = mj, j, sj, mk , s )). Moreover, as the security definition is in functional notation, whereas Construction 10.13 is algorithmic, let the current value skjemp be redefined in terms of the history, i.e., as the result of applying sign to the messages from m, given the original temporary secret key and the random string from sk. ... 

If, as usual in such schemes, pk is a function of prek and the original temporary secret key skjemp, one can derive one more lower bound on the secret key. 

Remark 11.18. If a scheme with prekey is given and all the preconditions of Theorem 11.15 hold, and if the public key is a function of the original temporary secret key and the prekey, then... 

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