{HEAD ~ A signature generation apparatus} and {TAIL ~ a signature verification apparatus} of the present invention have an operational effect of being capable of preventing the occurrence of norm zero vector forgery attack, and therefore the present invention is significantly useful 
{ HEAD ~ A signature generation apparatus } and { TAIL ~ a signature verification apparatus } of the present invention have an operational effect of being capable of preventing the occurrence of norm zero vector forgery attack , and therefore the present invention is significantly useful
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