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Questions on "A CERTIFIED DIGITAL SIGNATURE" Pg. 19

no flag

Referenced paper here.

Page 19 of Attached paper

The above excerpt is from Page 19 of attached paper. I have a few questions.

  1. y = F^9(x) is equivalent of F(F(F(F(F(F(F(F(F(x))))))))) ?
  2. The excerpt says that this allows us to sign 4 bits of information. Shouldn't it allow a person to sign any size message(ex: 100 bits) not just 4 bits by just running the hash function repeatedly(ex. if the message to be signed has the value 247869, I would just run the function 247869 times repeatedly)?
  3. I didn't understand the part that reads "Anyone can check F^7(F^9(x)) = y, thus confirming that F^9(x) was made public, but no one can generate that value".

Thank you for you time!

Score:4
ru flag
  1. Yes, that is correct.
  2. No, the value $f^{16}(x)$ should be thought of as computed and published prior to any signatures being generated. Only if the signer has the foresight to compute and publish $f^n(x)$ for some $n>24789$ would they be able to sign the value 24789.
  3. The claimed signature value $s$ can be repeatedly hashed 7 times and compared to $y$ i.e. one can check if $f^7(s)=y$. This is highly unlikely to be true for any $s$ generated by an adversary; but a legitimate signer is able to set $s=f^9(x))$ so that $f^7(s)=f^7(f^9(x))=f^{16}(x)=y$.
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