Why is it necessary in confidential transactions to have two generators?

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So as i understand it (though im not sure if its the same w/ bulletproofs so please correct me if im wrong), a commitment is generated like this;



commitment = (blinding_secret . G) + (value . H)


where G and H are both different generators on the same curve. But why is it necessary to have the second generator, H, instead of just using G twice?






cryptography confidential-transactions







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    up vote
    2
    down vote

    favorite












    So as i understand it (though im not sure if its the same w/ bulletproofs so please correct me if im wrong), a commitment is generated like this;



    commitment = (blinding_secret . G) + (value . H)


    where G and H are both different generators on the same curve. But why is it necessary to have the second generator, H, instead of just using G twice?






    cryptography confidential-transactions







    share|improve this question























      up vote
      2
      down vote

      favorite









      up vote
      2
      down vote

      favorite











      So as i understand it (though im not sure if its the same w/ bulletproofs so please correct me if im wrong), a commitment is generated like this;



      commitment = (blinding_secret . G) + (value . H)


      where G and H are both different generators on the same curve. But why is it necessary to have the second generator, H, instead of just using G twice?






      cryptography confidential-transactions







      share|improve this question













      So as i understand it (though im not sure if its the same w/ bulletproofs so please correct me if im wrong), a commitment is generated like this;



      commitment = (blinding_secret . G) + (value . H)


      where G and H are both different generators on the same curve. But why is it necessary to have the second generator, H, instead of just using G twice?






      cryptography confidential-transactions




      cryptography confidential-transactions






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      asked 2 hours ago









      cookiekid

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          Normally C = xG + aH where a is the amount and x is the blinding factor.



          The point of a Pedersen Commitment is to commit you to a certain value of a. If instead you had C = xG + aG, then this simplifies to C = (x+a)G. So you could claim any value of a later by claiming you'd used a different blinding factor. Using H, which has an unknown DL w.r.t. G, prevents you from doing this.






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            up vote
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            accepted










            Normally C = xG + aH where a is the amount and x is the blinding factor.



            The point of a Pedersen Commitment is to commit you to a certain value of a. If instead you had C = xG + aG, then this simplifies to C = (x+a)G. So you could claim any value of a later by claiming you'd used a different blinding factor. Using H, which has an unknown DL w.r.t. G, prevents you from doing this.






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              up vote
              3
              down vote



              accepted










              Normally C = xG + aH where a is the amount and x is the blinding factor.



              The point of a Pedersen Commitment is to commit you to a certain value of a. If instead you had C = xG + aG, then this simplifies to C = (x+a)G. So you could claim any value of a later by claiming you'd used a different blinding factor. Using H, which has an unknown DL w.r.t. G, prevents you from doing this.






              share|improve this answer






















                up vote
                3
                down vote



                accepted







                up vote
                3
                down vote



                accepted






                Normally C = xG + aH where a is the amount and x is the blinding factor.



                The point of a Pedersen Commitment is to commit you to a certain value of a. If instead you had C = xG + aG, then this simplifies to C = (x+a)G. So you could claim any value of a later by claiming you'd used a different blinding factor. Using H, which has an unknown DL w.r.t. G, prevents you from doing this.






                share|improve this answer












                Normally C = xG + aH where a is the amount and x is the blinding factor.



                The point of a Pedersen Commitment is to commit you to a certain value of a. If instead you had C = xG + aG, then this simplifies to C = (x+a)G. So you could claim any value of a later by claiming you'd used a different blinding factor. Using H, which has an unknown DL w.r.t. G, prevents you from doing this.







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                answered 1 hour ago









                knaccc

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