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Edited ch08_signatures.adoc with Atlas code editor

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clenser 2023-10-19 12:58:02 +00:00
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@ -302,17 +302,17 @@ Provable security::
computers). computers).
Linearity:: Linearity::
Schnorr signatures have a property that mathematicians call Schnorr signatures have a property that mathematicians ((("linearity")))call
_linearity_, which applies to functions with two particular _linearity_, which applies to functions with two particular
properties. The first property is that summing together two or more properties. The first property is that summing together two or more
variables and then running a function on that sum will produce the variables and then running a function on that sum will produce the
same value as running the function on each of the variables same value as running the function on each of the variables
independently and then summing together the results, e.g., independently and then summing together the results, e.g.,
+f(x + y + z) == f(x) + f(y) + f(z)+; this property is called +f(x + y + z) == f(x) + f(y) + f(z)+; this property is((("additivity"))) called
_additivity_. The second property is that multiplying a variable and _additivity_. The second property is that multiplying a variable and
then running a function on that product will produce the same value as then running a function on that product will produce the same value as
running the function on the variable and then multiplying it by the running the function on the variable and then multiplying it by the
same amount, e.g., +f(a * x) == a * f(x)+; this property is called same amount, e.g., +f(a * x) == a * f(x)+; this property is ((("homogeneity of degree 1")))called
_homogeneity of degree 1_. _homogeneity of degree 1_.
+ +
In cryptographic operations, some functions may be private (such In cryptographic operations, some functions may be private (such