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4

See NIST SP 800-107, section 5.3.4: The effective security strength of the HMAC key is the minimum of the security strength of $K$ and the value of $2C$. That is, security strength = min(security strength of $K$, $2C$). For example, if the security strength of $K$ is 128 bits, and SHA-1 is used, then the effective security strength of the HMAC key is 128 ...


3

You cannot uniquely invert it. Your hash will have the form $$y_1 \quad y_2 \quad \dots \quad y_m$$ with $y_i=\sum_{k=1}^m x_k^{i-1}.$ First look at the special case $m=2$. $y_1$ will always be $y_1=m=2,\,$ the other equation is $y_2=x_1 + x_2$. You cannot uniquely determine both $x_1,x_2$. In the general case you have $y_1=m$ and $m-1$ equations for the ...


3

I think you could calculate it manually or write code to solve this. You need to calculate X values from starting with end. For example : $X_{32}$ = 84 = $X_{32}^{31}$ $mod_{117} $ When you get $X_{32}$ value then you can calculate $X_{31}$: $X_{31}$ = 62 = $X_{31}^{30}$+$X_{32}^{30}$ $mod_{117} $ The only unknown value is $X_{31}$ here. You need ...


2

Use the number of occurrences of each letter as the unknowns you're solving for. This gives you 32 linear equations to solve for 16 unknowns. Use standard approaches for solving systems of linear equations. Finally use the fact that the letters are ordered alphabetically to reconstruct the $x_i$ values.



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