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Suppose all the values and operations are defined over a finite field $\mathbb{F}_p$ where $p$ is a large prime number. Assume all values are non-zero. Here $(z)^{-1}$ denotes multiplicative inverse of value $z$.

We give away the values $v_1$ and $v_2$ to an adversary and ask him to compute their product:

• $v_1=a\cdot z_1$
• $v_2=b \cdot z_2 \cdot (z_1)^{-1}$

So, the adversary computes $v_3= v_1\cdot v_2=a\cdot b \cdot z_2$.

The values $z_i$ are picked uniformly at random from the field. But $a$ and $b$ are fixed values of the field.

Questions:

1. Given the three values $v_3, v_1$ and $v_2$ can the adversary learn anything about the fixed values $a$ and $b$ (and the $z_i$ values)? If yes/no Why?

In other worlds, given the above three values, can the adversary infer anything about $a$ and $b$?

2. Let $v_1=a\cdot z_1$ and $v_2=(z_1)^{-1}\cdot z_2$.

If we give $v_1$ and $v_2$ to the adversary and ask him to compute their product: $v_3=v_1\cdot v_2=a\cdot z_2$ would it learn the secret value $a$ (and $z_i$ values)?

Suppose all the values and operations are defined over a finite field $\mathbb{F}_p$ where $p$ is a large prime number. Assume all values are non-zero. Here $(z)^{-1}$ denotes multiplicative inverse of value $z$.

We give away the values $v_1$ and $v_2$ to an adversary and ask him to compute their product:

• $v_1=a\cdot z_1$
• $v_2=b \cdot z_2 \cdot (z_1)^{-1}$

So, the adversary computes $v_3= v_1\cdot v_2=a\cdot b \cdot z_2$.

The values $z_i$ are picked uniformly at random from the field. But $a$ and $b$ are fixed values of the field.

Questions:

1. Given the three values $v_3, v_1$ and $v_2$ can the adversary learn anything about the fixed values $a$ and $b$ (and the $z_i$ values)? If yes/no Why?

   In other worlds, given the above three values, can the adversary infer anything about $a$ and $b$?

2. Let $v_1=a\cdot z_1$ and $v_2=(z_1)^{-1}\cdot z_2$.

   If we give $v_1$ and $v_2$ to the adversary and ask him to compute their product: $v_3=v_1\cdot v_2=a\cdot z_2$ would it learn the secret value $a$ (and $z_i$ values)?

Suppose all the values and operations are defined over a finite field $\mathbb{F}_p$ where $p$ is a large prime number. Assume all values are non-zero. Here $(z)^{-1}$ denotes multiplicative inverse of value $z$.

We give away the values $v_1$ and $v_2$ to an adversaryand ask him to compute their product:

• $v_1=a\cdot z_1$

• $v_2=b \cdot z_2 \cdot (z_1)^{-1}$

So the adversary computes $v_3= v_1\cdot v_2=a\cdot b \cdot z_2$.

The values $z_i$ are picked uniformly at random from the field. But $a$ and $b$ are fixed values of the field.

Question 1 : Given the three values $v_3, v_1$ and $v_2$ can the adversary learn anything about the fixed values $a$ and $b$ (and the $z_i$ values)? If yes/no Why?

In other worlds, given the above three values, can the adversary infer anything about $a$ and $b$?

Let $v_1=a\cdot z_1$ and $v_2=(z_1)^{-1}\cdot z_2$.

Question 2 : If we give $v_1$ and $v_2$ to the adversary and ask him to compute their product: $v_3=v_1\cdot v_2=a\cdot z_2$ would it learn the secret value $a$ (and $z_i$ values)?

Suppose all the values and operations are defined over a finite field $\mathbb{F}_p$ where $p$ is a large prime number. Assume all values are non-zero. Here $(z)^{-1}$ denotes multiplicative inverse of value $z$.

We give away the values $v_1$ and $v_2$ to an adversary and ask him to compute their product:

• $v_1=a\cdot z_1$
• $v_2=b \cdot z_2 \cdot (z_1)^{-1}$

So, the adversary computes $v_3= v_1\cdot v_2=a\cdot b \cdot z_2$.

The values $z_i$ are picked uniformly at random from the field. But $a$ and $b$ are fixed values of the field.

Questions:

1. Given the three values $v_3, v_1$ and $v_2$ can the adversary learn anything about the fixed values $a$ and $b$ (and the $z_i$ values)? If yes/no Why?

In other worlds, given the above three values, can the adversary infer anything about $a$ and $b$?

2. Let $v_1=a\cdot z_1$ and $v_2=(z_1)^{-1}\cdot z_2$.

If we give $v_1$ and $v_2$ to the adversary and ask him to compute their product: $v_3=v_1\cdot v_2=a\cdot z_2$ would it learn the secret value $a$ (and $z_i$ values)?

Suppose all the values and operations are defined over a finite field $\mathbb{F}_p$ where $p$ is a large prime number. Assume all values are non-zero.

We give away the values $v_1$ and $v_2$ to an adversaryand ask him to compute their product:

• $v_1=a\cdot z_1$

• $v_2=b \cdot z_2 \cdot (z_1)^{-1}$

So the adversary computes $v_3= v_1\cdot v_2=a\cdot b \cdot z_2$.

The values $z_i$ are picked uniformly at random from the field. But $a$ and $b$ are fixed values of the field.

Question 1 : Given the three values $v_3, v_1$ and $v_2$ can the adversary learn anything about the fixed values $a$ and $b$ (and the $z_i$ values)? If yes/no Why?

In other worlds, given the above three values, can the adversary infer anything about $a$ and $b$?

Let $v_1=a\cdot z_1$ and $v_2=(z_1)^{-1}\cdot z_2$.

Question 2 : If we give $v_1$ and $v_2$ to the adversary and ask him to compute their product: $v_3=v_1\cdot v_2=a\cdot z_2$ would it learn the secret value $a$ (and $z_i$ values)?

Suppose all the values and operations are defined over a finite field $\mathbb{F}_p$ where $p$ is a large prime number. Assume all values are non-zero. Here $(z)^{-1}$ denotes multiplicative inverse of value $z$.

We give away the values $v_1$ and $v_2$ to an adversaryand ask him to compute their product:

• $v_1=a\cdot z_1$

• $v_2=b \cdot z_2 \cdot (z_1)^{-1}$

So the adversary computes $v_3= v_1\cdot v_2=a\cdot b \cdot z_2$.

The values $z_i$ are picked uniformly at random from the field. But $a$ and $b$ are fixed values of the field.

Question 1 : Given the three values $v_3, v_1$ and $v_2$ can the adversary learn anything about the fixed values $a$ and $b$ (and the $z_i$ values)? If yes/no Why?

In other worlds, given the above three values, can the adversary infer anything about $a$ and $b$?

Let $v_1=a\cdot z_1$ and $v_2=(z_1)^{-1}\cdot z_2$.

Question 2 : If we give $v_1$ and $v_2$ to the adversary and ask him to compute their product: $v_3=v_1\cdot v_2=a\cdot z_2$ would it learn the secret value $a$ (and $z_i$ values)?