Word Count : 562

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To sign the message \( M = 20 \) using the Digital Signature Algorithm (DSA), Alice will follow these steps: ### 1. Parameter Setup Alice already has the following parameters: - \( p = 83 \) (a large prime number) - \( q = 41 \) (a divisor of \( p - 1 \), used to form the group order) - \( g = 2 \) (the generator element) - \( a = 3 \) (her private key, which is secret) - \( M = 20 \) (the message to be signed) - \( k = 8 \) (a secret random value, used only once) ### 2. Compute \( r \) Alice computes the value \( r \) using the formula: \[ r = (g^k \mod p) \mod q \] Plugging in the values: \[ r = (2^8 \mod 83) ________ _________ _________ ________ _________ _______ ___ ______.
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