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Using GP/PARI how would you solve this randomised Elgamal question?

kw flag

I know how to solve this question manually, but I don't know how to solve it using the program gp/pari. It is based on randomised Elgamal

Let p = 739. Given the following ciphertext of some message m1 encrypted using randomized Elgamal, what is the ciphertext of m1 · m2, where m2 ≡ 2 (mod p)? (c1,c2) = (246,609)

kodlu avatar
sa flag
specify how you would solve it by hand, and the exact details of what you are referring to as randomised el-gamal. what's its relation to hashed el-gamal
fgrieu avatar
ng flag
The problem statement's second phrase is wrong. Read: _“Given the following ciphertext of some message $m_1$ encrypted using randomized ElGamal, what is a ciphertext for $m_1·m_2\bmod p$, where $m_2=2$?”_ Hint: write the equations for ciphertext under randomized ElGamal. Assume the same random is used to encrypt $m_1$ and $m_3=m_1\cdot m_2\bmod p$. How can you deduce the later ciphertext from the former? GP/Pari is overkill: all computations can be done mentally, or pen and paper, or any calculator, depending on fluency with numbers.
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