# Discrete Logarithm problem with selected order

If the order of group ($$p$$)selected by attacker then discrete logarithm is still hard?

• Welcome to Cryptography. What is the source of this question? What is the order of the group? What about pre-computation with a small group like the small group attack on the elliptic curve cryptography. Nov 8 '20 at 15:37
• Thanks for your answer but my means that the group order p is a large prime number. In this situation what's the answer? Nov 9 '20 at 13:00

If the attacker can pick, say, an order $$p=3$$, then it's easy.
However, if the attacker is constrained to pick a large order, that may not be enough. If the attacker is able to select a smooth group order, that is, an order $$p$$ which is the product of a multiset of small primes, then the discrete log problem is easy (using the Pohlig-Hellman algorithm).
• Thanks for your answer but my means that the group order $p$ is a large prime number. In this situation what's the answer? Nov 9 '20 at 12:53
• @mehdimahdavioliaiy Did you read the last paragraph on the Poncho's answer? And next time, please be more specific about your problem. Writing $p$ doesn't mean it is a prime, we say like "for a prime $p$". Still, what is the source of this question? why do you need this question? Nov 9 '20 at 13:04