# Computing discrete logarithms in the subgroup generated by 1 + N

When I read about DLP, I found that there are groups where the computation is easy. I found that it is known that computing discrete logarithms in the subgroup generated by 1 + N is easy. For example : $$(1+N)^{x} = 1+ xN$$. Is this correct? And what is the mathematical foundation of this computation? Why is considered as easy compared to the other groups?

• subgroup of which group? – kelalaka May 25 at 20:12
• If we are in $\Bbb Z_N$, it holds $(1+N)^x=1=1+x\,N$ making the generated group rather boring. Thus it's essential to state what base ring (or other algebraic structure) is used. – fgrieu May 25 at 20:45
• This is true in the Paillier group and the property is exploited in the decryption procedure. – Occams_Trimmer May 25 at 21:42
• Occams_Trimmer, could you please provide me more details? – sof May 25 at 22:25
• The Wikipedia entry (Background section) is quite detailed. – Occams_Trimmer May 25 at 22:46