Correcting the translation : 

• Special criminal law 

Explanation: 

• First,It is so important to distinguish the difference between criminal law and private law since these are distinct legal systems. 
• moreover the term “ private criminal law “ is completely incorrect and this is due to a misleading translation from Arabic to English and even french too! Of a one term used to define what is the responsibility of special criminal law .
• In conclusion, Special criminal law is devoted to the study of criminal offenses, the different elements of these offenses and the penalties that punish them and this is exactly what we mean by the translation above.