This Regulation also lays down the conditions under which requests for the comparison of biometric or alphanumeric data with Eurodac data for the purpose of preventing, detecting, or investigating terrorist offences or other serious criminal offences should be allowed and the necessary safeguards to ensure the protection of the fundamental right to respect for the private life of individuals whose personal data are processed in Eurodac. The strictness of those conditions reflects the fact that the Eurodac database registers biometric and alphanumeric data of persons who are not presumed to have committed a terrorist offence or other serious criminal offence. It is acknowledged that law enforcement authorities and Europol do not always have the biometric data of the suspect or victim whose case they are investigating, which might hamper their ability to check biometric matching databases such as Eurodac. It is important to equip law enforcement authorities and Europol with the necessary tools to prevent, detect and investigate terrorist offences or other serious criminal offences where it is necessary to do so. In order to contribute further to the investigations carried out by those authorities and Europol, searches based on alphanumeric data should be allowed in Eurodac, in particular in cases where no biometric evidence can be found but where those authorities and Europol possess evidence of the personal details or identity documents of the suspect or victim.