Booming telemedicine applications makes it deemed necessary to provide security services for such applications. The algorithms proposed in this field can be grouped into three classes: watermarking-based algorithms, crypto-based algorithms and hybrid algorithms. In this study, the authors propose two crypto-based algorithms capable of providing confidentiality, authenticity and integrity services to medical images exchanged in telemedicine applications. Strong cryptographic functions with internally generated symmetric keys and hash codes are used. The advanced encryption standard-Galois counter mode is used with the whirlpool hash function to provide confidentiality and authenticity, and the elliptic curve digital signature algorithm is used to provide authenticity and integrity. The proposed algorithms are based on the digital imaging and communication in medicine (DICOM) standard; however, unlike the standard, the algorithms provide confidentiality, authenticity and integrity for the header data, as well as for the pixel data of the DICOM images. Effectiveness of the proposed algorithms is evaluated and demonstrated through extensive experimentation using a benchmark set of DICOM images.