Is a stream cipher algorithm (Encryption) has to be always symmetric? Wikipedia has mentioned it but without a reason. This site also portrays some information about it, but not clearly why only symmetric keys are used to encrypt stream cipher but not asymmetric?
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I remember that the teacher explained in class that the encryption and decryption speed of asymmetric ciphers is relatively slow, and stream encryption requires high speed, which may be one of the reasons.
You can check here, Salsa20 has 408MB/s and 4.3 cycles per byte, I do not think any asymmetric ciphers can reach this speed, you have to exchange key everytime you want to send any infomations, the same key cannot be encrypted twice in cryptography.