Does anyone know what’s the reason base64 encoded strings uses the characters + and / ?
Why not @ and #, or ^ and * ?
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The stated design goal for base64 is given in the MIME RFCs and their precedessors. The earliest I found is RFC 1113, whose encoding method was reused almost without change in MIME base64. Quoting the oldest MIME RFC, RFC 1341
RFC 1113 makes the following point:
Of the characters you specifically suggest,
@,#and^do not exist in many variants of ISO 646 (which were in common use in the early 1990s).