Recent　years　have　seen　the　importance　of　ensuring　the　safety　and　confidentiality　of　communication　and　digital　data　storage.　Thus,　secure　cryptosystems　are　needed　to　guarantee　security　issues.　Among　them　are　asymmetric　cryptography　algorithms,　which　have　been　widely　applied　for　carrying　out　key　distribution　and　digital　signature.　This　paper　focuses　on　the　current　mainstream　types　of　asymmetric　cryptography,　including　the　Rivest-Shamir-Adleman　(RSA)　algorithm,　the　Elgamal　algorithm,　and　the　Elliptic　curve　cryptography　(ECC)　algorithm,　and　discuss　their　characteristics,　advantages　as　well　as　prospects,　respectively.　©　2021　IEEE.