Why can't we use MD5/SHA1
Too fast, easily cracked by brute force. Nowadays, graphics cards can count billions of times per second.
Modern Hash Algorithm
Bcrypt: Classic choice, slow hashing. Argon2: Champion of Password Hash Competition, highly recommended. PBKDF2: NIST recommendation, good compatibility.
Practical suggestions
Add salt; Select high cost parameter; Regularly upgrade algorithms; Don't invent hashing yourself.
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