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; Pre-image resistance: Given a hash value {{math|''h''}}, it should be difficult to find any message {{math|''m''}} such that {{math|1=''h'' = hash(''m'')}}. This concept is related to that of a [[one-way function]]. Functions that lack this property are vulnerable to [[preimage attack]]s.
; Second pre-image resistance: Given an input {{math|''m''{{sub|1}}}}, it should be difficult to find a different input {{math|''m''{{sub|2}}}} such that {{math|1=hash(''m''{{sub|1}}) = hash(''m''{{sub|2}})}}. This property is sometimes referred to as ''weak collision resistance''. Functions that lack this property are vulnerable to [[
; [[Collision resistance]]: It should be difficult to find two different messages {{math|''m''{{sub|1}}}} and {{math|''m''{{sub|2}}}} such that {{math|1=hash(''m''{{sub|1}}) = hash(''m''{{sub|2}})}}. Such a pair is called a cryptographic [[hash collision]]. This property is sometimes referred to as ''strong collision resistance''. It requires a hash value at least twice as long as that required for pre-image resistance; otherwise, collisions may be found by a [[birthday attack]].{{sfn|Katz|Lindell|2014|pp=155–157, 190, 232}}
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