No reduction from CPA Security to IND$-CPA Security

A reduction of class unstated from CPA Security to IND$-CPA Security would imply a contradiction.

Statement

Migrated verbatim from symmetric-key-encryption § IND$-CPA Security:

is negligible. IND$-CPA implies CPA security, but not vice versa.

Notes

source: folklore: the claim carried no citation on the page it was migrated from, and none was invented.

class: unstated: no citing page says which notion of reduction is meant. Recording a class the wiki does not state would add a claim.

Recorded during migration and not fixed — these are claims about the source text, not changes to it:

• The ‘but not vice versa’ half is a separation stated with no counterexample and no citation.
• Separation is unconditional-by-counterexample (a CPA-secure scheme with structured ciphertexts), which the page does not give.