Why the index is not used ?

Hi

I would like to submit the following problem to the PostgreSQL community. In my company, we have data encryption needs.
So I decided to use the following procedure :

(1)    Creating a table with a bytea type column to store the encrypted data
CREATE TABLE cartedecredit(card_id SERIAL PRIMARY KEY, username VARCHAR(100), cc bytea);

(2)    inserting encrypted data
INSERT INTO cartedecredit(username,cc)  SELECT 'individu ' || x.id, pgp_sym_encrypt('test value ' || x.id, 'motdepasse','compress-algo=2, cipher-algo=aes256') FROM generate_series(1,100000) AS x(id);  

(3)    Querying the table
SELECT pgp_sym_decrypt(cc, 'motdepasse') FROM cartedecredit WHERE pgp_sym_decrypt(cc, 'motdepasse')='test value 32';

pgp_sym_decrypt

-----------------

test value 32

(1 row)

Time: 115735.035 ms (01:55.735)
-> the execution time is very long. So, I decide to create an index

(4)    Creating an index on encrypted data
CREATE INDEX idx_cartedecredit_cc02 ON cartedecredit(cc);

(5)    Querying the table again

SELECT pgp_sym_decrypt(cc, 'motdepasse') FROM cartedecredit WHERE pgp_sym_decrypt(cc, 'motdepasse')='test value 32';
pgp_sym_decrypt

-----------------

test value 32

(1 row)

Time: 118558.485 ms (01:58.558) -> almost 2 minutes !!
postgres=# explain analyze SELECT pgp_sym_decrypt(cc, 'motdepasse') FROM cartedecredit WHERE pgp_sym_decrypt(cc, 'motdepasse')='test value 32';

                                                      QUERY PLAN

----------------------------------------------------------------------------------------------------------------------

Seq Scan on cartedecredit  (cost=0.00..3647.25 rows=500 width=32) (actual time=60711.787..102920.509 rows=1 loops=1)

   Filter: (pgp_sym_decrypt(cc, 'motdepasse'::text) = 'test value 32'::text)

   Rows Removed by Filter: 99999

Planning time: 0.112 ms

Execution time: 102920.585 ms

(5 rows)

è the index is not used in the execution plan. maybe because of the use of a function in the WHERE clause. I decide to modify the SQL query

(6)    Querying the table
SELECT pgp_sym_decrypt(cc, 'motdepasse') FROM cartedecredit WHERE cc=pgp_sym_encrypt('test value 32', 'motdepasse');
pgp_sym_decrypt

-----------------

(0 rows)

Time: 52659.571 ms (00:52.660)

è The execution time is very long and I get no result (!?)

                                                    QUERY PLAN

-------------------------------------------------------------------------------------------------------------------

Seq Scan on cartedecredit  (cost=0.00..3646.00 rows=1 width=32) (actual time=61219.989..61219.989 rows=0 loops=1)

   Filter: (cc = pgp_sym_encrypt('test value 32'::text, 'motdepasse'::text))

   Rows Removed by Filter: 100000

Planning time: 0.157 ms

Execution time: 61220.035 ms

(5 rows)

è My index is not used.

QUESTIONS :
-      why I get no result ?

-        why the index is not used?

Thanks in advance

Best Regards
Didier