yes, the card needs to support all algorithms,
crypto_newsession() does this:

        /*
         * The algorithm we use here is pretty stupid; just use the
         * first driver that supports all the algorithms we need. Do
         * a double-pass over all the drivers, ignoring software ones
         * at first, to deal with cases of drivers that register after
         * the software one(s) --- e.g., PCMCIA crypto cards.
         *
         * XXX We need more smarts here (in real life too, but that's
         * XXX another story altogether).
         */

-m

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