Nidah 26a - Shiur of Shofar is a Tefach

The gemara lists 5 items that have a minimum shiur of a tefach. At the end of the sugya, the gemara explains that all of these items are כתיבן ולא מפרשי שיעורייהו, meaning they are d'oraysa, but the Torah itself doesn't tell us their shiur. It isn't clear from the gemara whether the intention is that the torah doesn't have a shiur, and the entire shiur is only rabbinic, or whether the Rabbonon are needed to tell us what the shiur d'oraysa is. Rashi explains that the beam of a mavoy doesn't make it into the list because it is only rabbinic - דכל מצותו מדברי סופרים. From Rashi one can deduce that for the 5 that are listed, they are all Torah mitzvos, but their shiur may only be Rabbinic. However, the simpler understanding is that the Torah doesn't clearly teach the shiur, but the shiur is considered to be a d'oraysa shiur.

The shiur given for shofar is כדי שיאחזנו בידו ויראה לכאן ולכאן טפח. The difficulty is that if the shiur were to make the shofar visible when held by one's hand, it is not really a shiur of a tefach, rather a method of making it visible. And if the shiur were truly a tefach, why do we need a reason given for the shiur being a tefach? If the shiur was only m'drabonon then we can accept the shiur not really being a tefach, rather making sure the shofar was visible so it didn't look like one was blowing in their hand. The Rosh in Maseches Rosh HaShana (3:6) writes explicitly that the reason for the shiur being that it must extend out of one's hand is כדי שלא יאמרו לתוך ידו הוא תוקע. From the Rosh it would seem that the entire shiur of tefach was only d'rabonon. Minchas Chinuch (end of mitzvah 405) cites Pri Megadim who says explicitly that the shiur is only d'rabonon and that min ha'torah there is no shiur at all. The Minchas Chinch disagrees by citing Tosafos in Succah 7b who indicates that the shiurim of tefach are min ha'torah, not merely rabbinic. The Biur Halacha suggest that even according to the Rosh who implies that the shiur of tefach is only rabbinic, doesn't undermine the concept of shiur d'oraysa. It could be that on a torah level the shiur is that it be large enough to blow through, then the rabbonon institute the shiur of a tefach.

The Tosafei HaRosh on our gemara writes that really the shiur of holding it and being visible on both sides is equal to a tefach, but the braisa wants to teach the reason for this shiur - ונקטינן בהאי לישנא כדי לפרש הטעם. It seems from the Rosh as he writes in Rosh Hashana that the shiur of being visible is to prevent the appearance that he is blowing into his hand. It is not clear whether this would be subjective. Meaning, one who has very large hands and is blowing shofar should perhaps require a larger shofar.
Tosafos questions why we don't mention the shiur tefach that we find in chulin in the context of treifos. Tosafos writes that according to the conclusion of the gemara that we are only speaking about things which are Rabbinic, only shiurim of things that are in the Torah when the shiur isn't explicit in the Torah. The Maharatz Chiyus point out that this is implies that shiurim by treifos are only d'rabonon. This contradicts the general assumption that they are d'oraysa from a halacha l'moshe mi'sinai.