1) A COMPLEX GEZEIRAH SHAVAH
QUESTION: The Gemara derives the punishment (Malkus) for Motzi Shem Ra from a protracted Gezeirah Shavah. The Gezeirah Shavah begins with a word in the verse which discusses Motzi Shem Ra (Devarim 22:18), links it to a word in the Parshah of Ben Sorer u'Moreh (Devarim 21:18), and then links that word to a word in the Parshah of Malkus (Devarim 25:2).
The Gemara earlier (45b) records a similarly protracted Gezeirah Shavah, which teaches that a Na'arah Me'urasah must be executed by the gate to her city. That Gezeirah Shavah begins with a word in the verse which discusses Motzi Shem Ra (Devarim 22:21), links it to a word in the Parshah about the Mishkan (Bamidbar 4:25), and then links that word to a word in the Parshah of Avodah Zarah (Devarim 17:5). RASHI there explains that the Gezeirah Shavah is only an Asmachta (and is not d'Oraisa).
Rashi apparently maintains that such a multiple Gezeirah Shavah is not a true form of Gezeirah Shavah and therefore is only mid'Rabanan. The RASHASH there (45b) explains that a source for Rashi's words may be found in Eruvin (51a), where the Gemara derives from a similar protracted Gezeirah Shavah the source for the Isur of Techumin of 2000 Amos on Shabbos, and yet the Isur of Techumin is only mid'Rabanan.
How, then, does Rashi understand the complex Gezeirah Shavah here from which the Gemara learns that the punishment for Motzi Shem Ra is Malkus? The Malkus of Motzi Shem Ra certainly is mid'Oraisa and not mid'Rabanan, as is clear from the Gemara earlier (end of 45b). If a protracted Gezeirah Shavah is only mid'Rabanan, there is no source for Malkus mid'Oraisa for Motzi Shem Ra! (RASHASH)
ANSWER: The RASHASH answers that there is a significant difference between these two multiple Gezeirah Shavahs. In the Gezeirah Shavah that teaches that a Na'arah Me'urasah is punished by the gate to her city, the word "Pesach" in the verse of Motzi Shem Ra (Devarim 22:21) is linked to the word "Pesach" in the verse about the Mishkan (Bamidbar 4:25), where "Pesach" is written next to the word "Sha'ar." The word "Sha'ar" is then linked to the word "She'arecha" in the Parshah of Avodah Zarah (Devarim 17:5), which teaches the Halachah of executing a person next to the gate of the city. The law that a Na'arah Me'urasah who was Mezanah is executed next to the gate of the city cannot be derived without first making an association of words -- "Pesach" and "Sha'ar" -- in the Parshah of the Mishkan. In such a case, the Gezeirah Shavah is only mid'Rabanan.
In contrast, in the Gezeirah Shavah that teaches that the punishment for Motzi Shem Ra is Malkus, the Halachah of Malkus is learned directly from Ben Sorer u'Moreh, which also has Malkus. That is, the word "v'Yisru" in the verse of Motzi Shem Ra (Devarim 22:18) is linked to the word "v'Yisru" in the Parshah of Ben Sorer u'Moreh (Devarim 21:18). The source that a Ben Sorer u'Moreh has Malkus is an independent Gezeirah Shavah of "Ben Ben" from the Parshah of Malkus (Devarim 25:2). Hence, Malkus for Motzi Shem Ra is learned directly from Ben Sorer u'Moreh, without the need to associate words first. It is a valid Gezeirah Shavah mid'Oraisa to learn one thing that was itself derived from another thing (as the Gemara says in Zevachim 49b).
Rashi may allude to this in his unusually lengthy explanation of this Gezeirah Shavah. This explanation is even more evident in the words of Rashi in Sanhedrin (71b, DH Lamadnu).

46b----------------------------------------46b

2) THE SOURCE THAT A FATHER MAY MARRY OFF HIS DAUGHTER WHO IS A NA'ARAH
QUESTION: The Gemara searches for the source that a father may accept and keep the money of Kidushin for his daughter when she is a Na'arah. The Gemara points out that the Torah gives the father the right to keep the payments of Boshes and Pegam when his daughter is raped. The Gemara suggests that perhaps that law is the source that the father also keeps the money of Kidushin.
The Gemara rejects this suggestion and asserts that there is a logical reason for why the father receives the money of Boshes and Pegam. Since "it pertains to him," he has legal entitlement to those payments, whereas Kidushin does not pertain to him. RASHI explains, based on the Gemara earlier (40b), that the reason why Boshes and Pegam are given to the father is that it was in his power to torment his daughter with Boshes and Pegam by marrying her off to a Menuval (a loathsome, repulsive person) or Mukeh Shechin (leper) and receive the money of Kidushin for doing so. Therefore, he is rightfully entitled to the money paid for her Boshes and Pegam.
Rashi's words are perplexing. The Gemara does not yet know that a man may marry off his Na'arah daughter and receive the money of Kidushin -- the Gemara is still seeking a source for that law! How can the Gemara say that he receives the payments of Boshes and Pegam because he could marry her off when we do not yet know that he may marry her off? (TOSFOS, Kidushin 3b)
ANSWERS:
(a) TOSFOS in Kidushin (3b, DH v'Chi Teima) answers that the Gemara means that the father receives the money of Boshes and Pegam since he may marry her off while she is a Ketanah. Since he could marry her off to a Menuval or Mukeh Shechin and she would continue to suffer Boshes and Pegam when she becomes a Na'arah, he is entitled to receive the payments of Boshes and Pegam even when she is a Na'arah (even if he could not marry her off at that stage). There is a source that the father may marry off his daughter when she is a Ketanah, as the Gemara earlier teaches.
Tosfos rejects this approach, however, because if the father is entitled to receive the payments of Boshes and Pegam when his daughter is a Na'arah since he could have married her off while she was a Ketanah, then he should also receive those payments even after she becomes a Bogeres! After all, he could have married her off when she was a Ketanah to a Menuval or Mukeh Shechin and she would still suffer from it as a Bogeres.
The CHASAM SOFER (Kesuvos 40b) has another objection to this approach. Even if her father marries her off to a Menuval or Mukeh Shechin, after the Nisu'in the husband can be forced to divorce her, as the Mishnah says later in Kesuvos (77a). (The Hagahos Ya'avetz here makes this point as well.)
TOSFOS earlier (40b, DH d'Iy Ba'i) gives a variation of this answer. Normally, a Ketanah is capable of receiving and keeping payments for physical damages done to her, as the Gemara says in Bava Kama (87b). However, payments for Boshes and Pegam are still given to her father and not to her. The Gemara attempts to learn from that law that the Kidushin of a Na'arah should also be given to the father even though the Na'arah has a "Yad" and is able to accept her own Kidushin.
The Gemara rejects this suggestion by saying that the payments of Boshes and Pegam of a Ketanah rightfully belong to her father (even though she is capable of receiving payment for physical damages), since he could have married her off while she was a Ketanah and received money for causing her to suffer Boshes and Pegam. There is a source that a father may marry off his daughter when she is a Ketanah, and therefore the Gemara's logic is sound. The Gemara is not saying that he could marry her off while she is a Na'arah.
(b) TOSFOS and the TOSFOS YESHANIM (40b) suggest that when the Gemara says that "it pertains to him," the Gemara does not mean that her father could marry her off to a Menuval or Mukeh Shechin. Rather, it means that her father himself suffers from the embarrassment and affliction experienced by his daughter. Therefore, there is more reason to give the payments of Boshes and Pegam to him than to give the money of Kidushin to him.
This answer is lacking, however, because the Gemara (40b) does not give this as the reason for why the father is entitled to the payments of Boshes and Pegam of his daughter. The Gemara says that he receives those payments because he could marry her off to a Menuval or Mukeh Shechin, as Rashi here writes. Why, then, does the Gemara here not respond that Boshes and Pegam cannot be a source for letting the father keep the money of Kidushin because -- on the contrary -- the fact that he receives the money of Kidushin is the source for why he receives the Boshes and Pegam?
Tosfos answers that the Gemara means to say that even if another source is found for why the Boshes and Pegam is given to the father, we still would not be able to learn from Boshes and Pegam that the father receives the money of Kidushin.
(c) TOSFOS in Kidushin (3b, and as cited by the Rishonim here) suggests that the Gemara understands that a Na'arah can become Mekudeshes either by herself or by her father. (This is in fact the way Reish Lakish understands the opinion of the Chachamim in Kidushin 43b.) Accordingly, the Gemara knows that the father may accept Kidushin for his daughter when she is a Na'arah and keep the money of Kidushin. The Gemara is asking for a source that even when the Na'arah marries herself off, the father still receives the money of Kidushin. The Gemara says that the source cannot be from Boshes and Pegam, because those payments are given to the father due to his ability to marry her off to a Menuval or Mukeh Shechin. (The Gemara in Kidushin 44a, however, concludes like Rebbi Yochanan who says that only the father may marry off his Na'arah daughter, and not the Na'arah herself.)
(This approach of Tosfos answers another question posed by Rashi (DH Ketanah). Rashi asks why the Gemara does not derive from "Es Biti Nasati" (Devarim 22:16) that the father may marry off his daughter when she is a Na'arah. According to Tosfos, although we learn from there that he may marry her off, the Gemara is asking why he receives the money of Kidushin when she marries herself off.)
(d) None of the above approaches conforms with the way Rashi (DH d'Shayach Bah) explains this Gemara. Perhaps Rashi has a different approach altogether.
Rashi may understand that the Gemara knows all along that a father may marry off his daughter who is a Na'arah, and that the Na'arah herself may not marry herself off. That Halachah may be derived from the Halachah of Hafaras Nedarim, since both are laws of Isur (as Tosfos himself asks as a question, DH Mamona). Thus, when the Gemara asks that we should learn that the father may marry her off and keep the money of Kidushin from the fact that he receives the money of Boshes and Pegam, it already knows that the father may marry off his Na'arah daughter but did not yet know that the money of the Kidushin goes to the father.
This answers another question. If we do not yet know that the father has the right to marry her off, then how can the Gemara derive that right from Boshes and Pegam? The law of Boshes and Pegam does not state that her father may marry her off, but only to whom the payments are given. It must be that the Gemara knows all along that the father may marry her off. The only question is when he does marry her off, who receives the money of the Kidushin, the father or the daughter?
Why does the Gemara not prove that the father receives the money of Kidushin from the Kal v'Chomer that it mentions earlier? If he is the one who marries her off, certainly he should receive the money. The answer is that the Gemara there means that if the father receives the money of Kidushin in order to marry her off, certainly he keeps that money and does not have to give it to his daughter after he effects the Kidushin by receiving the money. The verse of "Es Biti Nasati" implies that he may accept the money of Kidushin in order to make the Kinyan of Kidushin (and not just that he may agree to the Kidushin) when his daughter is a Ketanah, and if he may accept the money he certainly gets to keep it. In the case of a Na'arah, though, we know only that he may marry her off to someone, but we do not know who accepts the money. May the father accept the money (and keep it) or does the daughter accept the money?
The Gemara attempts to prove from Boshes and Pegam that the father should be the one to accept and keep the money, since it is similar to any other profit that his daughter makes (which he is entitled to keep). The Gemara rejects this proof on the basis that the reason the father may keep the money of Boshes and Pegam is because he may marry her off to a Menuval or Mukeh Shechin (and receive money of Kidushin for causing her to suffer Boshes and Pegam).
This explanation sheds light on another perplexing point in the words of Rashi. When the Gemara rejects the proof from Boshes and Pegam, Rashi explains that the father could take money for marrying her off with "Kidushei Bi'ah" to a Menuval or Mukeh Shechin. Why does Rashi mention Kidushei Bi'ah? The father could marry her off with any type of Kidushin, including Kesef and Shtar (and afterwards the Menuval will be Bo'el her)!
Rashi may mean that the Gemara knows already that the father has the right to agree to or refuse the Kidushin; the question is only who accepts the money or Shtar of the Kidushin. Since it is possible that the daughter is the one who accepts the Kesef or Shtar, the Gemara cannot be saying that the father has the ability to give his daughter to a Menuval in exchange for being Mekadesh her with Kidushei Kesef or Shtar, because even though the father agrees to the Kidushin, if his daughter refuses to accept (and make a Kinyan on) the Kesef or Shtar the Kidushin cannot take effect. Therefore, it is not within the father's power to effect such a Kidushin against his daughter's will. However, he could tell a Menuval or Mukeh Shechin to go and be Bo'el his daughter and be Mekadesh her with Bi'ah. Even if the Mukeh Shechin does that against the will of the Na'arah, the Kidushin will be valid because it is done with the consent of the father. Consequently, the father is entitled to take the money for the Boshes and Pegam, even if he is not entitled to take the money of Kidushei Kesef.
In contrast, Rashi earlier (40b) says that Boshes and Pegam go to the father since he could be Mekadesh her with Kidushei Kesef, Shtar, or Bi'ah to a Menuval or Mukeh Shechin. Rashi there is following the conclusion of the Gemara here, that a father may accept Kesef or a Shtar for his daughter's Kidushin. (M. Kornfeld)