MARCUS, Circuit Judge:
In December 1999, Christina Aragao and her two children were abducted and held hostage for several days before being freed by police. For their roles in the kidnapping, appellants Jean Carlo Ferreira, Pedro Rafael Caraballo-Mar-tinez, and Ewin Oscar Martinez were convicted of hostage taking and conspiracy to commit hostage taking in violation of the Hostage Taking Act, 18 U.S.C. § 1203, carjacking and conspiracy to commit carjacking in violation of 18 U.S.C. §§ 371, 2119(2), and [for] using and carrying a firearm during and in relation to a crime of violence in violation of 18 U.S.C. § 924(c). Each was sentenced to life in prison. In this appeal, they raise three significant challenges to their convictions and sentences — that the Hostage Taking Act is unconstitutional because it discriminates impermissibly on the basis of alien-age and that Congress lacked the power to enact it; that Congress likewise lacked the power to enact the firearms statute; and, finally, that the district court erred in applying a six-level enhancement pursuant to U.S.S.G. § 2A4.1(b)(l) because a ransom note was never delivered. We are unpersuaded by those arguments and, accordingly, affirm.
I.
As they are relevant to the appeal, the following facts were established at trial and during the sentencing proceedings. On December 13, 1999, Christina Aragao and her two children, Alceu Aragao, Jr. (“Junior”), age nine, and Alexander Ara-gao, age one, were attacked by three men in a parking garage near their condominium home in Aventura, Florida. Mrs. Ara-gao was shocked repeatedly with stun guns. The electric shocks caused her to drop her baby to the floor of the garage. She screamed loudly and was struck in her face five or six times by one of the attackers. Junior attempted to flee but was shot in the head and neck with a stun gun and caught by another of the attackers. The Aragaos then were forced into one of the family’s cars, a Lincoln Navigator SUV, to which the attackers had previously obtained keys, and driven to a house approximately fifteen minutes away.
Inside the house, the attackers tied Mrs. Aragao’s hands and legs to a chair and placed her in a closet. They did the same to Junior and placed him in a different closet. The baby was kept in another room. The next day, Mrs. Aragao and Junior were removed from the closet and required to stay in shuttered rooms. Mrs. Aragao was permitted to care for the baby, but because her arm was still numb from the electric shocks, she was unable to lift or change him. When their captors left the house, Mrs. Aragao and Junior once again were tied to chairs and put into closets. At night, Junior was forced to sleep in his underwear in a bed with Martinez.
The Aragaos were held captive in the North Miami house for four and one-half days. During that time, Mrs. Aragao was required to use her cellular phone to make a series of calls to her husband, a successful businessman, requesting that he meet with Martinez. Each time, Martinez dictated what she was to say. When the phone calls did not result in a meeting, Martinez required Mrs. Aragao to type a letter that he dictated requesting a meeting with Mr. Aragao. The letter was mailed to Ipanema Enterprises, the company owned by Mr. Aragao.
By tracing one of the cellular phone calls, the FBI was able to locate the house at which the Aragaos were being held captive, and the family was rescued on the morning of December 18, 1999. Martinez and Caraballo-Martinez were arrested at that time. Among other evidence in the house, the police found a torn letter addressed to Mr. Aragao in a trash can. When reconstructed, the letter stated that if Mr. Aragao did not turn over all of his money, he and his family would be killed. An identical letter was found in a file on Martinez’s laptop computer.
At trial, Mrs. Aragao and Junior identified Martinez and Caraballo-Martinez as two of the three men who abducted them. Ferreira was not identified as the third abductor. Rather, he was the parking lot attendant at the Aragao’s condominium complex and had provided the keys to the Aragao’s Lincoln Navigator. Additionally, Junior testified that Ferreira had asked him about the family’s plans for the evening of the abduction. Telephone records showed that during the time the Aragao’s were held captive, a cellular phone registered to Ferreira made 22 calls to a cellular phone registered to Martinez and found in the North Miami house.
A grand jury indicted Martinez, Cara-ballo-Martinez, and Ferreira for violating the Hostage Taking Act, carjacking, and using a firearm during a crime of violence. Martinez also was charged with knowingly possessing child pornography in violation of 18 U.S.C. § 2252A(a)(5)(B). The child pornography count was severed, and the three appellants were tried jointly. The trial ended on June 2, 2000, and the jury found the appellants guilty on the remaining counts.
In the presentence investigation report (PSI), the offenses were grouped into three categories based on the three victims, and a base offense level of 24 was determined for the abduction. The PSI recommended enhancements on the grounds that the children were vulnerable victims, that Mrs. Aragao and Junior suffered serious, permanent, or life-threatening bodily injuries, that a dangerous weapon was used, and that the appellants obstructed justice by lying at trial.
See
U.S.S.G. §§ 2A4.1(b)(2), 2A4.1(b)(3), 3A1.1(b)(1), 3C1.1.
Additionally, the PSI recommended a six-level enhancement for each appellant pursuant to U.S.S.G. § 2A4.1(b)(1) because a ransom demand was made. The district judge adopted each of the recommendations,
and sentenced each defendant to life imprisonment for Counts I and II, 60 months for Count III, and 300 months for Count IY, to be served concurrently, and a consecutive term of 60 months for Count V.
II.
We review
de novo
appellants’ challenges to the Hostage Taking Act and to the firearms statute.
See United States v. Gray,
260 F.3d 1267, 1271 (11th Cir. 2001) (citations omitted) (reviewing
de novo
a challenge to the constitutionality of a criminal statute). A challenge to the application of the sentencing guideline is a mixed question of law and fact. We review the district court’s findings of fact for clear error and its application of the sentencing guidelines to those facts
de novo. United States v. Jamieson,
202 F.3d 1293, 1295 (11th Cir.2000). Moreover, “[(Interpretation of the Sentencing Guidelines is similar
to
statutory interpretation and is subject to de
novo
review on appeal.”
United States v. Goolsby,
908 F.2d 861, 863 (11th Cir.1990) (citations omitted).
A.
Each of the appellants was convicted of conspiracy to commit hostage taking and hostage taking in violation of the Hostage Taking Act, 18 U.S.C. § 1203. In relevant part, that provision states that:
(a) Except as provided in subsection (b) of this section, whoever, whether inside or outside the United States, seizes or detains and threatens to kill, to injure, or to continue to detain another person in order to compel a third person or a governmental organization to do or abstain from doing any act as an explicit or implicit condition for the release of the person detained, or attempts or conspires to do so, shall be punished by imprisonment for any term of years or for life and, if the death
of
any person results, shall be punished by death or life imprisonment.
(b)(1) It is not an offense under this section if the conduct required for the offense occurred outside the United States unless—
(A) the offender or the person seized or detained is a national of the United States;
(B) the offender is found in the United States; or
(C) the governmental organization sought to be compelled is the Government of the United States.
(2) It is not an offense under this section if the conduct required for the offense occurred inside the United States, each alleged offender and each person seized or detained are nationals of the United States, and each alleged offender is found in the United States, unless the governmental organization sought to be compelled is the Government of the United States.
18 U.S.C. § 1203.
Initially, appellants say that the Hostage Taking Act violates their Fifth Amendment right to equal protection by discriminating impermissibly on the basis of alien-age. The government concedes that the Act “by its own terms applies only to aliens and, consequently, treats aliens differently than United States citizens,” (Gov’t Br. at 25),
but disagrees that the classification is unconstitutional.
Appellants’ argument is grounded on the erroneous foundation that congressional classifications based on alienage are subject to strict scrutiny. While it is true that strict scrutiny applies to
state
classifications of aliens, we have held expressly that
congressional
classifications based on alienage are subject to rational basis review.
See Rodriguez v. United States,
169 F.3d 1342, 1347 (11th Cir.1999);
Tefel v. Reno,
180 F.3d 1286,1298-99 (11th Cir.1999);
Yeung v. I.N.S.,
76 F.3d 337, 339 (11th Cir.1996). In other words, Congress can pass laws regulating the conduct of non-citizens within the United States, and those laws do not violate equal protection so long as they are rationally related to a legitimate government interest. The reasons behind the dichotomy between federal and state authority lie in Congress’s “broad power over naturalization and immigration,” which enables the Congress, not the states, to make rules applicable to aliens that “would be unacceptable if applied to citizens.”
Mathews v. Diaz,
426 U.S. 67, 79-80, 96 S.Ct. 1883, 1891, 48 L.Ed.2d 478 (1976). As the Supreme Court explained:
For reasons long recognized as valid, the responsibility for regulating the relationship between the United States and our alien visitors has been committed to the political branches of the Federal Government. Since decisions in these matters may implicate our relations with foreign powers, and since a wide variety of classifications must be defined in the light of changing political and economic circumstances, such decisions are frequently of a character more appropriate to either the Legislature or the Executive than to the Judiciary.
Id.
at 81, 96 S.Ct. at 1892. Accordingly, the Court found that “decisions made by the Congress or the President in the area of immigration and naturalization” are subject to “a narrow standard of review” that is equivalent to rational basis scrutiny.
Id.
at 82, 96 S.Ct. at 1892.
See also Rodriguez,
169 F.3d at 1347.
Appellants’ efforts to avoid this conclusion and distinguish these cases are unper
suasive. The majority of the cases they cite apply strict scrutiny to
state
laws and, therefore, are plainly inapplicable in this context.
See, e.g., Graham v. Richardson,
403 U.S. 365, 371-72, 91 S.Ct. 1848, 1851-52, 29 L.Ed.2d 534 (1971) (applying strict scrutiny to a state law classification based on alienage). Appellants also attempt to distinguish
Rodriguez
and
Mathews
on the grounds that the law at issue in this case is criminal rather than civil and that those cases were based on Congress’s special authority over aliens with respect to immigration and naturalization matters and not to classifications of aliens more generally. They do not, however, provide any case law or rationale to support those arguments, and we are not persuaded by them. The Supreme Court did not limit its holding in
Mathews
to civil cases, and we can find no persuasive reason to do so in this case. Moreover, the Court’s language in
Mathews
is applicable to congressional classifications of aliens generally and not simply to its classification of aliens during the immigration or naturalization process.
See Mathews,
426 U.S. at 80, 96 S.Ct. at 1891 (“The fact that an Act of Congress treats aliens differently from citizens does not in itself imply that such disparate treatment is ‘invidious.’ ”).
We agree with every other circuit court of appeals that has confronted this issue, and apply rational basis review to the statute.
See United States v. Montenegro,
231 F.3d 389, 395 (7th Cir.2000) (concluding that the Hostage Taking Act survives rational basis review);
United States v. Santos-Riviera,
183 F.3d 367, 373 (5th Cir. 1999) (rejecting the contention that the Hostage Taking Act should be reviewed using strict scrutiny);
United States v. Lue,
134 F.3d 79, 87 (2d Cir.1998) (“As long as the Hostage Taking Act is rationally related to a legitimate government interest it satisfies principles of equal protection in this context.”);
United States v. Lopez-Flores,
63 F.3d 1468, 1473-74 (9th Cir.1995) (“The same principles that animate both the Constitution’s grant of plenary control over immigration legislation to Congress and the attendant low level of judicial review of such legislation dictate a similarly low level of review here, where foreign policy interests are strongly implicated.”).
Accordingly, the Hostage Taking Act is a valid exercise of congressional authority so long as it is “rationally related to the achievement of a legitimate government purpose.”
Joel v. City of Orlando,
232 F.3d 1353, 1357 (11th Cir.2000) (citation omitted),
cert. denied,
532 U.S. 978, 121 S.Ct. 1616, 149 L.Ed.2d 480 (2001). We apply a two-step analysis in determining whether that standard is met:
The first step in determining whether legislation survives rational-basis scrutiny is identifying a legitimate government purpose — a goal — which the enacting government body
could
have been pursuing. The
actual
motivations of the enacting governmental body are entirely irrelevant.... The second step of rational-basis scrutiny asks whether a rational basis exists for the enacting governmental body to believe that the legislation would further the hypothesized purpose. The proper inquiry is concerned with the
existence
of a conceivably rational basis, not whether that basis was actually considered by the legislative body. As long as reasons for the legislative classification may have been considered to be true, and the relationship between the classification and the goal is not so attenuated as to render the distinction arbitrary or irrational, the legislation survives rational-basis scrutiny.
Id.
at 1358 (quoting
Haves v. City of Miami,
52 F.3d 918, 921-22 (11th Cir.1995)) (emphasis in original).
The first of those requirements — a legitimate government purpose — is easily satisfied because Congress passed the Hostage Taking Act to implement the International Convention Against the Taking of Hostages, Dec. 18, 1979, T.I.A.S., No. 11,081 (“Convention”). Thus, as the Second Circuit noted, the purpose of the Act is “to address a matter of grave concern to the international community: hostage taking as a manifestation of international terrorism.”
Lue,
134 F.3d at 87. Indeed the wording of the Act tracks precisely the language of the Convention.
See
Convention, art. I, II (requiring the implementing country to make “seizing] or detain[ing] and threaten[ing] to kill, to injure or to continue to detain another person ... in order to compel a third party, namely, a State, an international intergovernmental organization, a natural or juridical person, or a group of persons, to do or abstain from doing any act ... punishable by appropriate penalties”).
Second, although, as appellants point out, there are state laws designed to combat domestic terrorism, Congress enacted the Act because it believed that kidnapping involving foreign nationals has serious international ramifications, which are Congress’s unique responsibility. Thus, the second prong is met because, as the Second Circuit held,
Congress rationally concluded that a hostage taking within our jurisdiction involving a noncitizen is sufficiently likely to involve matters implicating foreign policy or immigration concerns as to warrant a federal criminal proscription. The connection between the act and its purpose is not so attenuated as to fail to meet the rational-basis standard.
Lue,
134 F.3d at 87. Accordingly, we agree with all of the other circuits to have confronted the issue that the Hostage Taking Act is rationally related to a legitimate government interest.
See id.; Montenegro,
231 F.3d at 395 (adopting the holding of Lue);
Santos-Riviera,
183 F.3d at 373 (same);
Lopez-Flores,
63 F.3d at 1475.
Appellants also suggest that Congress lacked the authority under any of its constitutionally enumerated powers to enact the Hostage Taking Act, whether that power derives from the Commerce Clause, the Law of Nations Clause, or from its broad power to regulate immigration and naturalization. Those arguments, however, are misplaced. The Hostage Taking Act was passed in order to implement the International Convention Against the Taking of Hostages, and thus congressional authority may be found in the Necessary and Proper Clause.
The Necessary and Proper Clause provides that “Congress shall have Power ... [t]o make all Laws which shall be necessary and proper for carrying into Execution the foregoing Powers, and all other Powers vested by this Constitution in the Government of the United States, or in any Department or Officer thereof.” U.S. Const., art I, § 8. As the Second Circuit noted in
Lue,
because “Congress’s authority under the Necessary and Proper Clause extends beyond those powers specifically enumerated in Article I, section 8[, it] may enact laws necessary to effectuate the treaty power, enumerated in Article II of the Constitution.”
Lue,
134 F.3d at 82 (citing
Missouri v. Holland,
252 U.S. 416, 432, 40 S.Ct. 382, 383, 64 L.Ed. 641 (1920);
Neely v. Henkel,
180 U.S. 109, 121, 21 S.Ct. 302, 306, 45 L.Ed. 448 (1901)). Thus, “[i]f the Hostage Taking Convention is a valid exercise of the Executive’s treaty power, there is little room to dispute that the legislation passed to effectuate the treaty is valid under the Necessary and Proper Clause.”
Id.
at 84 (citing
Holland,
252 U.S. at 432, 40 S.Ct. at 383, for the proposition that, under normal circum
stances, “[i]f the treaty is valid there can be no dispute about the validity of [a] statute [passed] under Article I, Section 8, as a necessary and proper means to execute the powers of the Government”).
We agree with the Second Circuit’s analysis and conclusion that “the Hostage Taking Convention is well within the boundaries of the Constitution’s treaty power,”
id.
at 83, and similarly conclude that Congress had authority under the Necessary and Proper Clause to enact the Hostage Taking Act.
B.
In addition to being found guilty of the hostage taking and carjacking counts, each appellant was convicted under the firearms statute making it a federal crime to use and carry a firearm during a crime of violence.
See
18 U.S.C. § 924(c) (providing additional penalties for a person “who, during and in relation to any crime of violence, ... uses or carries a firearm, or who, in furtherance of any such crime, possesses a firearm....”). Appellant Caraballo-Martinez argues that those convictions cannot stand because Congress lacked the power under the Commerce Clause to enact that provision.
In making that argument, Caraballo-Martinez relies primarily on
United States v. Lopez,
514 U.S. 549, 115 S.Ct. 1624, 131 L.Ed.2d 626 (1995). After the Court’s decision in
Lopez,
however, we squarely rejected precisely the same argument Caraballo-Martinez now makes.
See United States v. DePace,
120 F.3d 233, 235 n. 2 (11th Cir.1997) (agreeing with those courts that have rejected the idea “that 18 U.S.C. § 924(c) is an unconstitutional effort to regulate intrastate, non-economic activity”) (citing
United States v. Brown,
72 F.3d 96, 96-97 (8th Cir.1995);
United States v. Leshuk,
65 F.3d 1105, 1111-12 (4th Cir. 1995)). We add that nothing in the Supreme Court’s recent rulings in
Jones v. United States,
529 U.S. 848, 120 S.Ct. 1904, 146 L.Ed.2d 902 (2000), or
United States v. Morrison,
529 U.S. 598, 120 S.Ct. 1740, 146 L.Ed.2d 658 (2000), alters that conclusion.
Cf. Gray,
260 F.3d at 1270 (concluding that “nothing in
Morrison
or
Jones
alters our previous conclusion that, to convict a defendant for Hobbs Act robbery, the Government must prove a minimal, but not substantial, effect on interstate commerce.”).
C.
Finally, the district court enhanced the appellants’ sentences under U.S.S.G. § 2A4.1(b)(l), which provides for a six-level increase “[i]f a ransom demand or demand upon government was made” in the course of a kidnapping or abduction. U.S.S.G. § 2A4.1(b)(l). The parties agree that, although a ransom letter was drafted on Martinez’s computer and was printed, it was never actually delivered to Mr. Aragao. Appellants Ferreira and Martinez argue, therefore, that the enhancement was
improper
because § 2A4.1(b)(l) requires that a ransom demand “was made.”
The district court rejected that contention, as do we. The district court held that the guideline language must be read
in pari materia
with the application notes accompanying it. Specifically, Application Note Five to § 2A4.1 states that “[i]n the case of a conspiracy, attempt, or solicitation to kidnap, § 2X1.1 (Attempt, Solicitation or Conspiracy) requires that the court apply any adjustment that can be determined with reasonable certainty.” U.S.S.G. § 2A4.1, comment, (n.5). Reading the commentary alongside the guideline language, the district court concluded that an enhancement is appropriate if it could be determined “with reasonable certainty” that a ransom demand would have been made but for the appellants’ capture.
The district court then found that the repeated phone calls to Mr. Aragao together with the torn letter made it “reasonably certain” that the appellants would have made a ransom demand if doing so had been feasible.
Appellants argue that the district court erred in relying on the application note in this case because the guideline language plainly requires that the ransom demand “was made.” In making that argument, they cite our opinion in
United States v. Chastain,
198 F.3d 1338 (11th Cir.1999), for the proposition that, where the Guidelines provide for an enhancement based on a completed act, as evidenced by the use of the past tense, the act must actually have occurred in order for the enhancement to apply. In
Chastain,
the defendants attempted to use a private plane to import narcotics, but the plane crashed before the crime could be executed. During sentencing, the district court granted a two-level enhancement pursuant to U.S.S.G. § 2Dl.l(b)(2), which is entitled “Unlawful Manufacturing, Importing, Exporting, or Trafficking (Including Possession with Intent to Commit These Offenses); Attempt or Conspiracy,” and permits the increase “[i]f the defendant unlawfully imported or exported a controlled substance under circumstances in which an aircraft other than a regularly scheduled commercial air carrier was used to import or export the controlled substance....” In granting the two-level enhancement, the district court relied on the words “attempt or conspiracy” in the title.
Id.
at 1353. On appeal, we determined that the language required that the airplane was “used to import” and, therefore, contemplated a “completed event, an actual importation.”
Id.
Accordingly, we found it unnecessary to look to the title of the guideline to explain what was clear in'the text and reversed because there was no completed importation.
Id.
Appellants’ reliance on
Chastain,
however, is misplaced. In
Chastain,
there was no application note supporting U.S.S.G. § 2D1.1(b)(2), the provision at issue in that case. Had there been an application note, nothing in
Chastain
suggests that we would not have considered it. There is a substantial difference between the title of a guideline provision and commentary or an application note to a guideline provision. A stated purpose of the commentary is to “interpret the guideline or explain how it is to be applied.” U.S.S.G. § 1B1.7.
See also Stinson v. United States,
508 U.S. 36, 44, 113 S.Ct. 1913, 1918, 123 L.Ed.2d 598 (1993) (“[C]ommentary explains the guidelines and provides concrete guidance as to how even unambiguous guidelines are to be applied in practice.”). There is no such stated purpose for the title, and we have held that the title of a statutory provision may be useful only when it sheds light on some ambiguous word or phrase.
Adler v. Duval County Sch. Bd.,
206 F.3d 1070, 1087 (11th Cir.1999),
vac. on other grounds,
531 U.S. 801, 121 S.Ct. 31, 148 L.Ed.2d 3 (2000), and
opinion reinstated,
250 F.3d 1330 (11th Cir.2001),
cert. denied,
— U.S. , 122 S.Ct. 664, 151 L.Ed.2d 579 (2001). No restriction is placed on the use of the application notes and, in fact, exactly the contrary is true— the guideline and the commentary must be “read together.”
See, e.g., United States v. Pedragh,
225 F.3d 240, 244 (2d Cir.2000) (holding that, “since the commentary is part and parcel of the Sentencing Guidelines Manual and, as the Supreme Court has pointed out, is written by the same body that is charged with drafting the guidelines, the two are to be read together”).
See also United States v. Gay,
240 F.3d 1222, 1232 (10th Cir.2001).
Finally, the appellants’ contention that a ransom note must actually have been delivered is directly contrary to the applica
tion note’s requirement that the court apply any adjustment that can be determined with “reasonable certainty.” Thus, in order to adopt appellants’ reading of the guideline language, we would be required to ignore the application note entirely. That, we are unwilling to do. Rather, we conclude that the district court correctly interpreted U.S.S.G. § 2A4.1(b)(l). Because the phone calls to Mr. Aragao coupled with the letter found in the North Miami house made it “reasonably certain” that the appellants would have made a ransom demand if doing so had been feasible, the district court appropriately granted the six-level enhancement.
III.
In sum, we conclude that the Hostage Taking Act does not violate the Equal Protection Clause, that the codification of that statute and 18 U.S.C. § 924(c) are valid exercises of congressional authority, and that the district court appropriately granted a six-level enhancement upon a determination that the appellants intended to make a ransom demand. Accordingly, we find no error and affirm the appellants’ convictions and sentences.
AFFIRMED.