Defendant Edward A. Johnson was convicted of crimes which focused on sales between 1982 and 1987 to Chilean purchasers of zirconium which was made into cluster bombs sold to Iraq. Although the export of the zirconium for this purpose was prohibited by laws of the United States, Johnson sought to defend the charges against him by establishing that the United States — in particular, Presidents Ronald Reagan and George Bush, the Central Intelligence Agency and high ranking members of the military- — encouraged the Teledyne companies, Johnson’s employers, to export the zirconium, knowing the purchasers would use it to manufacture cluster bombs for Iraq, because at that time the United States was secretly supporting Iraq in its war with Iran. The district court held that the defendant failed to make his case in this regard. Rulings made in connection with that decision are at the heart of this appeal. We affirm.

Defendant Edward A. Johnson was convicted by a jury on four counts: criminal conspiracy, 18 U.S.C. § 371, making false statements to the government, 18 U.S.C. § 1001, and two counts of exporting zirconium compacts in violation of the Arms Export Control Act (“AECA”), 22 U.S.C. § 2778. He appeals with issues relating to the “materiality” requirement of false statement prosecutions, the definition of the United States Munitions List referred to in the AECA, the use of classified information as evidence in criminal trials, and the proper jury instruc[*1362] tions for the defense of good faith reliance on the advice of counsel. The government cross-appeals Johnson’s sentence.

CHARGES

The Arms Export Control Act authorizes the President to designate a special list of defense-related articles, known as the “Munitions List,” which require a special license from the Department of State before they legally may be exported from the United States. See 22 U.S.C. § 2778(a)(1) (1994). Defense-related articles which also have nonmilitary applications, known as “dual use” items, are excluded from the Munitions List and only require an export license from the Department of Commerce. See 22 C.F.R. § § 120.3-120.4(1985).

Johnson was convicted for his role in a conspiracy to illegally export zirconium compacts to Chile. Although the zirconium compacts were used to manufacture cluster bombs, the end-use statements used to procure export licenses stated that the zirconium would be used in industrial explosives. Johnson was charged with criminal conspiracy, exporting zirconium compacts designed for use in cluster bombs without a license from the Department of State, and making false statements to the government. All of the charges required the government to prove that Johnson acted with specific intent to commit these crimes.

FACTS

Between 1983 and 1988, Teledyne Wah Chang Albany (“TWCA”), an American manufacturing company, exported over $3.5 million worth of zirconium to Chile. Zirconium is a rare metal with incendiary properties. The zirconium was sold to Carlos Cardoen, an international arms merchant based in that country. The zirconium was used as an incendiary agent in cluster bombs that Car-doen was selling to Iraq for use in the Iran-Iraq war. Most of the zirconium sold to Cardoen was in the form of manufactured zirconium compacts specifically designed for use in cluster bombs. In 1982, before zirconium shipments commenced, TWCA asked the Department of State Office of Munitions Control (“OMC”) for a ruling on whether zirconium was on the Munitions List. It explained that TWCA wished to export zirconium for use in industrial explosives. In early 1983, OMC issued a commodities jurisdiction ruling stating that zirconium was a dual use item and therefore was excluded from the Munitions List. After receiving this favorable response from the Department of State, TWCA applied for export licenses from the Department of Commerce. Although Car-doen used the zirconium to manufacture cluster bombs, he provided TWCA with false end-use statements stating that the zirconium would be used as a booster material in industrial explosives sold to the mining industry. TWCA used these false end-use statements to procure export licenses from the Department of Commerce.

Edward Johnson was a sales manager of ordnance grade zirconium at TWCA. Although zirconium has civilian applications, the vast majority of Johnson’s zirconium customers used the material to manufacture munitions, particularly cluster bombs. Beginning in 1982, Carlos Cardoen began placing large zirconium orders through Johnson. Most of Cardoen’s orders were not for loose zirconium sponge, a raw material, but rather for zirconium sponge compacts, which are a manufactured component used in munitions such as cluster bombs. Throughout the period of the alleged conspiracy, Johnson continued to be one of Cardoen’s primary contacts at TWCA. He accepted and processed all of Cardoen’s zirconium orders and he negotiated pricing and shipping arrangements on behalf of TWCA.

PROCEEDINGS AT TRIAL

At trial, Johnson portrayed himself as a low-level salesman who had no idea that he was being used as a pawn in the international armaments game. He claimed that he had been duped into believing that the zirconium was being used to manufacture industrial explosives rather than cluster bombs, and that he had relied on management assurances that the zirconium shipments complied with export regulations. The jury was not convinced, and because Johnson received a fair trial, we will not disturb their verdict.

The evidence at trial provided ample grounds for a jury finding that Johnson was a knowing and willing participant in the con[*1363] spiracy. Johnson knew that TWCA faced potential environmental and safety liability if it did not find a profitable market for its excess zirconium. In 1984, Johnson traveled to Chile for meetings with Cardoen. He brought with him sample zirconium compacts which had been specifically designed for use in cluster bombs. The meetings in Chile centered around Cardoen’s arms business, and included detailed discussions of zirconium’s military applications. During later trips to Chile in 1987, Johnson visited Car-doen’s cluster bomb factory and witnessed burn testing of zirconium compacts TWCA had provided Cardoen for use in his MK 83/84 bombs. Several witnesses testified as to Johnson’s knowledge that the zirconium compacts exported to Cardoen were being used to manufacture Iraqi cluster bombs. James Meyerink testified that in 1984, he overheard Johnson and other employees of TWCA discussing that the zirconium would be used to manufacture cluster bombs and ridiculing the end-use statements they had provided to the government listing industrial explosives as the purpose of the exports. Richard Jenkins testified that Johnson told him that the zirconium pellets were being used to manufacture Iraqi cluster bombs. Augusto Giangrandi, Cardoen’s assistant, testified that he had several meetings with Johnson in which they ironed out pricing and shipping details relating to the zirconium exports. Giangrandi testified that Johnson knew that Cardoen was supplying cluster bombs containing zirconium to Iraq, and that the volume of future zirconium orders from TWCA depended on Iraq’s need for bombs. Giangrandi and Johnson also discussed the specific zirconium requirements of individual Iraqi bomb contracts Cardoen planned to bid for.

ISSUES ON APPEAL

Johnson raises four specific issues in this appeal. First, the district court committed reversible error when it held that Johnson’s false statements were material as a matter of law, rather than submitting the issue to the jury. Second, the commodities jurisdiction ruling issued by the Office of Munitions Control precluded liability under the Arms Export Control Act or required a jury instruction on uncertainty in the law. Third, the district court made reversible evidentiary rulings, concerning classified information. Fourth, the court’s supplemental jury instruction on his defense of good faith reliance on the advice of counsel incorrectly stated the law and misled the jury. We address each of these arguments in turn.

“MATERIALITY” OF FALSE STATEMENTS

In accordance with then-Circuit precedent, the district court ruled that the “materiality” element of a false-statement prosecution was a question for the judge, and directed the jury that the statements alleged were material. In United States, v. Gaudin, 515 U.S. 506, 115 S.Ct. 2310, 132 L.Ed.2d 444 (1995), the Supreme Court held that the Fifth and Sixth Amendments’ guarantees of due process and jury trial required courts to submit the “materiality” element of false statement prosecutions to the jury. That holding applies retroactively to cases on direct appeal at the time Gaudin was decided, as was this case. Griffith v. Kentucky, 479 U.S. 314, 328, 107 S.Ct. 708, 716, 93 L.Ed.2d 649 (1987). The Supreme Court and this Court have held that a Gaudin error is subject to the harmless error standard of review. See Johnson v. United States, — U.S. -, 117 S.Ct. 1544, 137 L.Ed.2d 718 (1997); United States v. Fern, 117 F.3d 1298 (11th Cir.1997).

Under this standard, “the government must show the absence of prejudice to the defendant’s substantial rights.” Fern, 117 F.3d at 1307. The government has carried its burden by showing that no reasonable jury could have found that Johnson’s falsehoods were not material.

A statement is material if it has a natural tendency to influence or the capability to influence government action. See United States v. Diaz, 690 F.2d 1352 (11th Cir.1982). The government is not actually required to rely upon the alleged false statements to make them material. United States v. Calhoon, 97 F.3d 518, 530 (11th Cir.1996). The purpose of the materiality requirement is to “insure that the reach of § 1001 is confined to reasonable bounds and not allowed to embrace trivial falsehoods.” United [*1364] States v. Gafyczk, 847 F.2d 685, 691 (11th Cir.1988).

Johnson’s theory is that in his case the false statements would have been incapable of influencing the government due to the CIA’s covert interest in assisting the Iraqi war effort. In making this argument, Johnson ignores that portion of the test making material statements with a “natural tendency” to influence. This Court has rejected the argument that individuals can defeat the materiality requirement by claiming that then-falsehoods were consistent with unwritten government policy. Defendants cannot claim that they “made their knowing falsification with no intent to deceive.” United States v. Lichenstein, 610 F.2d 1272, 1277 (5th Cir.1980). Actual knowledge by the government is not a defense to the “materiality” requirement of false statement prosecutions. See United States v. Whitaker, 848 F.2d 914, 916 (8th Cir.1988) (“The issue is whether the statements, viewed alone, were capable of influencing the function of the FDIC. It is irrelevant what the agent who heard the statement knew at the time of the statement.”); United States v. Rogers, 118 F.3d 466, 472 (6th Cir.1997); United States v. Johnson, 530 F.2d 52, 54-55 (5th Cir.1976) (“The natural and probable tendency of the affidavit to influence the decision to be made must be judged by the content of the document itself and not by any special knowledge possessed or acquired by the [Internal Revenue] Service.”). Because the plain meaning of the false end-use statements would influence the Commerce Department in deciding whether or not to grant the export licenses they were clearly material. The defendant was not prejudiced by the court’s failure to submit the materiality issue to the jury.

COMMODITIES JURISDICTION RULING

Johnson argues that because the OMC issued a Commodities Jurisdiction Ruling stating that zirconium metal is a dual-use item, he cannot be convicted for exporting items on the Munitions List without a license from the Department of State. Johnson was not convicted of exporting “zirconium” without a license, however, but rather of exporting zirconium compacts specifically designed for use in bombs without such a license. The district court properly held that such compacts were on the Munitions List. During the relevant time period, the Munitions List included:

All specifically designed components, parts, accessories, attachments, and associated equipment [of bombs].

See 22 C.F.R. § 121.01, Category IV(g) (1983).

Because the indictment and the jury instructions both made clear that Johnson was charged with exporting zirconium compacts specifically designed for bombs, the district court correctly determined that such items were on the Munitions List. See United States v. Tsai, 954 F.2d 155, 160 (3d Cir.1992) (holding evidence sufficient to prove that infra-red domes were specifically designed for missiles and therefore on the Munitions List).

Johnson alternatively argues that even if the zirconium compacts were on the Munitions List, he should have received a jury instruction on the uncertainty of the law, created, he says, by OMC’s jurisdiction letter for zirconium sponge. Reviewed for an abuse of discretion, it is apparent that Johnson is not entitled to a reversal based on this argument. The Government correctly argues that Johnson has not shown that.the law relating to export licensing was uncertain. Zirconium in its loose sponge or powder form was a dual-use item, the export of which was controlled by DOC. Zirconium compacted specifically for use in munitions is on the Munitions List and its export is controlled by DOS. The Commodities Jurisdiction ruling with regard to zirconium did not create any genuine uncertainty in the law with regard to the exportation of specially designed bomb components made out of zirconium. In eases involving criminal exports, the focus is on the defendant’s subjective understanding of the law as a requirement of the “willfulness” element of the crime. See United States v. Adames, 878 F.2d 1374 (11th Cir.1989); United States v. Tsai, 954 F.2d 155 (3d Cir.1992). The district court’s instructions clearly required the jury to find that Johnson knew that he was breaking the law. Because the jury found that Johnson knew that he was breaking the law, failure to[*1365] instruct on uncertainty of the law was not error.

RULINGS CONCERNING CLASSIFIED INFORMATION

Johnson argues that the district court erroneously refused discovery and use of evidence of the CIA’s covert policy to arm Iraq with Cardoen’s cluster bombs. He claims that classified materials were relevant to four defenses: the materiality of his false statements, the removal of zirconium from the Munitions List, entrapment by estoppel, and public authority. He also contends that the district court improperly restricted evidence of Johnson’s knowledge of TWCA management’s connections with the intelligence community. This Court reviews a district court’s evidentiary rulings for abuse of discretion. United States v. Noriega, 117 F.3d 1206, 1215 (11th Cir.1997).

Johnson devotes large portions of his appellate brief to arguments designed to convince us that the district court erroneously prevented him from presenting a “CIA” defense to the jury. The thrust of this defense was that, in an effort to execute a covert plan to assist Iraq in its war with Iran, the United States intelligence community secretly arranged for the zirconium shipments to bypass normal export regulations. According to this theory, government agents convinced Johnson, through a series of “winks and nods,” to arrange for zirconium shipments to go to Chile by using fraudulent end-use statements. Alternatively, Johnson argues, even if he was unaware of this plot at the time, the covert operation rendered his actions non-criminal as a matter of law.

Johnson sought extensive discovery of classified documents in an effort to lay the foundation for this defense. Such efforts are proeedurally controlled by the Classified Information Procedures Act (“CIPA”), 18 U.S.CApp. 3 (1994). This Act is designed to ensure that a trial court’s evidentiary rulings on the use of classified information are made prior to trial. The purpose of the law is to prevent criminal defendants from “graymailing” the government by threatening to reveal irrelevant but sensitive information during trial. CIPA has no substantive impact on the admissibility or relevance of probative evidence. See United States v. Noriega, 117 F.3d 1206, 1215 (11th Cir.1997); United States v. Baptista-Rodriguez, 17 F.3d 1354, 1363 (11th Cir.1994). The district court held a CIPA hearing and reviewed in camera all classified CIA documents potentially bearing on zirconium shipments to Chile. At the CIPA hearing, the district court properly limited Johnson’s proposed “CIA” defenses. The court carefully reviewed classified government documents and found no evidence supporting Johnson’s theory that the CIA had secretly arranged to supply Cardoen with zirconium. After our own review of these classified materials, we agree with the district court that the government did not withhold any evidence supporting Johnson’s “CIA” theory.

The court correctly held that Johnson could not use the defenses of entrapment by estoppel or public authority, unless he could show that he relied on official government communications before acting in a manner proscribed by law. See United States v. Cardoen, 898 F.Supp. 1563 (S.D.Fla.1995).

Entrapment by estoppel occurs when a government official incorrectly informs a defendant that certain conduct is legal, the defendant believes the government official and is then prosecuted for acting in conformity with the official’s advice. United States v. Thompson, 25 F.3d 1558,1564 (11th Cir.1994), United States v. Billue, 994 F.2d 1562, 1568 (11th Cir.1993). Johnson’s theory seems to be that, without actually telling Johnson that his actions were legal, the government “conveyed through winks and nods” that the CIA authorized the zirconium exports. Even if this theory could provide a valid defense, Johnson points to no evidence to support his position. Because a review of the classified materials confirms that there was no evidence to support a defense of entrapment by estoppel, the district court properly limited the introduction of classified evidence.

The actual authority defense requires proof that a defendant reasonably relied upon the actual authority of a government official to request participation in an illegal activity. See United States v. Anderson, 872 F.2d 1508, 1513-15 (11th Cir.[*1366] 1989); United States v. Rosenthal, 793 F.2d 1214, 1234-37 (11th Cir.1986). Because Johnson could not point to any sort of detrimental reliance on his part, or, for that matter, any governmental involvement in the conspiracy, the district court also properly refused to permit Johnson to present this version of his “CIA” defense to the jury.

Johnson argues that classified evidence was relevant to show that his falsehoods were not “material” and that the “real” reason for the OMC’s commodities jurisdiction ruling was to facilitate the Iraqi war effort. Johnson further suggests that' because the government presented evidence to the jury that the commodities jurisdiction ruling was fraudulently obtained, he had a constitutional right to challenge the government’s position by presenting evidence that zirconium was removed from the list for political purposes. After carefully reviewing the classified material produced by the government, we have determined there is no such evidence in the record and, therefore, could not have been wrongfully excluded.

Johnson argues that he should have been able to testify to his knowledge of and experience with his employer’s relationship with the intelligence community. He claims that such evidence was relevant to his lack of specific intent for three reasons: he had a right to explain the circumstances of his behavior, he had a right to show that his beliefs were reasonable, and he had a right to show Cardoen’s relationship with the United States government.

The district court properly refused this evidence because Johnson never laid a foundation for this evidence by suggesting that he relied on his co-conspirators’ close relationship with the intelligence community in making his decision to use false end-use statements and bypass the AECA. In the absence of reliance by Johnson, this evidence was irrelevant to Johnson’s state of mind and therefore properly excluded by the district court.

SUPPLEMENTAL JURY INSTRUCTION ON GOOD FAITH

During its deliberations, the jury submitted a question to the court asking whether the “good faith” defense applies when a defendant acquires new information but continues to follow outdated advice previously obtained from counsel. Because Johnson had consulted a lawyer early in the conspiracy, the district court had originally given jury instructions on both a general “good faith” defense based upon lack of intent, and a good faith reliance on advice of counsel defense. The gravamen of Johnson’s complaint is that the court’s supplemental jury instruction confused the jury on the requirements of these two separate but related defenses. A challenged supplemental jury instruction is reviewed as part of the entire jury charge, in light of the indictment, evidence presented and argument of counsel “to determine whether the jury was misled and whether the jury understood the issues.” Johns v. Jarrard, 927 F.2d 551, 554 (11th Cir.1991) (citations omitted).

Although the jury’s question was not a model of clarity, we agree with the district court that it related to the advice of counsel defense rather than to Johnson’s lack of specific intent. In an abundance of caution, the district court repeated its entire good faith instruction before giving the contested supplemental instruction. The court reiterated that “good faith is a complete defense” and that “one who expresses an opinion honestly held by him is not chargeable with fraudulent intent.” It then correctly answered the jury’s question by instructing that “good faith reliance upon the advice of counsel requires not only full and complete disclosure of the facts then known but also of material facts or information later acquired....” Because this was a correct statement of the law, and because we believe that this instruction did not mislead the jury, there was no error in the court’s supplemental jury instruction.

SENTENCING CROSS-APPEAL

The government appeals the sentence imposed on the conspiracy conviction. Count I charged Johnson with conspiracy to make false statements, conspiracy to violate the AECA, and conspiracy to violate the Export Administration Act (“EAA”). Although the jury acquitted Johnson on the substantive EAA charge, it convicted Johnson by general[*1367] verdict on the conspiracy count. The district court sentenced Johnson as if only conspiracy to make false statements and conspiracy to violate the AECA had been proved. The government claims the district court did not make factual findings in support of this decision.

U.S.S.G. § 1B1.2 requires a district court to sentence a defendant convicted pursuant to a general jury verdict of a multiple count conspiracy by applying the guidelines for those objects of the conspiracy the court finds had been proved beyond a reasonable doubt. The district court can make this finding “either implicitly or explicitly.” United States v. McKinley, 995 F.2d 1020 (11th Cir.1993). The parties specifically brought Guideline 1B1.2 to the attention of the district court at the sentencing hearing. After careful consideration, the district court refused to impose the guidelines sentence for conspiracy to violate the Export Administration Act. Under these circumstances, there was an implicit finding by the district court supporting its sentencing decision.

AFFIRMED.