Question: Operation "Greif" was a special operation during a battle where which forces incurred their  highest casualties of any operation during the war ?

Context paragraphs:
Battle of Suoi Bong Trang: The Battle of Suoi Bong Trang (23–24 February 1966) was an engagement fought between US, Australian and New Zealand forces, and the Viet Cong and North Vietnamese Army during the Vietnam War.  The battle occurred during Operation Rolling Stone, an American security operation to protect engineers building a tactically important road in the vicinity of Tan Binh, in central Binh Duong Province, 30 km north-west of Bien Hoa airbase.  During the fighting, soldiers from the US 1st Brigade, 1st Infantry Division and the 1st Battalion, Royal Australian Regiment (1 RAR), which had been attached for the operation, fought off a regimental-sized Viet Cong night assault.  Repulsed by massed firepower from artillery and tanks, the Viet Cong suffered heavy casualties and were forced to withdraw by morning.  After the attack, the Americans and Australians made no attempt to pursue the Viet Cong, focusing on securing the battlefield and evacuating their own casualties.  The Viet Cong continued to harass the American sappers with occasional sniper and mortar fire, but these tactics proved ineffective, and the road was completed by 2 March.

Joint Special Operations Command (Jordan): The Special Operation Forces of the Jordanian Armed Forces serve as Jordan's premiere special forces unit.  Founded on April 15, 1963 on the orders of the late King Hussein, its primary roles include reconnaissance, counter-terrorism, search and evacuation, intelligence gathering combat, and the protection of key sites.  The Special Operation Forces are also charged with carrying out precision strikes against critical enemy targets.  The 14,000-strong unit are equipped and trained to be able to operate behind enemy lines for long periods without any logistical support, and is considered one of the finest special forces units in the world.

Republic of Korea Army Special Warfare Command: Republic of Korea Army Special Warfare Command (ROK-SWC; Korean: 대한민국 육군 특수전사령부 or 특전사 ; Hanja: 大韓民國陸軍 特殊戰司令部), also known as the Republic of Korea Army Special Forces "Black Berets"(R.O.K-Special Forces) is the military command of the Republic of Korea Army responsible for their special operation forces.  ROK Special Forces brigades work in close relationship with their counterparts in the United States Army Special Forces "Green Berets".  ROK Special Forces brigades were modelled after United States Army Special Forces (Green Berets).

Battle of Hiep Hoa: The Battle of Hiệp Hòa was a minor battle of the Vietnam War.  On the night of November 22, 1963, an estimated 500 Vietcong fighters overrun the Hiệp Hòa Special Forces Camp, resulting in four American personnel MIA.  South Vietnamese commando units and the American special operation forces resisted heavily using machine guns but were overwhelmed by the arrival of a NVA mortar unit.  It was the first CIDG camp to be overrun during the war.  Isaac Camacho, one of the four missing Americans, later became the first American to escape from a Vietcong POW camp.

Korean People's Army Special Operation Force: The North Korean special operation force (NKSOF), officially the Korean People's Army Special Operation Force, consists of specially equipped and trained elite military units trained to perform military, political, or psychological operations for North Korea.  The units are active in testing the defenses of South Korea and have been detected operating in or around South Korea many times in the decades since the end of the Korean War.  There are about 180,000 special operational forces soldiers.

Battle of Go Cong: The Battle of Go Cong was a small battle during the Vietnam War.  It took place on September 3, 1963, after the General Staff of the Viet Cong (NLF) called for "another Ap Bac" on South Vietnamese forces.  The intent of the operation was to drive out the rebels who had survived the earlier Ap Bac engagement.  The battle was won by American and South Vietnamese forces, after inflicting heavy casualties on the Viet Cong, using artillery to slaughter rebel fighters fleeing American special operation troops who ambushed them with intense sniper fire.  It was later discovered that the 91 of the captured NLF troops were new recruits, and did not have weapons.

Operation Greif: Operation "Greif" (German: "Unternehmen Greif" ; ] , meaning "Griffin") was a special operation commanded by Waffen-SS commando Otto Skorzeny during the Battle of the Bulge in World War II.  The operation was the brainchild of Adolf Hitler, and its purpose was to capture one or more of the bridges over the Meuse river before they could be destroyed.  German soldiers, wearing captured British and US Army uniforms and using captured Allied vehicles, were to cause confusion in the rear of the Allied lines.  A lack of vehicles, uniforms, and equipment limited the operation and it never achieved its original aim of securing the Meuse bridges.  Skorzeny's postwar trial set a precedent clarifying article 4 of the Geneva Convention: as the German soldiers removed the Allied uniforms before engaging in combat, they were not to be considered francs-tireurs.

Operation Keyhole: Operation Keyhole was a British special operation to recapture Thule Island in the South Sandwich Islands during Operation Corporate in the 1982 Falklands War.  The operation took place from 19 to 20 June 1982.

Battle of the Bulge: The Battle of the Bulge (16 December 1944 – 25 January 1945) was the last major German offensive campaign on the Western Front during World War II.  It was launched through the densely forested Ardennes region of Wallonia in eastern Belgium, northeast France, and Luxembourg, towards the end of World War II.  The surprise attack caught the Allied forces completely off guard.  American forces bore the brunt of the attack and incurred their highest casualties of any operation during the war.  The battle also severely depleted Germany's armored forces, and they were largely unable to replace them.  German personnel and, later, Luftwaffe aircraft (in the concluding stages of the engagement) also sustained heavy losses.

Operation Mandibles: During World War II, Operation Mandibles was a planned 1940/1941 British amphibious assault on Rhodes, Leros and the Dodecanese Islands in the Aegean Sea.  Planned by Roger Keyes of the Special Operation branch, it was never executed.  See Operation Hercules and Operation Accolade."

Supporting paragraphs: Operation Greif Battle of the Bulge
Answer: American forces