It has been suggested that the name of Kidara, the eponymous founder of the Kidarite Huns, can be traced to Turkic *kidirti “west.” The term, to my knowledge, is attested only in Qakas (Khakas) as kider s.m. If Kidara is to be understood as a personal name, then the suggestion is rendered unlikely. In any case, the Kidarite Huns were already a faction under the Red Huns, a southern division of the Hunnish horde.
As remnants of the Northern Xuŋa (Xiongnu), the ancestors of the Qıdır Xunı were part of the migrating Hunnish people known as the Xunı (Huns). They belonged to a sub-group of Xunı identified by the 6th century historian Theophanes Byzantius as the Kermixuna (Κερμιχίωνα) “Red Huns” (from Iranian Karmir Xyon s.m.). The designation “red” referred to the group’s status as a southern division of the Xunı. The Zand-i Wahman Yasn, a medieval Zoroastrian text written under the Sasanians, divides the Xunı into the Xyon, Heftal (Hephthalites), Karmir Xyon, and Spet Xyon “White Huns.”
In the Central States, the Red Huns were known as the “Greater Yuezhi.” This was a misconception stemming from the fact that the Red Huns then occupied the region once ruled by the Greater Yuezhi. It may also stem from the fact that the Kushan kings, the true descendants of the Greater Yuezhi, were conquered puppets of the Red Huns.
The Book of Wei states that the Red Huns originally held their capital at Lu Jianshi ((盧監氏) LH *la kam-tśe), a location west of Badaxşan (Badakhshan). Schuessler (2014) sees Lu Jianshi as a transcription of Khulm. This is, however, phonetically problematic. It seems likelier that the word transcribes Kapişa (It is unclear why the character 盧 was added or what it may represent). The city was said to be 14,500 li (7250 km) west of Dai Commandery. At the time, it bordered the Yedivar (Hephthalites), whose frequent raids from the north pushed the Red Huns westwards. There, they established their new capital at Baqlo (Balkh), said to be 2,100 li (1050 km) from Badaxşan (Badakhshan).
Presumably, the Red Huns first began settling in Bactria during the early mid-4th century C.E. under their king Qırat (Kirada), likely from Turkic *kɨr “steppe” and *at “horse.” Jongeward et al. (2014) date the earliest coins of Qırat somewhere between ca. 335 and 345 C.E. He was at some point succeeded by Peroz. According to the Roman historian Ammianus Marcellinus, in 356 C.E. the Red Huns were at war with Eranşahr (the Sasanian Empire) in its eastern borders. However, by 358 C.E. a treaty was signed between the two. As a result, the Red Huns accompanied the Eranşahr emperor Şabuhr II on his campaign against the Romans. While Peroz, who accompanied Şabuhr II on his campaign, was the king of the Red Huns, he was noted accompanying another Red Hun king known as Qurumbat (Grumbates). It may be that Peroz was the Eastern king, while Qurumbat was the Western king. The Xunı were known to practice dual kingship