Just where does the Scripture say this? Paul is apparently quoting here from Isaiah 28:16, which is the following: "Therefore thus saith the Lord God, Behold, I lay in Zion for a foundation a stone, a tried stone, a precious corner stone, a sure foundation: he that believeth shall not make haste."
The question is: Why did Paul change the Hebrew word for "make haste" to the Greek word for "be ashamed"? He did the same thing in Romans 9:33. "As it is written, Behold, I lay in Sion a stumblingstone and rock of offence: and whosoever believeth on Him shall not be ashamed." This verse makes the question even more involved, because here Paul combines the quote with Isaiah 8:14: "And he shall be for a sanctuary; but for a stone of stumbling and for a rock of offence." Note also 1 Peter 2:6-8, which combines both verses with Psalm 118:22: "The stone which the builders refused is become the head stone of the corner."
The Greek Septuagint translation apparently rendered "make haste" (which is the correct meaning of the Hebrew word, as confirmed by all its other uses in the Old Testament) by a Greek word meaning something like "put to shame." More importantly, however, these passages illustrate the truth that the Holy Spirit (the real Author of the Bible) has a perfect right to interpret His writing however He will. And He interpreted "make haste" to mean "be ashamed."
That is, when we believe on Christ, we never need to flee in haste from His enemies, for we can never be put to shame when anchored on this sure foundation. As the Lord said in another passage: "They shall not be ashamed that wait for me" (Isaiah 49:23). HMM