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As far as my understanding goes social security number should be given only to certain places such as banks, employer, credit card and for loan etc. No company unless they hire you have a right to ask for SSN.
Infact following things are also prohibited in an interview according to US laws -
Asking about Race, Cast, Married / unmarried status, Age etc. These laws are set because the decision to hire you should not be biased by any factor apart from your qualification and capabilities. If you find any partiality like this you report this.
Desi companies are too much. They will go to any extent for exploitation. You can directly tell them that you are not supposed to give it to them and if you want you can report this issue. If they want to check your background, they can do so through the references.