One thing I know about the Vernam cipher is that the key must not be repeated over the plain-text, for example:
Plain-text (hex): 48 65 6C 6C 6F 57 6F 72 6C 64 // HelloWorld
One-time-pad (hex): 47 72 61 70 65 47 72 61 70 65 // GrapeGrape
Cipher-text (hex): 15 23 13 28 10 16 29 19 28 01 // ??????????
Notice that in the one-time-pad, the sequence 47 72 61 70 65
is repeated.
How does this constitute a vulnerability, and how can the one-time-pad be discovered through its repetition?
Side-note: I'd be especially interested to know how it would be possible to determine a single repeated byte pad, for example:
Plain-text (hex): 48 65 6C 6C 6F 57 6F 72 6C 64 // HelloWorld
One-time-pad (hex): 56 56 56 56 56 56 56 56 56 56 // VVVVVVVVVV
Cipher-text (hex): 1E-33-3A-3A-39-01-39-24-3A-32 // ??????????