This note describes a Di\ufb03e-Hellman oracle, constructed using standard Trusted Platform Module (TPM) signature APIs. The oracle allows one to compute the exponentiation of an arbitrary group element to a speci\ufb01ed TPM-protected private key. By employing the oracle, the security provided by a group of order p is reduced by logk bits, provided k oracle queries are made and p\u00b11 is divisible by k. The security reduction follows from a straightforward application of results from Brown and Gallant (IACR ePrint 2004\/306) and Cheon (Eurocrypt 2006) on the strong Di\ufb03e-Hellman problem. On a more positive note, the oracle may allow a wider range of cryptographic protocols to make use of the TPM.<\/p>\n","protected":false},"excerpt":{"rendered":"
This note describes a Di\ufb03e-Hellman oracle, constructed using standard Trusted Platform Module (TPM) signature APIs. The oracle allows one to compute the exponentiation of an arbitrary group element to a speci\ufb01ed TPM-protected private key. 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