A TPM Diffie-Hellman Oracle - Acar, Tolga; Zaverucha, Greg; Nguyen, Lan (Microsoft Research, 2013)
This note describes a Diﬃe-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 speciﬁed 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±1 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 Diﬃe-Hellman problem. On a more positive note, the oracle may allow a wider range of cryptographic protocols to make use of the TPM.