9 research outputs found
Quantum resource estimates for computing elliptic curve discrete logarithms
We give precise quantum resource estimates for Shor's algorithm to compute
discrete logarithms on elliptic curves over prime fields. The estimates are
derived from a simulation of a Toffoli gate network for controlled elliptic
curve point addition, implemented within the framework of the quantum computing
software tool suite LIQ. We determine circuit implementations for
reversible modular arithmetic, including modular addition, multiplication and
inversion, as well as reversible elliptic curve point addition. We conclude
that elliptic curve discrete logarithms on an elliptic curve defined over an
-bit prime field can be computed on a quantum computer with at most qubits using a quantum circuit of at most Toffoli gates. We are able to classically simulate the
Toffoli networks corresponding to the controlled elliptic curve point addition
as the core piece of Shor's algorithm for the NIST standard curves P-192,
P-224, P-256, P-384 and P-521. Our approach allows gate-level comparisons to
recent resource estimates for Shor's factoring algorithm. The results also
support estimates given earlier by Proos and Zalka and indicate that, for
current parameters at comparable classical security levels, the number of
qubits required to tackle elliptic curves is less than for attacking RSA,
suggesting that indeed ECC is an easier target than RSA.Comment: 24 pages, 2 tables, 11 figures. v2: typos fixed and reference added.
ASIACRYPT 201
Security analysis of a chaotic map-based authentication scheme for telecare medicine information systems
Many authentication schemes have been proposed for telecare medicine information systems (TMIS) to ensure the privacy, integrity, and availability of patient records. These schemes are crucial for TMIS systems because otherwise patients’ medical records become susceptible to tampering thus hampering diagnosis or private medical conditions of patients could be disclosed to parties who do not have a right to access such information. Very recently, Hao et al. proposed a chaotic map-based authentication scheme for telecare medicine information systems in a recent issue of Journal of Medical Systems. They claimed that the authentication scheme can withstand various attacks and it is secure to be used in TMIS. In this paper, we show that this authentication scheme is vulnerable to key-compromise impersonation attacks, off-line password guessing attacks upon compromising of a smart card, and parallel session attacks. We also exploit weaknesses in the password change phase of the scheme to mount a denial-of-service attack. Our results show that this scheme cannot be used to provide security in a telecare medicine information system