Establishing a strong link between the paper medium and the data represented on it is an interesting alternative to defeat unauthorised copy and content modification attempts. Many applications would benefit from it, such as show tickets, contracts, banknotes or medical prescripts. In this study, the authors present a low-cost solution that establishes such a link by combining digital signatures, physically unclonable functions and fuzzy extractors. The proposed protocol provides two levels of security that can be used according to the time available for verifying the signature and the trust in the paper holder. In practice, this solution uses ultra-violet fibres that are poured into the paper mixture. Fuzzy extractors are then used to build identifiers for each sheet of paper and a digital signature is applied to the combination of these identifiers and the data to be protected from copy and modification. The authors additionally provide a careful statistical analysis of the robustness and amount of randomness reached by the extractors. The authors conclude that identifiers of 72 bits can be derived, which is assumed to be sufficient for the proposed application. However, more randomness, robustness and unclonability could be obtained at the cost of a more expensive process, keeping exactly the same methodology.

Modular multiplication and inversion/division are the most common primitives in today's public key cryptography. Elliptic curve public key cryptosystems (ECPKC) are becoming increasingly popular for use in mobile appliances where bandwidth and chip area are strongly constrained. For the same level of security, ECPKC use much smaller key length than the commonly used RSA but need modular inversion/division. This work presents an improved algorithm for prime field Montgomery modular inversion. The first important contribution lies in the reduction of the number of operations needed. Resource sharing is also used to lighten the control part of the algorithm. The second contribution is the minimization of the set of different instructions to enable powerful FPGA implementations. Resulting 256-bit circuit achieves a ratio throughput/area improved by at least 70% compared to the only known Montgomery inverse design in FPGA technology. Though the implementations are first oriented towards FPGA, some improvements are generic. So, they could prove to be also efficient for ASIC designs in terms of area and power consumption.