Amit Behera

Amit Behera, Or Sattath, Uriel Shinar

Message Authentication Code or MAC, is a well-studied cryptographic primitive that is used in order to authenticate communication between two parties sharing a secret key. A Tokenized MAC or TMAC is a related cryptographic primitive, introduced by Ben-David & Sattath (QCrypt'17) which allows limited signing authority to be delegated to third parties via the use of single-use quantum signing tokens. These tokens can be issued using the secret key, such that each token can be used to sign at most one document. We provide an elementary construction for TMAC based on BB84 states. Our construction can tolerate up to 14% noise, making it the first noise-tolerant TMAC construction. The simplicity of the quantum states required for our construction combined with its noise tolerance, makes it practically more feasible than the previous TMAC construction. The TMAC is existentially unforgeable against adversaries with signing and verification oracles (i.e., analogous to EUF-CMA security for MAC), assuming post-quantum one-way functions exist.

Amit Behera, Or Sattath

In a quantum money scheme, a bank can issue money that users cannot counterfeit. Similar to bills of paper money, most quantum money schemes assign a unique serial number to each money state, thus potentially compromising the privacy of the users of quantum money. However in a quantum coins scheme, just like the traditional currency coin scheme, all the money states are exact copies of each other, providing a better level of privacy for the users. A quantum money scheme can be private, i.e., only the bank can verify the money states, or public, meaning anyone can verify. In this work, we propose a way to lift any private quantum coin scheme -- which is known to exist based on the existence of one-way functions, due to Ji, Liu, and Song (CRYPTO'18) -- to a scheme that closely resembles a public quantum coin scheme. Verification of a new coin is done by comparing it to the coins the user already possesses, by using a projector on to the symmetric subspace. No public coin scheme was known prior to this work. It is also the first construction that is very close to a public quantum money scheme and is provably secure based on standard assumptions. Finally, the lifting technique, when instantiated with the private quantum coins scheme~\cite{MS10}, gives rise to the first construction that is close to an inefficient unconditionally secure public quantum money scheme.