Abstract: Methods, systems, and computer-readable storage mediums are described for effecting practical use of a dual currency which is a currency that can be electronically created and stored, and further for which there is a secret key (e.g., the secret key of a public key/secret key pair as used in public key cryptography) such that: an entity that does not possess the secret key cannot, in practice, create notes of the currency; and an entity that does possess the secret key can, in practice, create notes of the currency without assistance from entities that do not possess the secret key.

Abstract: Computer and communications systems and methods are provided in which a first computing system sends a second computing system a message and an associated deep-string and the second computing system applies a key of a cryptographic system or a one-way function to the deep-string to determine the deep-string's deep-string-depth. The second computing device then uses the determined deep-string-depth in determining subsequent behavior regarding the message. In some environments, a third computing device may generate and provide deep-strings of various deep-string-depths to the first computing device to ensure more favorable behavior of the second computing device.

Abstract: Computer and communications systems and methods are provided in which a first computing system sends a second computing system a message and an associated deep-string and the second computing system applies a key of a cryptographic system or a one-way function to the deep-string to determine the deep-string's deep-string-depth. The second computing device then uses the determined deep-string-depth in determining subsequent behavior regarding the message. In some environments, a third computing device may generate and provide deep-strings of various deep-string-depths to the first computing device to ensure more favorable behavior of the second computing device.

Abstract: Computer and communications systems and methods are provided in which a first computing system sends a second computing system a message and an associated deep-string and the second computing system applies a key of a cryptographic system or a one-way function to the deep-string to determine the deep-string's deep-string-depth. The second computing device then uses the determined deep-string-depth in determining subsequent behavior regarding the message. In some environments, a third computing device may generate and provide deep-strings of various deep-string-depths to the first computing device to ensure more favorable behavior of the second computing device.