Abstract: Methods, systems, and computer programs for generating cryptographic function parameters are described. In some examples, astronomical data from an observed astronomical event is obtained. A pseudorandom generator is seeded based on the astronomical data. After seeding the pseudorandom generator, an output from the pseudorandom generator is obtained. A parameter for a cryptographic function is generated by operation of one or more data processors. The parameter is generated from the output from the pseudorandom generator.

Abstract: A method for operating a pseudorandom generator is disclosed. The method may be implemented by a processor of a mobile computing device. The method includes: collecting raw sensor data from at least one sensor associated with the mobile computing device; selecting a subset of the raw sensor data; retrieving first representation representing accumulated entropy associated with one or more previously acquired raw sensor data sets for the at least one sensor; and generating a seed for a pseudorandom generator based on combining the first representation and the selected subset of raw sensor data.

Abstract: A method at a computing device in a public ledger cryptography system, the method including creating a purpose string, the purpose string defining transaction parameters for an account within the public ledger cryptography system; using the purpose string to create a private key and associated public key for an account within the public ledger cryptography system; and providing the purpose string for use in verification of a transaction from the account within the public ledger cryptography system.

Abstract: Devices and methods of managing data stored within a container. The container may be associated with at least one registered user. The data within the container may be encrypted by a data encryption key (DEK). A computing device includes: a security module including a crypto-processor, a main processor, and memory. The memory stores instructions that, when executed, configure a processor to: authenticate a user based on a user secret associated with the container and generate a soft key based on the user secret. The instructions cause a crypto-processor to generate a secure generator output including a crypto key component and generate a hardened user key based on a key agreement protocol using the soft key and the crypto key component. The instructions cause a processor to construct an unencrypted DEK associated with the hardened user key and decrypt the subset of data using the unencrypted DEK.

Abstract: Methods, systems, and computer programs for generating cryptographic function parameters are described. In some examples, source code that defines seed information and a pseudorandom function is accessed. A parameter for a cryptographic function by operation of one or more data processors is generated. The parameter is generated from the seed information and the pseudorandom function. The parameter has a larger size in memory than the source code that defines the seed information and the pseudorandom function.

Abstract: Methods, systems, and computer programs for using an implicit certificate are disclosed. In some aspects, a message and an implicit certificate are accessed. The implicit certificate is associated with an entity. A modified message is generated by combining the message with a value based on the implicit certificate. A digital signature can be generated based on the modified message and transmitted to a recipient. In some aspects, a digital signature from an entity and a message to be verified based on the digital signature are accessed. An implicit certificate associated with the entity is accessed. A modified message is generated by combining the message with a value based on the implicit certificate. The message is verified based on the digital signature and the modified message.

Abstract: A method for providing Cheon-resistance security for a static elliptic curve Diffie-Hellman cryptosystem (ECDH), the method including providing a system for message communication between a pair of correspondents, a message being exchanged in accordance with ECDH instructions executable on computer processors of the respective correspondents, the ECDH instructions using a curve selected from a plurality of curves, the selecting including choosing a range of curves; selecting, from the range of curves, curves matching a threshold efficiency; excluding, within the selected curves, curves which may include intentional vulnerabilities; and electing, from non-excluded selected curves, a curve with Cheon resistance, the electing comprising a curve from an additive group of order q, wherein q is prime, such that q?1=cr and q+1=ds, where r and s are primes and c and d are integer Cheon cofactors of the group, such that cd?48.

Abstract: A method for operating a pseudorandom generator is disclosed. The method may be implemented by a processor of a mobile computing device. The method includes: collecting raw sensor data from at least one sensor associated with the mobile computing device; selecting a subset of the raw sensor data; retrieving first representation representing accumulated entropy associated with one or more previously acquired raw sensor data sets for the at least one sensor; and generating a seed for a pseudorandom generator based on combining the first representation and the selected subset of raw sensor data.

Abstract: Devices and methods of managing data stored within a container. The container may be associated with at least one registered user. The data within the container may be encrypted by a data encryption key (DEK). A computing device includes: a security module including a crypto-processor, a main processor, and memory. The memory stores instructions that, when executed, configure a processor to: authenticate a user based on a user secret associated with the container and generate a soft key based on the user secret. The instructions cause a crypto-processor to generate a secure generator output including a crypto key component and generate a hardened user key based on a key agreement protocol using the soft key and the crypto key component. The instructions cause a processor to construct an unencrypted DEK associated with the hardened user key and decrypt the subset of data using the unencrypted DEK.

Abstract: An elliptic curve random number generator avoids escrow keys by choosing a point Q on the elliptic curve as verifiably random. An arbitrary string is chosen and a hash of that string computed. The hash is then converted to a field element of the desired field, the field element regarded as the x-coordinate of a point Q on the elliptic curve and the x-coordinate is tested for validity on the desired elliptic curve. If valid, the x-coordinate is decompressed to the point Q, wherein the choice of which is the two points is also derived from the hash value. Intentional use of escrow keys can provide for back up functionality. The relationship between P and Q is used as an escrow key and stored by for a security domain. The administrator logs the output of the generator to reconstruct the random number with the escrow key.

Abstract: A method for providing Cheon-resistance security for a static elliptic curve Diffie-Hellman cryptosystem (ECDH), the method including providing a system for message communication between a pair of correspondents, a message being exchanged in accordance with ECDH instructions executable on computer processors of the respective correspondents, the ECDH instructions using a curve selected from a plurality of curves, the selecting including choosing a range of curves; selecting, from the range of curves, curves matching a threshold efficiency; excluding, within the selected curves, curves which may include intentional vulnerabilities; and electing, from non-excluded selected curves, a curve with Cheon resistance, the electing comprising a curve from an additive group of order q, wherein q is prime, such that q?1=cr and q+1=ds, where r and s are primes and c and d are integer Cheon cofactors of the group, such that cd?48.

Abstract: Methods, systems, and computer programs for using an implicit certificate are disclosed. In some aspects, a message and an implicit certificate are accessed. The implicit certificate is associated with an entity. A modified message is generated by combining the message with a value based on the implicit certificate. A digital signature can be generated based on the modified message and transmitted to a recipient. In some aspects, a digital signature from an entity and a message to be verified based on the digital signature are accessed. An implicit certificate associated with the entity is accessed. A modified message is generated by combining the message with a value based on the implicit certificate. The message is verified based on the digital signature and the modified message.

Abstract: An elliptic curve random number generator avoids escrow keys by choosing a point on the elliptic curve as verifiably random. An arbitrary string is chosen and a hash of that string computed. The hash is then converted to a field element of the desired field, the field element regarded as the x-coordinate of a point on the elliptic curve and the x-coordinate is tested for validity on the desired elliptic curve. If valid, the x-coordinate is decompressed to the point , wherein the choice of which is the two points is also derived from the hash value. Intentional use of escrow keys can provide for back up functionality. The relationship between P and is used as an escrow key and stored by for a security domain. The administrator logs the output of the generator to reconstruct the random number with the escrow key.

Abstract: Systems, methods, and software can be used to improve security of an authentication process in a cargo shipping system. In some aspect, an authentication request message is received at a sensor from a cargo tracking device. The authentication request message includes a key that the sensor will use to decrypt its encrypted public key/private key pair. In response to the authentication request message, the sensor sends an authentication response message to the cargo tracking device that is encrypted using a derived symmetric key. The cargo tracking device sends an authentication confirmation message to the sensor in response to the authentication response message.

Abstract: A method for key agreement between a first party and a second party over a public communications channel, the method including selecting, by the first party, from a semigroup, a first value “a”; multiplying the first value “a” by a second value “b” to create a third value “d”, the second value “b” being selected from the semigroup; sending the third value “d” to the second party; receiving, from the second party, a fourth value “e”, the fourth value comprising the second value “b” multiplied by a fifth value “c” selected by the second party from the semigroup; and creating a shared secret by multiplying the first value “a” with the fourth value “e”, wherein the shared secret matches the third value “d” multiplied by the fifth value “c”.

Abstract: A method for providing Cheon-resistance security for a static elliptic curve Diffie-Hellman cryptosystem (ECDH), the method including providing a system for message communication between a pair of correspondents, a message being exchanged in accordance with ECDH instructions executable on computer processors of the respective correspondents, the ECDH instructions using a curve selected from a plurality of curves, the selecting including choosing a range of curves; selecting, from the range of curves, curves matching a threshold efficiency; excluding, within the selected curves, curves which may include intentional vulnerabilities; and electing, from non-excluded selected curves, a curve with Cheon resistance, the electing comprising a curve from an additive group of order q, wherein q is prime, such that q?1=cr and q+1=ds, where r and s are primes and c and d are integer Cheon cofactors of the group, such that cd?48.

Abstract: In some aspects, a message and an implicit certificate are accessed. The implicit certificate is associated with an entity. A modified message is generated by combining the message with a value based on the implicit certificate. A digital signature can be generated based on the modified message and transmitted to a recipient. In some aspects, a digital signature from an entity and a message to be verified based on the digital signature are accessed. An implicit certificate associated with the entity is accessed. A modified message is generated by combining the message with a value based on the implicit certificate. The message is verified based on the digital signature and the modified message.

Abstract: A method for key agreement between a first party and a second party over a public communications channel, the method including selecting, by the first party, from a semigroup, a first value “a”; multiplying the first value “a” by a second value “b” to create a third value “d”, the second value “b” being selected from the semigroup; sending the third value “d” to the second party; receiving, from the second party, a fourth value “e”, the fourth value comprising the second value “b” multiplied by a fifth value “c” selected by the second party from the semigroup; and creating a shared secret by multiplying the first value “a” with the fourth value “e”, wherein the shared secret matches the third value “d” multiplied by the fifth value “c”.

Abstract: A method at a computing device in a public ledger cryptography system, the method including creating a purpose string, the purpose string defining transaction parameters for an account within the public ledger cryptography system; using the purpose string to create a private key and associated public key for an account within the public ledger cryptography system; and providing the purpose string for use in verification of a transaction from the account within the public ledger cryptography system.

Abstract: Methods, systems, and computer programs for using an implicit certificate are disclosed. In some aspects, a message and an implicit certificate are accessed. The implicit certificate is associated with an entity. A modified message is generated by combining the message with a value based on the implicit certificate. A digital signature can be generated based on the modified message and transmitted to a recipient. In some aspects, a digital signature from an entity and a message to be verified based on the digital signature are accessed. An implicit certificate associated with the entity is accessed. A modified message is generated by combining the message with a value based on the implicit certificate. The message is verified based on the digital signature and the modified message.