Abstract: A method for verification at a computing device of a signed message received from a first party over a public communications channel, the method including extracting a message digest “a” belonging to a semigroup from the signed message; obtaining a public key [c,e] for the first party, including a fixed value checker “c” and an endpoint “e”, checker “c” and endpoint “e” belonging to the semigroup and the endpoint comprising a multiplication of a private key “b” for the first party and the checker “c”, multiplying the message digest “a” and the endpoint “e” to create an endmatter “ae”; extracting a signature “d” from the signed message, the signature “d” belonging to the semigroup and being a multiplication of message digest “a” and private key “b”; multiplying the signature “d” and the checker “c” to create a signcheck “dc”; and verifying that the endmatter “ae” matches the signcheck “dc”.

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: 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 verification at a computing device of a signed message received from a first party over a public communications channel, the method including extracting a message digest “a” belonging to a semigroup from the signed message; obtaining a public key [c,e] for the first party, including a fixed value checker “c” and an endpoint “e”, checker “c” and endpoint “e” belonging to the semigroup and the endpoint comprising a multiplication of a private key “b” for the first party and the checker “c”, multiplying the message digest “a” and the endpoint “e” to create an endmatter “ae”; extracting a signature “d” from the signed message, the signature “d” belonging to the semigroup and being a multiplication of message digest “a” and private key “b”; multiplying the signature “d” and the checker “c” to create a signcheck “dc”; and verifying that the endmatter “ae” matches the signcheck “dc”.

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 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: 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, a first value “a”; multiplying the first value “a” by a second value “b” using Knuth multiplication to create a third value “d”, the third value “d” being a semistandard tableau; sending the third value “d” to the second party; receiving, from the second party, a fourth value “e”, the fourth value being a second semistandard tableau comprising the second value “b” multiplied by a fifth value “c” selected by the second party; and creating a shared secret by multiplying the first value “a” with the fourth value “e” using Knuth multiplication, wherein the shared secret matches the third value “d” multiplied by the fifth value “c” using Knuth multiplication.

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

Abstract: A method for verification at a computing device of a signed message received from a first party over a public communications channel, the method including extracting a message digest “a” belonging to a semigroup from the signed message; obtaining a public key [c,e] for the first party, including a fixed value checker “c” and an endpoint “e”, checker “c” and endpoint “e” belonging to the semigroup and the endpoint comprising a multiplication of a private key “b” for the first party and the checker “c”, multiplying the message digest “a” and the endpoint “e” to create an endmatter “ae”; extracting a signature “d” from the signed message, the signature “d” belonging to the semigroup and being a multiplication of message digest “a” and private key “b”; multiplying the signature “d” and the checker “c” to create a signcheck “dc”; and verifying that the endmatter “ae” matches the signcheck “dc”.

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: 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: 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, a first value “a”; multiplying the first value “a” by a second value “b” using Knuth multiplication to create a third value “d”, the third value “d” being a semistandard tableau; sending the third value “d” to the second party; receiving, from the second party, a fourth value “e”, the fourth value being a second semistandard tableau comprising the second value “b” multiplied by a fifth value “c” selected by the second party; and creating a shared secret by multiplying the first value “a” with the fourth value “e” using Knuth multiplication, wherein the shared secret matches the third value “d” multiplied by the fifth value “c” using Knuth multiplication.

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: 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: 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.