Abstract: Various embodiments relate to a key protocol exchange that provide a simple but still secure key exchange protocol. Security of key exchange protocols has many aspects; providing and proving all these properties gets harder with more complex protocols. These security properties may include: perfect forward secrecy; forward deniability; key compromise impersonation resistance; security against unknown key share attack; explicit or implicit authentication; key confirmation; protocol is (session-)key independent; key separation (different keys for encryption and MACing); extendable, e.g. against DOS attacks . . . (e.g. using cookies, . . . ); support of early messages; small communication footprint; and support of for public-key and/or password authentication.

Abstract: A method is provided for generating an elliptic curve cryptography key pair that uses two topologically identical pseudo-random number generators operating in parallel and in step with each other. One generator operates in the scalar number domain and the other generator operates in the elliptic curve point domain. Parallel sequences of pseudo-random elliptic curve points aG and corresponding scalars a are generated in this manner. A scalar a becomes a private key and an elliptic curve point aG is a public key of a key pair. Each generator is advanced by one iteration successively, and the isomorphic relationship ensures that the point domain generator always contains values which are multiples of the system base point according to values contained in the corresponding position in the number domain generator. In one embodiment, the pseudo-random number generators are each characterized as being lagged Fibonacci generators.

Abstract: Various embodiments relate to a method of hashing a message M using a block cipher, including: producing N block cipher inputs by XORing message indices i, . . . i+N?1 respectively with state values S0, . . . SN?1, wherein N is an integer greater than 1; producing N block cipher keys by XORing N different blocks of message M and at least one of state values S0, . . . SN?1 for each of the N block cipher keys; encrypting the N block cipher inputs using the respective N block cipher keys to produce N block cipher outputs; combining the N block cipher outputs with N block cipher inputs to produce N block cipher combined outputs Tt, for t=0, . . . , N?1; calculating Y0=T0; calculating Yt=Yt?1?Tt, for t=1, . . . , N?1, calculating SN?1?=YN?1<<<a, where a is a number of bits to rotate where S0?, . . . , SN?1? are new state values; and calculating St?=Yt?SN?1?, for t=0, . . . , N?2.

Abstract: Various embodiments relate to a key protocol exchange that provide a simple but still secure key exchange protocol. Security of key exchange protocols has many aspects; providing and proving all these properties gets harder with more complex protocols. These security properties may include: perfect forward secrecy; forward deniability; key compromise impersonation resistance; security against unknown key share attack; explicit or implicit authentication; key confirmation; protocol is (session-)key independent; key separation (different keys for encryption and MACing); extendable, e.g. against DOS attacks . . . (e.g. using cookies, . . . ); support of early messages; small communication footprint; and support of for public-key and/or password authentication.

Abstract: Various embodiments relate to a method of hashing a message M using a block cipher, including: producing N block cipher inputs by XORing message indices i, . . . i+N?1 respectively with state values S0, . . . SN?1, wherein N is an integer greater than 1; producing N block cipher keys by XORing N different blocks of message M and at least one of state values S0, . . . SN?1 for each of the N block cipher keys; encrypting the N block cipher inputs using the respective N block cipher keys to produce N block cipher outputs; combining the N block cipher outputs with N block cipher inputs to produce N block cipher combined outputs Tt, for t=0, . . . , N?1; calculating Y0=T0; calculating Yt=Yt?1?Tt, for t=1, . . . , N?1, calculating SN?1?=YN?1<<<a, where a is a number of bits to rotate where S0?, . . . , SN?1? are new state values; and calculating St?=Yt?SN?1?, for t=0, . . . , N?2.

Abstract: A method is provided for performing elliptic curve cryptography that reduces the number of required computations to produce, for example, a key pair. The number of computations is reduced by changing how a random nonce used in the computations is selected. In an embodiment, a look-up table is generated having pre-computed scalar values and elliptic curve points. Every time a new pseudo-random value is created for use in the ECDSA, a combination of the look-up table values is used to create multiple intermediate values. One of the multiple intermediate values is randomly chosen as a replacement value for one of the existing table entries. Each time the look-up table is used, multiple entries in the look-up table are updated to new look-up table values as described. In this manner, new randomness is provided in every step to generate the next pseudo-random nonce as a combination of multiple internally stored temporary look-up table values. Alternately, another mathematical group may be used.

Abstract: A method is provided for performing elliptic curve cryptography that reduces the number of required computations to produce, for example, a key pair. The number of computations is reduced by changing how a random nonce used in the computations is selected. In an embodiment, a look-up table is generated having pre-computed scalar values and elliptic curve points. Every time a new pseudo-random value is created for use in the ECDSA, a combination of the look-up table values is used to create multiple intermediate values. One of the multiple intermediate values is randomly chosen as a replacement value for one of the existing table entries. Each time the look-up table is used, multiple entries in the look-up table are updated to new look-up table values as described. In this manner, new randomness is provided in every step to more e?ciently generate the next pseudo-random nonce as a combination of multiple internally stored temporary look-up table values. Alternately, another mathematical group may be used.

Abstract: A method is provided for generating an elliptic curve cryptography key pair that uses two topologically identical pseudo-random number generators operating in parallel and in step with each other. One generator operates in the scalar number domain and the other generator operates in the elliptic curve point domain. Parallel sequences of pseudo-random elliptic curve points aG and corresponding scalars a are generated in this manner. A scalar a becomes a private key and an elliptic curve point aG is a public key of a key pair. Each generator is advanced by one iteration successively, and the isomorphic relationship ensures that the point domain generator always contains values which are multiples of the system base point according to values contained in the corresponding position in the number domain generator. In one embodiment, the pseudo-random number generators are each characterized as being lagged Fibonacci generators.