Abstract: Various embodiments relate to a method for masked decoding of a polynomial a using an arithmetic sharing a to perform a cryptographic operation in a data processing system using a modulus q, the method for use in a processor of the data processing system, including: subtracting an offset ? from each coefficient of the polynomial a; applying an arithmetic to Boolean (A2B) function on the arithmetic shares of each coefficient ai of the polynomial a to produce Boolean shares âi that encode the same secret value ai; and performing in parallel for all coefficients a shared binary search to determine which of coefficients ai are greater than a threshold t to produce a Boolean sharing value {circumflex over (b)} of the bitstring b where each bit of b decodes a coefficient of the polynomial a.

Abstract: A true random number generator circuit includes a ring oscillator and a plurality of sampling circuits. The ring oscillator includes a plurality of series-connected stages coupled together in a ring. An output of a last stage of the ring oscillator is coupled to an input of a first stage of the ring oscillator. A sampling circuit of the plurality of sampling circuits has an input coupled to a node located between two adjacent stages of the plurality of series-connected stages. Every node of the ring oscillator is coupled to a corresponding sampling circuit of the plurality of sampling circuits. In another embodiment, a method for generating a random number is provided.

Abstract: Various embodiments relate to a method for masked decoding of a polynomial a using an arithmetic sharing a to perform a cryptographic operation in a data processing system using a modulus q, the method for use in a processor of the data processing system, including: subtracting an offset ? from each coefficient of the polynomial a; applying an arithmetic to Boolean (A2B) function on the arithmetic shares of each coefficient ai of the polynomial a to produce Boolean shares âi that encode the same secret value ai; and performing in parallel for all coefficients a shared binary search to determine which of coefficients ai are greater than a threshold t to produce a Boolean sharing value {circumflex over (b)} of the bitstring b where each bit of b decodes a coefficient of the polynomial a.

Abstract: Various embodiments relate to a method for generating a bit stream in a physical unclonable function (PUF) system, including: receiving a set of values from a plurality of physical devices in the PUF system in a first order; sorting the set of values into a second order; for each of the L highest values, setting a corresponding levelTag value to a first bit value and setting a corresponding usageTag value to a first usage value that indicates that the levelTag for the corresponding value is to be used to generate the bit stream, wherein L is a level setting; for each of the L lowest values, setting a corresponding levelTag value to a second bit value and setting a corresponding usageTag value to the first usage value, wherein the first bit value is different from the second bit value; setting the usageTag value for all other values that are not the highest L values or the lowest L values to a second usage value that indicates that the corresponding value is not to be used to generate the bit stream; generatin

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; support of early messages; small communication footprint; and support of for public-key and/or password authentication.

Abstract: Various embodiments relate to a method for generating a bit stream in a physical unclonable function (PUF) system, including: receiving a set of values from a plurality of physical devices in the PUF system in a first order; sorting the set of values into a second order; for each of the L highest values, setting a corresponding levelTag value to a first bit value and setting a corresponding usageTag value to a first usage value that indicates that the levelTag for the corresponding value is to be used to generate the bit stream, wherein L is a level setting; for each of the L lowest values, setting a corresponding levelTag value to a second bit value and setting a corresponding usageTag value to the first usage value, wherein the first bit value is different from the second bit value; setting the usageTag value for all other values that are not the highest L values or the lowest L values to a second usage value that indicates that the corresponding value is not to be used to generate the bit stream; generatin

Abstract: Various embodiments relate to a method and system for encoding data to be stored in a memory, including: encoding the data to be stored in memory with an error detection code (EDC), that can detect up to 4 bit errors, as first encoded data; determining the Hamming weight of the first encoded data; inverting the determined Hamming weight; concatenating the first encoded data and three copies of the inverted Hamming weight as concatenated data; encoding the concatenated data with an error correcting code (ECC), that can correct 1 bit error, as second encoded data; and storing the second encoded data in the memory.

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; support of early messages; small communication footprint; and support of for public-key and/or password authentication.

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.