A random number generator resistant to side-channel attacks. The random number generator includes an entropy unit generating random pulses, a random frequency clock generator generating random frequencies by receiving random pulses output from the entropy unit, and an MCU externally masking a specific operation or a specific instruction based on a random frequency received from the random frequency clock generator.

A random number generator resistant to side-channel attacks. The random number generator includes an entropy unit generating random pulses, a random frequency clock generator generating random frequencies by receiving random pulses output from the entropy unit, and an MCU externally masking a specific operation or a specific instruction based on a random frequency received from the random frequency clock generator.

A communication system includes: a transmitter including: an arithmetic decoder configured to generate an output symbol based on input bits and a symbol frequency table that sets frequencies of excluded symbols to 0 and frequencies of allowed symbols to non-zero values, the transmitter being configured to iteratively generate a sequence of restricted packets and an ending state, the sequence of restricted packets excluding instances of the one or more excluded symbols and to transmit the sequence of restricted packets and the ending state on a channel; and a receiver including: an arithmetic encoder configured to compute an output state based on an input state, an input symbol, and the symbol frequency table, the receiver being configured to: supply an ending state received from the channel and the restricted packets to the arithmetic encoder to iteratively generate a final state, and recover a bit sequence from the final state.

A secure random number that follows a binomial distribution is generated without performing successive communication. A secure computation apparatus (1.sub.i) generates a share [r].sub.i of a random number r that follows a binomial distribution. A parameter storage unit (10) stores a pseudorandom function PRF, at least one set of a key k.sub.A and a polynomial f.sub.A. A pseudorandom number generating unit (11) obtains a pseudorandom number p.sub.A for each of the keys k.sub.A by computing the pseudorandom function PRF(k.sub.A, a) using the keys k.sub.A. A bit counting unit (12) counts the number r.sub.A of 1s included in each pseudorandom number p.sub.A. A random number share generating unit (13) obtains the sum of products of the number r.sub.A of 1s and an output of the polynomial f.sub.A(i) corresponding to the number r.sub.A of 1s as the share [r].sub.i of the random number r.

A secure random number that follows a binomial distribution is generated without performing successive communication. A secure computation apparatus (1.sub.i) generates a share [r].sub.i of a random number r that follows a binomial distribution. A parameter storage unit (10) stores a pseudorandom function PRF, at least one set of a key k.sub.A and a polynomial f.sub.A. A pseudorandom number generating unit (11) obtains a pseudorandom number p.sub.A for each of the keys k.sub.A by computing the pseudorandom function PRF(k.sub.A, a) using the keys k.sub.A. A bit counting unit (12) counts the number r.sub.A of 1s included in each pseudorandom number p.sub.A. A random number share generating unit (13) obtains the sum of products of the number r.sub.A of 1s and an output of the polynomial f.sub.A(i) corresponding to the number r.sub.A of 1s as the share [r].sub.i of the random number r.

In an electronic gaming device, instances of a target symbol are swapped in to symbol positions of one or more reel strips using one or more index tables to identify the symbol positions at which to swap in the instances of the target symbol. The index table(s) can be configured to cluster instances of the target symbol according to a deterministic approach. Subsequently, spin results are determined for one or more spins of reels using the reel strips.

In an electronic gaming device, instances of a target symbol are swapped in to symbol positions of one or more reel strips using one or more index tables to identify the symbol positions at which to swap in the instances of the target symbol. The index table(s) can be configured to cluster instances of the target symbol according to a deterministic approach. Subsequently, spin results are determined for one or more spins of reels using the reel strips.

A pseudo speckle pattern generation apparatus includes a light source, a beam expander, and a spatial light modulator. The spatial light modulator has an intensity modulation distribution based on a pseudo speckle pattern calculated from a pseudo random number pattern and a correlation function, receives light output from the light source and increased in beam diameter by the beam expander, spatially modulates the received light according to the modulation distribution, and outputs modulated light.

A pseudo speckle pattern generation apparatus includes a light source, a beam expander, and a spatial light modulator. The spatial light modulator has an intensity modulation distribution based on a pseudo speckle pattern calculated from a pseudo random number pattern and a correlation function, receives light output from the light source and increased in beam diameter by the beam expander, spatially modulates the received light according to the modulation distribution, and outputs modulated light.

A true random metastable flip-flop (TRMFF) compiler generates an electrical architecture for a TRMFF chain. The compiler selects components for the TRMFF chain from a library of standard cells and logically connects these components in accordance with a primitive polynomial to generate the electrical architecture. The TRMFF chain provides a sequence of random numbers from one or more physical processes in accordance with the primitive polynomial. During operation, one or more microscopic phenomena inside and/or outside of the TRMFF chain can cause one or more low-level, statistically random entropy noise signals to be present within the TRMFF chain. The TRMFF chain advantageously utilizes the one or more low-level, statistically random entropy noise signals to provide the sequence of random numbers.