Al-Somani
Turki F. Al-Somani, Dhahran SA
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20090214023 | Method for elliptic curve scalar multiplication - The method for elliptic curve scalar multiplication may provide several countermeasures to protect scalar multiplication of a private key k by a point P to produce the product kP from power analysis attacks. First, the private key, k, is partitioned into a plurality of key partitions, which are processed in a random order, the resulting points being accumulated to produce the scalar product kP. Second, in each partition, the encoding is randomly selected to occur in binary form or in Non-Adjacent Form (NAF), with the direction of bit inspection being randomly assigned between most-to-least and least-to-most. Third, in each partition, each zero in the key may randomly perform a dummy point addition operation in addition to the doubling operation. The method may be implemented in software, smart cards, circuits, processors, or application specific integrated circuits (ASICs) designed to carry out the method. | 08-27-2009 |
Turki F. Al-Somani, Makkah SA
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20120008780 | METHOD FOR ELLIPTIC CURVE SCALAR MULTIPLICATION - The method for elliptic curve scalar multiplication may provide several countermeasures to protect scalar multiplication of a private key k by a point P to produce the product kP from power analysis attacks. First, the private key, k, is partitioned into a plurality of key partitions, which are processed in a random order, the resulting points being accumulated to produce the scalar product kP. Second, in each partition, the encoding is randomly selected to occur in binary form or in Non-Adjacent Form (NAF), with the direction of bit inspection being randomly assigned between most-to-least and least-to-most. Third, in each partition, each zero in the key may randomly perform a dummy point addition operation in addition to the doubling operation. The method may be implemented in software, smart cards, circuits, processors, or application specific integrated circuits (ASICs) designed to carry out the method. | 01-12-2012 |
20140105381 | METHOD FOR GENERIC-POINT PARALLEL ELLIPTIC CURVE SCALAR MULTIPLICATION - The method for generic-point parallel elliptic curve scalar multiplication replaces the pre-computation overhead of conventional elliptic curve scalar multiplication by post-computations that can be parallelized. This greatly increases the speed and efficiency of scalar multiplication performed in elliptic curve cryptography. According to the method, when scalar multiplication is required, the scalar integer is partitioned into a plurality of partitions, and calculations in each partition are performed simultaneously or in parallel on separate processors using conventional binary protocols. The bit size of each partition is adjusted to balance the load between the processors, i.e., so that each processor performs substantially the same number of point operations. The resulting calculations from each partition are accumulated or summed to produce the point that is the product of the scalar multiplication. | 04-17-2014 |
Turki Faisal Al-Somani, Makkah SA
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20140177824 | SYSTEM AND METHOD FOR SECURING SCALAR MULTIPLICATION AGAINST DIFFERENTIAL POWER ATTACKS - The system and method for securing scalar multiplication against differential power attacks (DPAs) delays required point additions in elliptic curve cryptosystem scalar multiplication. A buffer is used to store the points that will be added later in a random manner. Then, a randomly selected one of the stored points in the buffer is added to the accumulation point, or several randomly selected points are added consecutively. This makes the power trace appear as a repeated sequence of consecutive point doubling followed by consecutive point additions, which makes it very difficult for an attacker to know the exact value of the inspected bit during the scalar multiplication process. | 06-26-2014 |
20140177827 | SYSTEM AND METHOD FOR SECURING SCALAR MULTIPLICATION AGAINST SIMPLE POWER ATTACKS - The system and method for securing scalar multiplication against simple power attacks (SPAs) delays required point additions in elliptic curve cryptosystem scalar multiplication. A buffer is used to store the points that will be added later until the buffer is full or the last bit of a multiplier k is inspected, Then, the stored points in the buffer are added to the accumulation point. The same procedure is repeated whenever the buffer is full again. This makes the power trace appears as a repeated sequence of consecutive point doubling followed by consecutive point additions. This makes it very difficult for an attacker to know the exact value of the inspected bit during the scalar multiplication process. | 06-26-2014 |