Implementing the Rivest Shamir and Adleman Public Key Encryption Algorithm on a Standard Digital Signal Processor

By P. Barrett. 1986

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Citations in the corpus

HEAX: An Architecture for Computing on Encrypted Data (2019, methodology): “with at most w bits, given an integer x 2 q 0; (p 1)2 , precompute u = 22w=p , and compute z =x (mod p). We omit u from function inputs for simplicity. This follows the Barrett reduction algorithm in [8]. It can be used to reduce a single-word or double-word integer. Mod(a;p) performs Mod(a i; p) fo”
Handbook of Applied Cryptography (2018, unknown): “42) is due to Barrett [75].”
Accelerating Fully Homomorphic Encryption over the Integers with Super-size Hardware Multiplier and Modular Reduction (2013, methodology): “Generally, the modular reduction algorithms used in traditional long bit-length cryptography implementations are Montgomery [22] and Barrett reduction [15].”
Guide to Elliptic Curve Cryptography (2004, unknown): “14) is due to Barrett [29].”
A Custom Accelerator for Homomorphic Encryption Applications (2017, methodology): “In our design, however, we use Barrett’s algorithm [40] for modular reduction, which requires 33 33-bit multiplication operations, for which the utilized method is described in Algorithm 3.”
HEAX: High-Performance Architecture for Computation on Homomorphically Encrypted Data in the Cloud (2019, methodology): “This follows the Barrett reduction algorithm in [8].”
Speeding up the Number Theoretic Transform for Faster Ideal Lattice-Based Cryptography (2016, methodology): “We note that the first two methods use optimized variants of the Barrett reduction [4], whereas the latter combines Montgomery reduction (after multiplications) with Barrett reduction (after additions).”
A High-Speed Accelerator for Homomorphic Encryption using the Karatsuba Algorithm (2017, methodology): “The standard algorithm for such an operation is the Barrett reduction [18].”
Accelerating Fully Homomorphic Encryption in Hardware (2015, methodology): “We used the Barrett Modular Reduction Algorithm [4].”
Exploring the Feasibility of Fully Homomorphic Encryption (2015, methodology): “The most popular algorithms for modular reduction are the Montgomery reduction [18] and the Barrett reduction algorithms [19].”
HEPCloud: An FPGA-Based Multicore Processor for FV Somewhat Homomorphic Function Evaluation (2018, methodology): “After an integer multiplication, the result is reduced using the Barrett reduction circuit [2] shown in Fig.”
Accelerating Somewhat Homomorphic Evaluation using FPGAs (2015, methodology): “32-bit Modular Multiplication We use Barrett’s modular reduction algorithm [3] to perform modular multiplication operations.”
Accelerating integer-based fully homomorphic encryption using Comba multiplication (2014, unknown): “Algorithm 2: Barrett reduction [25], [26]”
High-Speed Fully Homomorphic Encryption Over the Integers (2014, methodology): “Generally, the modular reduction algorithms used in traditional long bit-length cryptographic implementations are Montgomery [27] and Barrett reduction [15].”