| References: [1] John Fry., Martin Langhammer (2019). FPGAs Lower Costs for RSA Cryptography, Electronic Engineering Times, September 26, 2003, accessed April 18, 2019, https://www.eetimes.com/document.asp?doc_id=1271927.
[2] Ronald L. Rivest., Adi Shamir., Leonard Adleman. (1978). A Method for Obtaining Digital Signatures and Public-Key Cryptosystems, Communications of the ACM, 21 (2), (1978): 120–126.
[3] Hankerson, D. C., et al. (2000). Coding Theory and Cryptography, 2nd ed. (New York: Marcel Dekker, 2000), 284.
[4] See Neal Koblitz. (2002). Algebraic Aspects of Cryptography, Algorithms and Computation in Mathematics 3 (New York: Springer, 2004), 1–16. For a detailed overview of salient number-theoretic issues involved in RSA cryptography, see Valery V.
Yaschenko, Cryptography: An Introduction, Student Mathematical Library 18 (Providence, RI: American Mathematical Society, 2002), chap. 4.
[5] Roland Schmitz. (2008). Public Key Cryptography: A Dynamical Systems Perspective, In: Proceedings of the 2008 Second International Conference on Emerging Security Information, Systems and Technologies (Cap Esterel, France, 2008), 211.
[6] Alfred J. Menezes., et al. (2001). Handbook of Applied Cryptography (Boca Raton, FL: CRC Press, 2001), 286–287.
[7] The early modular multiplication and exponentiation algorithms based on the Montgomery reduction technique required that the modulus be an odd integer. Koç work shows that with the help of the Chinese Remainder Theorem, the Montgomery reduction algorithm can be used to efficiently execute these modular arithmetic operations with respect to an even modulus. See Ç.K. Koç, Montgomery Reduction with Even Modulus, IEE Proceedings - Computers and Digital Techniques, 141, no. 5 (September 1994): 314–316.
[8] Peter L. Montgomery. (1985). Modular Multiplication Without Trial Division, Mathematics of Computation 44, no. 170 (April 1985), 519–521.
[9] The efficient computation of the modular exponentiations is very important for public-key crypto systems. For example, see Chia-Long Wu, Der-Chyuan Lou, and Te-Jen Chang, An Efficient Montgomery Exponentiation Algorithm for Cryptographic Applications, Informatica 16 (3) (2005): 449–468 as well as Corinne McIvor, Maire McLoone, and John V. McCanny, Modified Montgomery Modular Multiplication and RSA Exponentiation Techniques, IEEE Proceedings - Computers and Digital Techniques 151, no. 6 (November 2004): 402–408.
[10] Michael Welschenbach, Cryptography in C and C++, 2nd ed. (New York: Apress, 2005), 106–109.
[11] Menezes., et al. Handbook of Applied Cryptography, 602.
[12] Ibid., 619–620.
[13] Ibid., 290–291. |
