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Exponential by Unknown on Nov 25, 2005			Not available!
Hi, I would like to ask if anyone implement exponential calculation in vhdl and how to go about doing the algorithm. Most importantly, how to test the algorithm if it is working properly. Thanks. Hi, I would like to ask if anyone implement exponential calculation in vhdl and how to go about doing the algorithm. Most importantly, how to test the algorithm if it is working properly. Thanks.

Exponential by Unknown on Nov 25, 2005			Not available!
For positive integer exponents, and very large numbers, the BasicRSA project implements a square-and-multiply algorithm for modular exponentiation. It uses two copies of a shift-and-add multiplier, one to do modular squares, and one to do modular multiplication of dissimilar numbers. You have to do a square for every bit position in the exponent, and multiply the square by the result of the multiplication (hint, start with 1) every time the exponent bit position is 1. Testing can be a real pain, since you have to calculate all the exponents used in your test set and compare the correct results with whatever your core produces. I don't know a shortcut for that. -- Steven R. McQueen Phone: (951) 809-3232 Email: <A HREF="http://www.opencores.org/mailman/listinfo/cores">srmcqueen at mcqueentech.com</A> Web: www.mcqueentech.com On Fri, 2005-11-25 at 17:23 +0100, <A HREF="http://www.opencores.org/mailman/listinfo/cores">oceanfrea at hotmail.com</A> wrote: [q] Hi, I would like to ask if anyone implement exponential calculation in vhdl and how to go about doing the algorithm. Most importantly, how to test the algorithm if it is working properly. Thanks. _______________________________________________ <A HREF="http://www.opencores.org/mailman/listinfo/cores">http://www.opencores.org/mailman/listinfo/cores</A>[/q] For positive integer exponents, and very large numbers, the BasicRSA project implements a square-and-multiply algorithm for modular exponentiation. It uses two copies of a shift-and-add multiplier, one to do modular squares, and one to do modular multiplication of dissimilar numbers. You have to do a square for every bit position in the exponent, and multiply the square by the result of the multiplication (hint, start with 1) every time the exponent bit position is 1. Testing can be a real pain, since you have to calculate all the exponents used in your test set and compare the correct results with whatever your core produces. I don't know a shortcut for that. -- Steven R. McQueen Phone: (951) 809-3232 Email: srmcqueen at mcqueentech.com Web: www.mcqueentech.com On Fri, 2005-11-25 at 17:23 +0100, oceanfrea at hotmail.com wrote: Hi, I would like to ask if anyone implement exponential calculation in vhdl and how to go about doing the algorithm. Most importantly, how to test the algorithm if it is working properly. Thanks. _______________________________________________ http://www.opencores.org/mailman/listinfo/cores

Exponential by Unknown on Nov 27, 2005			Not available!
----- Original Message ----- From: Steven R. McQueen<<A HREF="http://www.opencores.org/mailman/listinfo/cores">srmcqueen at m...</A>> To: Date: Fri Nov 25 19:05:18 CET 2005 Subject: [oc] Exponential [q] For positive integer exponents, and very large numbers, the BasicRSA project implements a square-and-multiply algorithm for modular exponentiation. It uses two copies of a shift-and-add multiplier, one to do modular squares, and one to do modular multiplication of dissimilar numbers. You have to do a square for every bit position in the exponent, and multiply the square by the result of the multiplication (hint, start with 1) every time the exponent bit position is 1. Testing can be a real pain, since you have to calculate all the exponents used in your test set and compare the correct results with whatever your core produces. I don't know a shortcut for that. -- Steven R. McQueen Phone: (951) 809-3232 Email: srmcqueen at mcqueentech.com Web: www.mcqueentech.com On Fri, 2005-11-25 at 17:23 +0100, oceanfrea at hotmail.com wrote: [q]> Hi, I would like to ask if anyone implement exponential [/q] calculation in [q]> vhdl and how to go about doing the algorithm. Most [/q] importantly, how to [q]> test the algorithm if it is working properly. Thanks. > _______________________________________________ > <A HREF="http://www.opencores.org/mailman/listinfo/cores">http://www.opencores.org/mailman/listinfo/cores</A> [/q] what about negative integer exponents? Can I implement the same [/q] stuff as you had mentioned? ----- Original Message ----- From: Steven R. McQueensrmcqueen at m...> To: Date: Fri Nov 25 19:05:18 CET 2005 Subject: [oc] Exponential For positive integer exponents, and very large numbers, the BasicRSA project implements a square-and-multiply algorithm for modular exponentiation. It uses two copies of a shift-and-add multiplier, one to do modular squares, and one to do modular multiplication of dissimilar numbers. You have to do a square for every bit position in the exponent, and multiply the square by the result of the multiplication (hint, start with 1) every time the exponent bit position is 1. Testing can be a real pain, since you have to calculate all the exponents used in your test set and compare the correct results with whatever your core produces. I don't know a shortcut for that. -- Steven R. McQueen Phone: (951) 809-3232 Email: srmcqueen at mcqueentech.com Web: www.mcqueentech.com On Fri, 2005-11-25 at 17:23 +0100, oceanfrea at hotmail.com wrote: > Hi, I would like to ask if anyone implement exponential calculation in > vhdl and how to go about doing the algorithm. Most importantly, how to > test the algorithm if it is working properly. Thanks. > _______________________________________________ > http://www.opencores.org/mailman/listinfo/cores what about negative integer exponents? Can I implement the same stuff as you had mentioned?

Exponential by Unknown on Nov 27, 2005			Not available!
On Sun, 2005-11-27 at 16:59 +0100, <A HREF="http://www.opencores.org/mailman/listinfo/cores">oceanfrea at hotmail.com</A> wrote: [q] ----- Original Message ----- From: Steven R. McQueen<<A HREF="http://www.opencores.org/mailman/listinfo/cores">srmcqueen at m...</A>> To: Date: Fri Nov 25 19:05:18 CET 2005 Subject: [oc] Exponential [q]> For positive integer exponents, and very large numbers, the > BasicRSA > project implements a square-and-multiply algorithm for modular > exponentiation. It uses two copies of a shift-and-add multiplier, > one to > do modular squares, and one to do modular multiplication of > dissimilar > numbers. You have to do a square for every bit position in the > exponent, > and multiply the square by the result of the multiplication (hint, > start > with 1) every time the exponent bit position is 1. > Testing can be a real pain, since you have to calculate all the > exponents used in your test set and compare the correct results > with > whatever your core produces. I don't know a shortcut for that. > -- > Steven R. McQueen > Phone: (951) 809-3232 > Email: srmcqueen at mcqueentech.com > Web: www.mcqueentech.com > On Fri, 2005-11-25 at 17:23 +0100, oceanfrea at hotmail.com wrote: [q] > Hi, I would like to ask if anyone implement exponential [/q] > calculation in [q] > vhdl and how to go about doing the algorithm. Most [/q] > importantly, how to [q] > test the algorithm if it is working properly. Thanks. > _______________________________________________ > <A HREF="http://www.opencores.org/mailman/listinfo/cores">http://www.opencores.org/mailman/listinfo/cores</A> [/q] > > what about negative integer exponents? Can I implement the same [/q] stuff as you had mentioned? _______________________________________________[/q] NO! Negative exponents, and real exponents, are floating point operations requiring techniques from your calculus or differential equations class. If you didn't keep the book(s), get a copy! You will probably not use it much, but when you need it, it will be essential. The RSA algorithm is concerned only with positive integers, and can take some special case shortcuts. Steve On Sun, 2005-11-27 at 16:59 +0100, oceanfrea at hotmail.com wrote: ----- Original Message ----- From: Steven R. McQueensrmcqueen at m...> To: Date: Fri Nov 25 19:05:18 CET 2005 Subject: [oc] Exponential > For positive integer exponents, and very large numbers, the > BasicRSA > project implements a square-and-multiply algorithm for modular > exponentiation. It uses two copies of a shift-and-add multiplier, > one to > do modular squares, and one to do modular multiplication of > dissimilar > numbers. You have to do a square for every bit position in the > exponent, > and multiply the square by the result of the multiplication (hint, > start > with 1) every time the exponent bit position is 1. > Testing can be a real pain, since you have to calculate all the > exponents used in your test set and compare the correct results > with > whatever your core produces. I don't know a shortcut for that. > -- > Steven R. McQueen > Phone: (951) 809-3232 > Email: srmcqueen at mcqueentech.com > Web: www.mcqueentech.com > On Fri, 2005-11-25 at 17:23 +0100, oceanfrea at hotmail.com wrote: > Hi, I would like to ask if anyone implement exponential > calculation in > vhdl and how to go about doing the algorithm. Most > importantly, how to > test the algorithm if it is working properly. Thanks. > _______________________________________________ > http://www.opencores.org/mailman/listinfo/cores > > what about negative integer exponents? Can I implement the same stuff as you had mentioned? _______________________________________________ NO! Negative exponents, and real exponents, are floating point operations requiring techniques from your calculus or differential equations class. If you didn't keep the book(s), get a copy! You will probably not use it much, but when you need it, it will be essential. The RSA algorithm is concerned only with positive integers, and can take some special case shortcuts. Steve

Exponential by thilo on Nov 30, 2005			thilo Posts: 3 Joined: Nov 19, 2009 Last seen: Apr 30, 2011
Steven R. McQueen wrote: [q]For positive integer exponents, and very large numbers, the BasicRSA project implements a square-and-multiply algorithm for modular exponentiation. It uses two copies of a shift-and-add multiplier, one to do modular squares, and one to do modular multiplication of dissimilar numbers. You have to do a square for every bit position in the exponent, and multiply the square by the result of the multiplication (hint, start with 1) every time the exponent bit position is 1. Testing can be a real pain, since you have to calculate all the exponents used in your test set and compare the correct results with whatever your core produces. I don't know a shortcut for that. [/q] practical hint: on unix is a tool called "bc" This is really cool for long long big big numbers (integer/fixed point only) :-) Steven R. McQueen wrote: For positive integer exponents, and very large numbers, the BasicRSA project implements a square-and-multiply algorithm for modular exponentiation. It uses two copies of a shift-and-add multiplier, one to do modular squares, and one to do modular multiplication of dissimilar numbers. You have to do a square for every bit position in the exponent, and multiply the square by the result of the multiplication (hint, start with 1) every time the exponent bit position is 1. Testing can be a real pain, since you have to calculate all the exponents used in your test set and compare the correct results with whatever your core produces. I don't know a shortcut for that. practical hint: on unix is a tool called "bc" This is really cool for long long big big numbers (integer/fixed point only) :-)

Basic RSA by mahtab14 on Aug 12, 2014			mahtab14 Posts: 1 Joined: Jul 14, 2013 Last seen: Sep 14, 2014
Hi I would like to ask is Implementation of RSA Crypto-Processor(BasicRSA ) Based on Montgomery Algorithm?? Thanks Hi I would like to ask is Implementation of RSA Crypto-Processor(BasicRSA ) Based on Montgomery Algorithm?? Thanks

RE: Exponential by srmcqueen on Aug 12, 2014			srmcqueen Posts: 3 Joined: Aug 17, 2003 Last seen: Aug 26, 2014
[q]Hi I would like to ask is Implementation of RSA Crypto-Processor(BasicRSA ) Based on Montgomery Algorithm?? Thanks [/q] I did develop the algorithm independently, but as nearly as I can tell, BasicRSA is, in fact, a brute force implementation of the Montgomery Algorithm. Montgomery seems to have done something tricky involving closed sets over 0-2^^n where 2^^n is greater than the modulus, with some magic at the end to make everything come out right. I, on the other hand, just applied the modulus to every calculation to keep the adders from becoming too big. I'm not really very good with set theory, so I cannot claim that I understand the Montgomery Algorithm correctly. Hi I would like to ask is Implementation of RSA Crypto-Processor(BasicRSA ) Based on Montgomery Algorithm?? Thanks I did develop the algorithm independently, but as nearly as I can tell, BasicRSA is, in fact, a brute force implementation of the Montgomery Algorithm. Montgomery seems to have done something tricky involving closed sets over 0-2^^n where 2^^n is greater than the modulus, with some magic at the end to make everything come out right. I, on the other hand, just applied the modulus to every calculation to keep the adders from becoming too big. I'm not really very good with set theory, so I cannot claim that I understand the Montgomery Algorithm correctly.

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