How does Matlab perform large integer modular arithmetics using Symbolic Math Toolbox?

2022 1 11
2 个回答
更新时间：2022 1 12
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I have implemented an ECC (Elliptic Curve Cryptography) model using Matlab symbolic tool by which the large integer arithmetics can be manipulated. Now I want to implement the algorithm with a 32-bit processor. I am looking for the algorithms that Matlab is using to implement modular addition, subtraction, multiplication and inverse, etc..

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回答（2 个）

John D'Errico
John D'Errico 2022-1-12

0 个投票

You won't get the exact algorithms. MathWorks does not hand out their internal code for this sort of thing, unless you have a job there.
Walter Roberson
Walter Roberson 2022-1-12
Ran in:

0 个投票

Ran in:
S1 = char(evalin(symengine, 'expose(symobj::powermod)'));
S1 = regexprep(S1, '\\n', '\n')
S1 =
'proc(pow : DOM_EXPR, m) : Type::Union(DOM_INT, stdlib::Undefined) name symobj::powermod; local a, n, res; begin assert(op(pow, 0) = #power); [a, n] := [op(pow)]; if ~testtype(a, Type::Integer) then error(message(\"symbolic:numlib:FirstArgumentInteger\")) end_if; if ~testtype(n, Type::Integer) then error(message(\"symbolic:arithmetic:ExpectingInteger2\")) end_if; if ~testtype(m, Type::NonNegInt) then error(message(\"symbolic:arithmetic:ExpectingNonnegativeInteger3\")) end_if; res := powermod(a, n, m); if res = FAIL then undefined else res end_if end_proc'
S2 = char(evalin(symengine, 'expose(powermod)'));
S2 = regexprep(S2, '\\n', '\n')
S2 =
'proc(p, n, m) name powermod; begin if args(0) < 1 then error(message(\"symbolic:arithmetic:IncorrectNumberOfArguments\")) else if p::dom::powermod <> FAIL then return(p::dom::powermod(args())) end_if end_if; if args(0) <> 3 then error(message(\"symbolic:arithmetic:IncorrectNumberOfArguments\")) end_if; case domtype(m) of DOM_INT do if domtype(n) <> DOM_INT then error(message(\"symbolic:arithmetic:ExpectingInteger2\")) end_if; if iszero(m) then return(p^n) end_if; case domtype(p) of DOM_INT do of DOM_RAT do if n < 0 then return(stdlib::powermod(1/p, -n, m)) else return(stdlib::powermod(args())) end_if of DOM_POLY do return(poly(poly(p, IntMod(m))^n, op(p, 2..3))) otherwise return(op(poly(p, IntMod(m))^n, 1)) end_case of DOM_POLY do if testargs() then if nops(op(m, 2)) <> 1 then error(message(\"symbolic:arithmetic:ExpectingUnivariatePolynomial3\")) else if domtype(n) <> DOM_INT then error(message(\"symbolic:arithmetic:ExpectingInteger2\")) end_if end_if end_if; if domtype(p) <> DOM_POLY then if p = FAIL then FAIL else op(powermod(poly(p, op(m, 2..3)), n, m), 1) end_if else if op(p, 2..3) = op(m, 2..3) then case n of 0 do return(p^0) of 1 do return(divide(p, m, Rem)) end_case; faclib::powermod_poly(args()) else if op(p, 3) = op(m, 3) then poly(powermod(poly(p, op(m, 2..3)), n, m), op(p, 2..3)) else error(message(\"symbolic:arithmetic:PolynomialTypesDiffer\")) end_if end_if end_if; break of DOM_FAIL do return(FAIL) otherwise m := poly(m); if testargs() then if type(m) <> DOM_POLY then error(message(\"symbolic:arithmetic:CannotConvertToPolynomial3\")) end_if; if type(n) <> DOM_INT then error(message(\"symbolic:arithmetic:ExpectingInteger2\")) end_if end_if; return(powermod(p, n, m)) end_case end_proc'
S3 = char(evalin(symengine, 'expose(stdlib::powermod)'));
S3 = regexprep(S3, '\\n', '\n')
S3 = 'builtin(1047, NIL, \"powermod\", NIL)'
So... at least some of the cases are built-in, source not published.

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