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#| BEGIN (Введите свое решение) |#
(define (square n)
(* n n))
(define (remainder-check x m)
(if (and
(not (= 1 x))
(not (= (- m 1) x))
(= (remainder (square x) m) 1))
0
(remainder (square x) m)))
(define (expmod-check base exp m)
(cond ((= exp 0) 1)
((even? exp)
(remainder-check (expmod-check base (/ exp 2) m) m))
(else
(remainder
(* base (expmod-check base (- exp 1) m))
m))))
(define (miller-rabin-test n)
(define (try-it a)
(= (expmod-check a (- n 1) n) 1))
(try-it (+ 1 (random (- n 1)))))
#| END |#
#| BEGIN (Введите свое решение) |#
(define (square x) (* x x))
(define (miller-rabin-expmod base exp m)
(define (squaremod-with-check x)
(define (check-nontrivial-sqrt1 x rem-square)
(if (and (= rem-square 1)
(not (= x 1))
(not (= x (- m 1))))
0
rem-square))
(check-nontrivial-sqrt1 x (remainder (square x) m)))
(cond [(= exp 0) 1]
[(even? exp) (squaremod-with-check (miller-rabin-expmod base (/ exp 2) m))]
[else (remainder (* base (miller-rabin-expmod base (- exp 1) m)) m)]))
(define (miller-rabin-test n)
(define (try-it a)
(define (check-it x)
(and (not (= x 0)) (= x 1)))
(check-it (miller-rabin-expmod a (- n 1) n)))
(try-it (+ 1 (random (- n 1)))))
#| END |#
#| BEGIN (Введите свое решение) |#
(define (square n)
(* n n))
(define (remainder-check x m)
(if (and
(not (= 1 x))
(not (= (- m 1) x))
(= (remainder (square x) m) 1))
0
(remainder (square x) m)))
(define (expmod-check base exp m)
(cond ((= exp 0) 1)
((even? exp)
(remainder-check (expmod-check base (/ exp 2) m) m))
(else
(remainder
(* base (expmod-check base (- exp 1) m))
m))))
(define (miller-rabin-test n)
(define (try-it a)
(= (expmod-check a (- n 1) n) 1))
(try-it (+ 1 (random (- n 1)))))
#| END |#
#| BEGIN (Введите свое решение) |#
(define (square x) (* x x))
(define (miller-rabin-expmod base exp m)
(define (squaremod-with-check x)
(define (check-nontrivial-sqrt1 x rem-square)
(if (and (= rem-square 1)
(not (= x 1))
(not (= x (- m 1))))
0
rem-square))
(check-nontrivial-sqrt1 x (remainder (square x) m)))
(cond [(= exp 0) 1]
[(even? exp) (squaremod-with-check (miller-rabin-expmod base (/ exp 2) m))]
[else (remainder (* base (miller-rabin-expmod base (- exp 1) m)) m)]))
(define (miller-rabin-test n)
(define (try-it a)
(define (check-it x)
(and (not (= x 0)) (= x 1)))
(check-it (miller-rabin-expmod a (- n 1) n)))
(try-it (+ 1 (random (- n 1)))))
#| END |#