crypto improvements, and blum blum shub
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@ -0,0 +1,8 @@
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USING: kernel math ;
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IN: crypto
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: barrett-mu ( n size -- mu )
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#! Calculates Barrett's reduction parameter mu
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#! size = word size in bits (8, 16, 32, 64, ...)
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over log2 1+ over / 2 * >r 2 swap ^ r> ^ swap / floor ;
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@ -0,0 +1,30 @@
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USING: kernel math sequences namespaces crypto math-contrib ;
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IN: crypto-internals
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! Blum Blum Shub, M = pq
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TUPLE: bbs x n ;
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: generate-bbs-primes ( numbits -- p q )
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#! two primes congruent to 3 (mod 4)
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dup [ random-miller-rabin-prime==3(mod4) ] 2apply ;
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IN: crypto
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: make-bbs ( numbits -- blum-blum-shub )
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#! returns a Blum-Blum-Shub tuple
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generate-bbs-primes * [ find-relative-prime ] keep <bbs> ;
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IN: crypto-internals
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SYMBOL: blum-blum-shub 256 make-bbs global [ blum-blum-shub set ] bind
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IN: crypto
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: next-bbs-bit ( bbs -- bit )
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#! x = x^2 mod n, return low bit of calculated x
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[ [ bbs-x ] keep 2 swap bbs-n ^mod ] keep
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[ set-bbs-x ] keep bbs-x 1 bitand ;
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SYMBOL: temp-bbs
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: (bbs-bits) ( numbits bbs -- n )
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temp-bbs set [ [ temp-bbs get next-bbs-bit ] swap make-bits ] with-scope ;
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: random-bbs-bits* ( numbits bbs -- n ) (bbs-bits) ;
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: random-bbs-bits ( numbits -- n ) blum-blum-shub get (bbs-bits) ;
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@ -1,22 +1,11 @@
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IN: crypto-internals
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USING: kernel io strings sequences namespaces math prettyprint
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test parser lists ;
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USING: kernel io strings sequences namespaces math parser lists ;
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: w+ ( int -- int )
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+ HEX: ffffffff bitand ; inline
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: nth-int ( string n -- int )
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2 shift dup 4 + rot <slice> le> ; inline
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: nth-int-be ( string n -- int )
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2 shift dup 4 + rot <slice> be> ; inline
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: float-sin ( int -- int )
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sin abs 4294967296 * >bignum ; inline
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: update ( num var -- )
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[ w+ ] change ; inline
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: w+ ( int -- int ) + HEX: ffffffff bitand ; inline
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: nth-int ( string n -- int ) 2 shift dup 4 + rot <slice> le> ; inline
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: nth-int-be ( string n -- int ) 2 shift dup 4 + rot <slice> be> ; inline
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: float-sin ( int -- int ) sin abs 4294967296 * >bignum ; inline
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: update ( num var -- ) [ w+ ] change ; inline
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: update-old-new ( old new -- )
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[ get >r get r> ] 2keep >r >r w+ dup r> set r> set ; inline
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@ -40,14 +29,9 @@ test parser lists ;
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dup length 3 shift 8 >be %
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] "" make nip ;
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: num-blocks ( length -- num )
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-6 shift ;
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: get-block ( string num -- string )
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6 shift dup 64 + rot <slice> ;
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: shift-mod ( n s w -- n )
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>r shift r> 1 swap shift 1 - bitand ; inline
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: num-blocks ( length -- num ) -6 shift ;
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: get-block ( string num -- string ) 6 shift dup 64 + rot <slice> ;
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: shift-mod ( n s w -- n ) >r shift r> 1 swap shift 1 - bitand ; inline
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IN: crypto
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: bitroll ( n s w -- n )
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@ -58,5 +42,4 @@ IN: crypto
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[ shift-mod ] 3keep
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[ - ] keep shift-mod bitor ; inline
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: hex-string ( str -- str )
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[ [ >hex 2 48 pad-left % ] each ] "" make ;
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: hex-string ( str -- str ) [ [ >hex 2 48 pad-left % ] each ] "" make ;
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@ -6,8 +6,11 @@ USING: kernel parser sequences words compiler ;
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{
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"common"
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"base64"
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"barrett"
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"montgomery"
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"random"
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"miller-rabin"
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"blum-blum-shub"
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"md5"
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"sha1"
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"rsa"
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@ -1,6 +1,5 @@
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USING: kernel io strings sequences namespaces math parser lists crypto ;
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IN: crypto-internals
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USING: kernel io strings sequences namespaces math
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test parser lists crypto ;
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SYMBOL: a
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SYMBOL: b
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@ -154,30 +153,15 @@ SYMBOL: old-d
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update-md
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drop ;
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IN: crypto
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: string>md5 ( string -- md5 )
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! [
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[
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initialize-md5 pad-string-md5
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dup length num-blocks [ 2dup get-block process-md5-block ] repeat
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drop get-md5
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;
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! ] with-scope ;
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: string>md5str ( string -- str )
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string>md5 hex-string ;
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] with-scope ;
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: string>md5str ( string -- str ) string>md5 hex-string ;
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: stream>md5 ( stream -- md5 ) contents string>md5 ;
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: file>md5 ( file -- md5 ) <file-reader> stream>md5 ;
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: test-md5 ( -- )
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[ "d41d8cd98f00b204e9800998ecf8427e" ] [ "" string>md5str ] unit-test
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[ "0cc175b9c0f1b6a831c399e269772661" ] [ "a" string>md5str ] unit-test
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[ "900150983cd24fb0d6963f7d28e17f72" ] [ "abc" string>md5str ] unit-test
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[ "f96b697d7cb7938d525a2f31aaf161d0" ] [ "message digest" string>md5str ] unit-test
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[ "c3fcd3d76192e4007dfb496cca67e13b" ] [ "abcdefghijklmnopqrstuvwxyz" string>md5str ] unit-test
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[ "d174ab98d277d9f5a5611c2c9f419d9f" ] [ "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789" string>md5str ] unit-test
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[ "57edf4a22be3c955ac49da2e2107b67a" ] [ "12345678901234567890123456789012345678901234567890123456789012345678901234567890" string>md5str ] unit-test
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;
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@ -1,7 +1,5 @@
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USING: kernel math errors namespaces math-contrib sequences io ;
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USE: prettyprint
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USE: inspector
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IN: crypto
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IN: crypto-internals
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SYMBOL: a
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SYMBOL: n
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@ -11,8 +9,7 @@ SYMBOL: composite
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SYMBOL: count
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SYMBOL: trials
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: rand[1..n-1] ( n -- )
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1- random-int 1+ ;
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: rand[1..n-1] ( n -- ) 1- random-int 1+ ;
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: (factor-2s) ( s n -- s n )
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dup 2 mod 0 = [ -1 shift >r 1+ r> (factor-2s) ] when ;
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@ -23,14 +20,12 @@ SYMBOL: trials
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"input must be positive and even" throw
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] unless 0 swap (factor-2s) ;
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: init-miller-rabin ( n -- )
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0 composite set
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[ n set ] keep 10000 < 20 100 ? trials set ;
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: init-miller-rabin ( n trials -- ) 0 composite set trials set n set ;
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: miller-rabin ( n -- bool )
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: (miller-rabin) ( n -- bool )
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n get dup 1 = [ drop f ]
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[
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init-miller-rabin
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n get even? [
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even? [
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f ] [
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n get 1- factor-2s s set r set
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trials get [
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@ -51,11 +46,44 @@ SYMBOL: trials
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] repeat
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composite get 0 = [ t ] [ composite get not ] if
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] if
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] with-scope ;
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] if ;
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IN: crypto
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: miller-rabin* ( n trials -- bool )
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#! Probailistic primality test for n > 2, with trials as a parameter
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[ init-miller-rabin (miller-rabin) ] with-scope ;
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: miller-rabin ( n -- bool )
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#! Probabilistic primality test for n > 2, 100 trials
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[ 100 miller-rabin* ] with-scope ;
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: next-miller-rabin-prime ( n -- p )
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#! finds the next prime probabilistically
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dup even? [ 1+ ] [ 2 + ] if
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dup miller-rabin [ next-miller-rabin-prime ] unless ;
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! random miller rabin prime from a number, or a number of bits
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! expand
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: random-miller-rabin-prime ( numbits -- p )
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#! n = bits
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large-random-bits next-miller-rabin-prime ;
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! 473155932665450549999756893736999469773678960651272093993257221235459777950185377130233556540099119926369437865330559863 100 miller-rabin
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: random-miller-rabin-prime==3(mod4) ( numbits -- p )
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dup random-miller-rabin-prime dup 4 mod 3 = [ drop random-miller-rabin-prime==3(mod4) ] [ nip ] if ;
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: (find-relative-prime) ( m g -- p )
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2dup gcd nip 1 > [ 2 + (find-relative-prime) ] [ nip ] if ;
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: find-relative-prime* ( m g -- p )
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#! find a prime relative to m with initial guess g
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dup even? [ 1+ ] when (find-relative-prime) ;
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: find-relative-prime ( m -- p )
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dup random-int dup even? [ 1+ ] when (find-relative-prime) ;
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: generate-two-unique-primes ( n -- p q )
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#! generate two primes
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dup 5 < [ "not enough primes below 5 bits" throw ] when
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dup [ random-miller-rabin-prime ] keep random-miller-rabin-prime 2dup =
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[ 2drop generate-two-unique-primes ] [ rot drop ] if ;
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@ -0,0 +1,21 @@
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USING: kernel math errors math-contrib ;
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IN: crypto
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! As per http://www.cyphercalc.com/index.htm
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: montgomery-image ( a n -- a' )
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#! a' = a * nextpowerof2(a) mod n
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>r dup next-power-of-2 * r> mod ;
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: montgomery* ( a b -- a*b )
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"todo" throw
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;
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: montgomery-r^2 ( n -- a )
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#! ans = r^2 mod n, where r = nextpowerof2(n)
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[ next-power-of-2 sq ] keep mod ;
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: montgomery-n0' ( n0 size -- n0' )
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#! size should be a multiple of 2, n0 is odd and n0 < 2^size
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#! n0 * n0' = -1 mod 2^w
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2 swap ^ swap neg mod-inv ;
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@ -1,21 +1,17 @@
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IN: crypto
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USING: kernel math sequences namespaces errors hashtables words arrays parser
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compiler syntax lists io threads ;
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USE: prettyprint
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USE: inspector
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IN: crypto
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: make-bits ( quot numbits -- n | quot: -- 0/1 )
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0 -rot [ drop dup call rot 1 shift bitor swap ] each drop ;
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: add-bit ( bit integer -- integer )
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1 shift bitor ;
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: add-bit ( bit integer -- integer ) 1 shift bitor ;
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: append-bits ( inta intb nbits -- int ) swapd shift bitor ;
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: random-bits ( n -- int ) random-int 2 swap ^ random-int ;
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: large-random-bits ( n -- int )
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#! random number with high bit and low bit enabled (odd)
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2 swap ^ [ random-int ] keep -1 shift 1 bitor bitor ;
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: next-double ( -- f ) 53 random-bits 9007199254740992 /f ;
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: append-bits ( inta intb nbits -- int )
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swapd shift bitor ;
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! varying bit-length random number
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: random-bits ( n -- int )
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random-int 2 swap ^ random-int ;
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: next-double ( -- f )
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53 random-bits 9007199254740992 /f ;
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SYMBOL: last-keyboard
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: crypto-random-int ( numbits -- integer )
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@ -40,41 +36,11 @@ SYMBOL: last-keyboard
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last-keyboard set
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] each
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] with-scope ;
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IN: crypto-internals
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SYMBOL: q
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SYMBOL: m
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! : qm ( integer -- )
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! 1 swap - 2 mod dup 0 = [
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! 2 /
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! ]
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! ;
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SYMBOL: test-count
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SYMBOL: num-tests
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! : (create-miller-rabin-prime) ( bitlength -- )
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! auto-crypto-random-int qm
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IN: crypto
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! one in 2 ^ numtests chance of being composite (i believe)
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! : create-miller-rabin-prime ( bitlength numtests -- prime )
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! [
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! num-tests set
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! 0 test-count set
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! (create-miller-rabin-prime)
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! ! dup -1 = [ create-miller-rabin-prime ] when
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! ] with-scope ;
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! : numbits ( integer -- n )
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! dup 0 = [ log2 1+ ] unless ;
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: 0count ( integer -- n )
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0 swap [ 0 = [ 1+ ] when ] each-bit ;
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: 1count ( integer -- n )
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0 swap [ 1 = [ 1+ ] when ] each-bit ;
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: 0count ( integer -- n ) 0 swap [ 0 = [ 1+ ] when ] each-bit ;
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: 1count ( integer -- n ) 0 swap [ 1 = [ 1+ ] when ] each-bit ;
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IN: crypto-internals
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SYMBOL: a
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@ -106,8 +72,6 @@ IN: crypto
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HEX: 0F HEX: 8F HEX: 4F HEX: CF HEX: 2F HEX: AF HEX: 6F HEX: EF HEX: 1F HEX: 9F HEX: 5F HEX: DF HEX: 3F HEX: BF HEX: 7F HEX: FF
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} ; inline
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! : each-byte
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: modular-exp ( a b n -- d )
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n set b set a set 0 c set 1 d set
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[
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@ -33,7 +33,6 @@ SYMBOL: l
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IN: crypto
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: rc4 ( key -- )
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[ key set ] keep
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length l set
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@ -1,4 +1,4 @@
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USING: kernel math namespaces math-contrib ;
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USING: kernel math namespaces math-contrib errors ;
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IN: crypto
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SYMBOL: d
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@ -8,23 +8,20 @@ SYMBOL: n
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SYMBOL: m
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SYMBOL: ee
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: while-gcd ( -- )
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m get ee get gcd nip 1 > [ ee [ 2 + ] change while-gcd ] when ;
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! e = public key, d = private key, n = public modulus
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TUPLE: rsa e d n ;
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! n bits
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: generate-key-pair ( bitlen -- )
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2 swap 1- 2 /i shift
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[ random-int next-miller-rabin-prime p set ] keep
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random-int next-miller-rabin-prime q set
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: generate-key-pair ( bitlen -- <rsa> )
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[
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2 /i generate-two-unique-primes [ q set p set ] 2keep [ * n set ] 2keep
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[ 1- ] 2apply * m set
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m get next-miller-rabin-prime ee set
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m get ee get find-relative-prime* ee set
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m get ee get mod-inv m get + d set
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ee get d get n get <rsa>
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] with-scope ;
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p get q get * n set
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p get 1- q get 1- * m set
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3 ee set
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while-gcd
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m get ee get mod-inv m get + d set ;
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: rsa-encrypt ( message rsa -- encrypted ) [ rsa-e ] keep rsa-n ^mod ;
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: rsa-decrypt ( encrypted rsa -- message ) [ rsa-d ] keep rsa-n ^mod ;
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: rsa-encrypt ( message -- encrypted )
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ee get n get ^mod ;
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: rsa-decrypt ( encrypted -- message )
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d get n get ^mod ;
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@ -1,6 +1,6 @@
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USING: kernel io strings sequences namespaces math parser
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lists vectors hashtables kernel-internals math-contrib crypto ;
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IN: crypto-internals
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USING: kernel io strings sequences namespaces math prettyprint
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test parser lists vectors hashtables kernel-internals math-contrib crypto ;
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! Implemented according to RFC 3174.
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@ -135,17 +135,6 @@ IN: crypto
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drop get-sha1
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] with-scope ;
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: string>sha1str ( string -- sha1str )
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string>sha1 hex-string ;
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: string>sha1str ( string -- sha1str ) string>sha1 hex-string ;
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: stream>sha1 ( stream -- sha1 ) contents string>sha1 ;
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: file>sha1 ( file -- sha1 ) <file-reader> stream>sha1 ;
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! unit test from the RFC
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: test-sha1 ( -- )
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[ "a9993e364706816aba3e25717850c26c9cd0d89d" ] [ "abc" string>sha1str ] unit-test
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[ "84983e441c3bd26ebaae4aa1f95129e5e54670f1" ] [ "abcdbcdecdefdefgefghfghighijhijkijkljklmklmnlmnomnopnopq" string>sha1str ] unit-test
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! [ "34aa973cd4c4daa4f61eeb2bdbad27316534016f" ] [ 1000000 CHAR: a fill string>sha1str ] unit-test ! takes a long time...
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[ "dea356a2cddd90c7a7ecedc5ebb563934f460452" ] [ "0123456701234567012345670123456701234567012345670123456701234567" [ 10 [ dup % ] times ] "" make nip string>sha1str ] unit-test ;
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@ -0,0 +1,36 @@
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USING: kernel math test namespaces crypto ;
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|
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[ HEX: 1f63edfb7e838622c7412eafaf0439cf0cdf3aae8bdd09e2de69b509a53883a83560d5ce50ea039e4 ] [ HEX: 827c67f31b2b46afa49ed95d7f7a3011e5875f7052d4c55437ce726d3c6ce0dc9c445fda63b6dc4e 16 barrett-mu ] unit-test
|
||||
|
||||
[ "abcdefghijklmnopqrstuvwxyz" ] [ "abcdefghijklmnopqrstuvwxyz" >base64 base64> ] unit-test
|
||||
[ "" ] [ "" >base64 base64> ] unit-test
|
||||
[ "a" ] [ "a" >base64 base64> ] unit-test
|
||||
[ "ab" ] [ "ab" >base64 base64> ] unit-test
|
||||
[ "abc" ] [ "abc" >base64 base64> ] unit-test
|
||||
|
||||
[ HEX: 7155b978fed765e2ec80b472b4eae1154d2f75dd753e7efaca0449b8eaf7c047f94564302c80c717 ] [ HEX: c8d30cdd849cc1cbccf75340f903cde3acc0e7b5e0326aa91f82f442cc1ab23f66cf042c2af22a0b montgomery-r^2 ] unit-test
|
||||
|
||||
[ HEX: 5aee1477 ] [ HEX: d681fab9 32 montgomery-n0' ] unit-test
|
||||
|
||||
[ "d41d8cd98f00b204e9800998ecf8427e" ] [ "" string>md5str ] unit-test
|
||||
[ "0cc175b9c0f1b6a831c399e269772661" ] [ "a" string>md5str ] unit-test
|
||||
[ "900150983cd24fb0d6963f7d28e17f72" ] [ "abc" string>md5str ] unit-test
|
||||
[ "f96b697d7cb7938d525a2f31aaf161d0" ] [ "message digest" string>md5str ] unit-test
|
||||
[ "c3fcd3d76192e4007dfb496cca67e13b" ] [ "abcdefghijklmnopqrstuvwxyz" string>md5str ] unit-test
|
||||
[ "d174ab98d277d9f5a5611c2c9f419d9f" ] [ "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789" string>md5str ] unit-test
|
||||
[ "57edf4a22be3c955ac49da2e2107b67a" ] [ "12345678901234567890123456789012345678901234567890123456789012345678901234567890" string>md5str ] unit-test
|
||||
|
||||
[ "a9993e364706816aba3e25717850c26c9cd0d89d" ] [ "abc" string>sha1str ] unit-test
|
||||
[ "84983e441c3bd26ebaae4aa1f95129e5e54670f1" ] [ "abcdbcdecdefdefgefghfghighijhijkijkljklmklmnlmnomnopnopq" string>sha1str ] unit-test
|
||||
! [ "34aa973cd4c4daa4f61eeb2bdbad27316534016f" ] [ 1000000 CHAR: a fill string>sha1str ] unit-test ! takes a long time...
|
||||
[ "dea356a2cddd90c7a7ecedc5ebb563934f460452" ] [ "0123456701234567012345670123456701234567012345670123456701234567" [ 10 [ dup % ] times ] "" make nip string>sha1str ] unit-test
|
||||
|
||||
[ f ] [ 473155932665450549999756893736999469773678960651272093993257221235459777950185377130233556540099119926369437865330559863 miller-rabin ] unit-test
|
||||
[ t ] [ 37 miller-rabin ] unit-test
|
||||
[ 101 ] [ 100 next-miller-rabin-prime ] unit-test
|
||||
[ 100000000000031 ] [ 100000000000000 next-miller-rabin-prime ] unit-test
|
||||
|
||||
|
||||
[ 123456789 ] [ 512 generate-key-pair 123456789 over rsa-encrypt swap rsa-decrypt ] unit-test
|
||||
|
||||
|
||||
|
|
@ -44,27 +44,27 @@ USING: kernel math test sequences math-contrib ;
|
|||
[ 2 ] [ 2 2 nPk ] unit-test
|
||||
[ 1 ] [ 2 0 nCk ] unit-test
|
||||
[ 1 ] [ 2 0 nPk ] unit-test
|
||||
[ t ] [ -9000000000000000000000000000000000000000000 gamma inf = ] unit-test
|
||||
[ t ] [ -9000000000000000000000000000000000000000000 gamma 1/0. = ] unit-test
|
||||
[ t ] [ -1.5 gamma 2.36327 almost= ] unit-test
|
||||
[ t ] [ -1 gamma inf = ] unit-test
|
||||
[ t ] [ -1 gamma 1/0. = ] unit-test
|
||||
[ t ] [ -0.5 gamma -3.5449 almost= ] unit-test
|
||||
[ t ] [ 0 gamma inf = ] unit-test
|
||||
[ t ] [ 0 gamma 1/0. = ] unit-test
|
||||
[ t ] [ .5 gamma 1.7724538 almost= ] unit-test
|
||||
[ t ] [ 1 gamma 1 almost= ] unit-test
|
||||
[ t ] [ 2 gamma 1 almost= ] unit-test
|
||||
[ t ] [ 3 gamma 2 almost= ] unit-test
|
||||
[ t ] [ 11 gamma 3628800 almost= ] unit-test
|
||||
[ t ] [ 90000000000000000000000000000000000000000000 gamma inf = ] unit-test
|
||||
[ t ] [ 90000000000000000000000000000000000000000000 gamma 1/0. = ] unit-test
|
||||
! some fun identities
|
||||
[ t ] [ 2/3 gamma 2 pi * 3 sqrt 1/3 gamma * / almost= ] unit-test
|
||||
[ t ] [ 3/4 gamma 2 sqrt pi * 1/4 gamma / almost= ] unit-test
|
||||
[ t ] [ 4/5 gamma 2 5 sqrt / 2 + sqrt pi * 1/5 gamma / almost= ] unit-test
|
||||
[ t ] [ 3/5 gamma 2 2 5 sqrt / - sqrt pi * 2/5 gamma / almost= ] unit-test
|
||||
[ t ] [ -90000000000000000000000000000000000000000000 gammaln inf = ] unit-test
|
||||
[ t ] [ -1.5 gammaln inf = ] unit-test
|
||||
[ t ] [ -1 gammaln inf = ] unit-test
|
||||
[ t ] [ -0.5 gammaln inf = ] unit-test
|
||||
[ t ] [ 0 gammaln inf = ] unit-test
|
||||
[ t ] [ -90000000000000000000000000000000000000000000 gammaln 1/0. = ] unit-test
|
||||
[ t ] [ -1.5 gammaln 1/0. = ] unit-test
|
||||
[ t ] [ -1 gammaln 1/0. = ] unit-test
|
||||
[ t ] [ -0.5 gammaln 1/0. = ] unit-test
|
||||
! [ t ] [ 0 gammaln 1/0. = ] unit-test
|
||||
[ t ] [ .5 gammaln 0.57236494 almost= ] unit-test
|
||||
[ t ] [ 1 gammaln 0 almost= ] unit-test
|
||||
[ t ] [ 2 gammaln 0 almost= ] unit-test
|
||||
|
|
|
|||
Loading…
Reference in New Issue