diff options
| author | Sven Eisenhauer <sven@sven-eisenhauer.net> | 2023-11-10 15:11:48 +0100 |
|---|---|---|
| committer | Sven Eisenhauer <sven@sven-eisenhauer.net> | 2023-11-10 15:11:48 +0100 |
| commit | 33613a85afc4b1481367fbe92a17ee59c240250b (patch) | |
| tree | 670b842326116b376b505ec2263878912fca97e2 /Master/Public-Key-Algorithmen | |
| download | Studium-master.tar.gz Studium-master.tar.bz2 | |
Diffstat (limited to 'Master/Public-Key-Algorithmen')
17 files changed, 2044 insertions, 0 deletions
diff --git a/Master/Public-Key-Algorithmen/Guide to ECC.pdf b/Master/Public-Key-Algorithmen/Guide to ECC.pdf Binary files differnew file mode 100644 index 0000000..b3426bd --- /dev/null +++ b/Master/Public-Key-Algorithmen/Guide to ECC.pdf diff --git a/Master/Public-Key-Algorithmen/PKA-Prakt1/.cproject b/Master/Public-Key-Algorithmen/PKA-Prakt1/.cproject new file mode 100644 index 0000000..b7f74da --- /dev/null +++ b/Master/Public-Key-Algorithmen/PKA-Prakt1/.cproject @@ -0,0 +1,607 @@ +<?xml version="1.0" encoding="UTF-8" standalone="no"?> +<?fileVersion 4.0.0?> + +<cproject storage_type_id="org.eclipse.cdt.core.XmlProjectDescriptionStorage"> +<storageModule moduleId="org.eclipse.cdt.core.settings"> +<cconfiguration id="cdt.managedbuild.config.gnu.exe.debug.115525757"> +<storageModule buildSystemId="org.eclipse.cdt.managedbuilder.core.configurationDataProvider" id="cdt.managedbuild.config.gnu.exe.debug.115525757" moduleId="org.eclipse.cdt.core.settings" name="Debug"> 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+<storageModule moduleId="org.eclipse.cdt.core.language.mapping"/> +<storageModule moduleId="org.eclipse.cdt.internal.ui.text.commentOwnerProjectMappings"/> +</cconfiguration> +</storageModule> +<storageModule moduleId="cdtBuildSystem" version="4.0.0"> +<project id="PKA-Prakt1.cdt.managedbuild.target.gnu.exe.434868846" name="Executable" projectType="cdt.managedbuild.target.gnu.exe"/> +</storageModule> +</cproject> diff --git a/Master/Public-Key-Algorithmen/PKA-Prakt1/.project b/Master/Public-Key-Algorithmen/PKA-Prakt1/.project new file mode 100644 index 0000000..0846f85 --- /dev/null +++ b/Master/Public-Key-Algorithmen/PKA-Prakt1/.project @@ -0,0 +1,81 @@ +<?xml version="1.0" encoding="UTF-8"?> +<projectDescription> + <name>PKA-Prakt1</name> + <comment></comment> + <projects> + </projects> + <buildSpec> + <buildCommand> + <name>org.eclipse.cdt.managedbuilder.core.genmakebuilder</name> + <triggers>clean,full,incremental,</triggers> + <arguments> + <dictionary> + <key>?name?</key> + <value></value> + </dictionary> + <dictionary> + <key>org.eclipse.cdt.make.core.append_environment</key> + <value>true</value> + </dictionary> + <dictionary> + <key>org.eclipse.cdt.make.core.autoBuildTarget</key> + <value>all</value> + </dictionary> + <dictionary> + <key>org.eclipse.cdt.make.core.buildArguments</key> + <value></value> + </dictionary> + <dictionary> + <key>org.eclipse.cdt.make.core.buildCommand</key> + <value>make</value> + </dictionary> + <dictionary> + <key>org.eclipse.cdt.make.core.buildLocation</key> + <value>${workspace_loc:/PKA-Prakt1/Debug}</value> + </dictionary> + <dictionary> + <key>org.eclipse.cdt.make.core.cleanBuildTarget</key> + <value>clean</value> + </dictionary> + <dictionary> + <key>org.eclipse.cdt.make.core.contents</key> + <value>org.eclipse.cdt.make.core.activeConfigSettings</value> + </dictionary> + <dictionary> + <key>org.eclipse.cdt.make.core.enableAutoBuild</key> + <value>false</value> + </dictionary> + <dictionary> + <key>org.eclipse.cdt.make.core.enableCleanBuild</key> + <value>true</value> + </dictionary> + <dictionary> + <key>org.eclipse.cdt.make.core.enableFullBuild</key> + <value>true</value> + </dictionary> + <dictionary> + <key>org.eclipse.cdt.make.core.fullBuildTarget</key> + <value>all</value> + </dictionary> + <dictionary> + <key>org.eclipse.cdt.make.core.stopOnError</key> + <value>true</value> + </dictionary> + <dictionary> + <key>org.eclipse.cdt.make.core.useDefaultBuildCmd</key> + <value>true</value> + </dictionary> + </arguments> + </buildCommand> + <buildCommand> + <name>org.eclipse.cdt.managedbuilder.core.ScannerConfigBuilder</name> + <arguments> + </arguments> + </buildCommand> + </buildSpec> + <natures> + <nature>org.eclipse.cdt.core.cnature</nature> + <nature>org.eclipse.cdt.managedbuilder.core.managedBuildNature</nature> + <nature>org.eclipse.cdt.managedbuilder.core.ScannerConfigNature</nature> + </natures> +</projectDescription> diff --git a/Master/Public-Key-Algorithmen/PKA-Prakt1/Debug/PKA-Prakt1 b/Master/Public-Key-Algorithmen/PKA-Prakt1/Debug/PKA-Prakt1 Binary files differnew file mode 100755 index 0000000..10f43c0 --- /dev/null +++ b/Master/Public-Key-Algorithmen/PKA-Prakt1/Debug/PKA-Prakt1 diff --git a/Master/Public-Key-Algorithmen/PKA-Prakt1/Debug/makefile b/Master/Public-Key-Algorithmen/PKA-Prakt1/Debug/makefile new file mode 100644 index 0000000..6832b8b --- /dev/null +++ b/Master/Public-Key-Algorithmen/PKA-Prakt1/Debug/makefile @@ -0,0 +1,44 @@ +################################################################################ +# Automatically-generated file. Do not edit! +################################################################################ + +-include ../makefile.init + +RM := rm -rf + +# All of the sources participating in the build are defined here +-include sources.mk +-include subdir.mk +-include src/subdir.mk +-include objects.mk + +ifneq ($(MAKECMDGOALS),clean) +ifneq ($(strip $(C_DEPS)),) +-include $(C_DEPS) +endif +endif + +-include ../makefile.defs + +# Add inputs and outputs from these tool invocations to the build variables + +# All Target +all: PKA-Prakt1 + +# Tool invocations +PKA-Prakt1: $(OBJS) $(USER_OBJS) + @echo 'Building target: $@' + @echo 'Invoking: GCC C Linker' + gcc -o"PKA-Prakt1" $(OBJS) $(USER_OBJS) $(LIBS) + @echo 'Finished building target: $@' + @echo ' ' + +# Other Targets +clean: + -$(RM) $(OBJS)$(C_DEPS)$(EXECUTABLES) PKA-Prakt1 + -@echo ' ' + +.PHONY: all clean dependents +.SECONDARY: + +-include ../makefile.targets diff --git a/Master/Public-Key-Algorithmen/PKA-Prakt1/Debug/objects.mk b/Master/Public-Key-Algorithmen/PKA-Prakt1/Debug/objects.mk new file mode 100644 index 0000000..224ef68 --- /dev/null +++ b/Master/Public-Key-Algorithmen/PKA-Prakt1/Debug/objects.mk @@ -0,0 +1,7 @@ +################################################################################ +# Automatically-generated file. Do not edit! +################################################################################ + +USER_OBJS := + +LIBS := diff --git a/Master/Public-Key-Algorithmen/PKA-Prakt1/Debug/sources.mk b/Master/Public-Key-Algorithmen/PKA-Prakt1/Debug/sources.mk new file mode 100644 index 0000000..57cf3c3 --- /dev/null +++ b/Master/Public-Key-Algorithmen/PKA-Prakt1/Debug/sources.mk @@ -0,0 +1,17 @@ +################################################################################ +# Automatically-generated file. Do not edit! +################################################################################ + +O_SRCS := +C_SRCS := +S_UPPER_SRCS := +OBJ_SRCS := +ASM_SRCS := +OBJS := +C_DEPS := +EXECUTABLES := + +# Every subdirectory with source files must be described here +SUBDIRS := \ +src \ + diff --git a/Master/Public-Key-Algorithmen/PKA-Prakt1/Debug/src/main.d b/Master/Public-Key-Algorithmen/PKA-Prakt1/Debug/src/main.d new file mode 100644 index 0000000..d1c377e --- /dev/null +++ b/Master/Public-Key-Algorithmen/PKA-Prakt1/Debug/src/main.d @@ -0,0 +1 @@ +src/main.d src/main.o: ../src/main.c diff --git a/Master/Public-Key-Algorithmen/PKA-Prakt1/Debug/src/subdir.mk b/Master/Public-Key-Algorithmen/PKA-Prakt1/Debug/src/subdir.mk new file mode 100644 index 0000000..3a430c3 --- /dev/null +++ b/Master/Public-Key-Algorithmen/PKA-Prakt1/Debug/src/subdir.mk @@ -0,0 +1,24 @@ +################################################################################ +# Automatically-generated file. Do not edit! +################################################################################ + +# Add inputs and outputs from these tool invocations to the build variables +C_SRCS += \ +../src/main.c + +OBJS += \ +./src/main.o + +C_DEPS += \ +./src/main.d + + +# Each subdirectory must supply rules for building sources it contributes +src/%.o: ../src/%.c + @echo 'Building file: $<' + @echo 'Invoking: GCC C Compiler' + gcc -O0 -g3 -Wall -c -fmessage-length=0 -MMD -MP -MF"$(@:%.o=%.d)" -MT"$(@:%.o=%.d)" -o"$@" "$<" + @echo 'Finished building: $<' + @echo ' ' + + diff --git a/Master/Public-Key-Algorithmen/PKA-Prakt1/src/main.c b/Master/Public-Key-Algorithmen/PKA-Prakt1/src/main.c new file mode 100644 index 0000000..2987966 --- /dev/null +++ b/Master/Public-Key-Algorithmen/PKA-Prakt1/src/main.c @@ -0,0 +1,88 @@ +/* + * main.c + * + * Created on: 23.04.2010 + * Author: sven + */ +#include <stdlib.h> +#include <stdint.h> +#include <stdio.h> +#include <time.h> +#include <sys/time.h> + +#define HI(x) (x >> 16) +#define LO(x) (x & 0x0000FFFF) + +void mulc(uint32_t *u, uint32_t *v, uint32_t a, uint32_t b) +{ + uint32_t t; + t = LO(a) * LO(b); + *v = LO(t); + t = HI(t) + HI(a) * LO(b); + *u = HI(t); + t = LO(t) + LO(a) * HI(b); + *v |= LO(t) << 16; + *u += HI(t) + HI(a) * HI(b); +} +void mula(uint32_t *u, uint32_t *v, uint32_t a, uint32_t b) +{ + asm + ( + "mov %2,%%eax\n" + "mul %3\n" + "mov %%edx, %0\n" + "mov %%eax, %1" + :"=r"(*u),"=r"(*v) + :"r"(a),"r"(b) + ); +} +void initRandomizer() +{ + srand(time(NULL)); +} +uint32_t getRandomUint32() +{ + uint32_t res = rand(); + if(res % 2) + { + return (res | 1<<31); + } + return res; +} +int main(int argc, char* argv[]) +{ + initRandomizer(); + uint32_t a = getRandomUint32(); + uint32_t b = getRandomUint32(); + uint32_t u,v; + uint32_t counter; + uint32_t outerCnt; + const uint32_t NUM_INNER_LOOPS = 1000000; + const uint32_t NUM_OUTER_LOOPS = 1000; + struct timeval startc; + struct timeval endc; + struct timeval starta; + struct timeval enda; + long diffCsum = 0,diffAsum = 0; + for(outerCnt=0;outerCnt<NUM_OUTER_LOOPS;outerCnt++) { + gettimeofday(&startc,0); + for (counter=0; counter < NUM_INNER_LOOPS; counter++) { + mulc(&u,&v,a,b); + } + gettimeofday(&endc,0); + diffCsum += (endc.tv_sec*1000000 + endc.tv_usec) - (startc.tv_sec*1000000 + startc.tv_usec); + printf("C %u * %u = %u.%u\n",a,b,u,v); + u=0; + v=0; + gettimeofday(&starta,0); + for (counter=0; counter < NUM_INNER_LOOPS; counter++) { + mula(&u,&v,a,b); + } + gettimeofday(&enda,0); + diffAsum += (enda.tv_sec*1000000 + enda.tv_usec) - (starta.tv_sec*1000000 + starta.tv_usec); + printf("ASM %u * %u = %u.%u\n",a,b,u,v); + } + printf("C: total %ld usec, avg %ld usec\n",diffCsum,(diffCsum / NUM_OUTER_LOOPS)); + printf("ASM: total %ld usec, avg %ld usec\n",diffAsum,(diffAsum / NUM_OUTER_LOOPS)); + return EXIT_SUCCESS; +} diff --git a/Master/Public-Key-Algorithmen/Prakt4/main.cpp b/Master/Public-Key-Algorithmen/Prakt4/main.cpp new file mode 100755 index 0000000..7215a9d --- /dev/null +++ b/Master/Public-Key-Algorithmen/Prakt4/main.cpp @@ -0,0 +1,447 @@ +#include <stdlib.h>
+//#include <windows.h>
+#include <time.h>
+#include <stdio.h>
+#include <Math.h>
+
+
+typedef unsigned int uint32_t;
+
+
+void initRandomizer();
+uint32_t getRandomUint32(uint32_t length);
+
+void f2m_rand(uint32_t t, uint32_t m, uint32_t *A);
+void f2m_print(uint32_t t, uint32_t *A);
+void f2m_assign(uint32_t t, uint32_t *A, uint32_t *B);
+void f2m_and(uint32_t t, uint32_t *A, uint32_t *B, uint32_t *C);
+void f2m_or(uint32_t t, uint32_t *A, uint32_t *B, uint32_t *C);
+void f2m_xor(uint32_t t, uint32_t *A, uint32_t *B, uint32_t *C);
+void f2m_shiftleft(uint32_t t, uint32_t *A, uint32_t *B);
+void f2m_shiftright(uint32_t t, uint32_t *A, uint32_t *B);
+uint32_t getbit(uint32_t U, uint32_t i);
+uint32_t f2m_bitm(uint32_t t, uint32_t m, uint32_t *A);
+
+uint32_t f2m_biti(uint32_t t,uint32_t i,uint32_t *A);
+void f2m_one(uint32_t t,uint32_t *A);
+void f2m_zero(uint32_t t,uint32_t *A);
+uint32_t f2m_is_equal(uint32_t t,uint32_t *A,uint32_t *B);
+uint32_t f2m_is_one(uint32_t t,uint32_t *A);
+uint32_t f2m_is_zero(uint32_t t,uint32_t *A);
+void f2m_mul(uint32_t t,uint32_t m,uint32_t *A,uint32_t *B,uint32_t *F,uint32_t *C,uint32_t *T1,uint32_t *T2);
+void f2m_inv(uint32_t t,uint32_t m,uint32_t *A,uint32_t *F,uint32_t *B,uint32_t *U,uint32_t *V,uint32_t *T1,uint32_t *T2);
+uint32_t f2m_deg(uint32_t,uint32_t,uint32_t*);
+void build_f(uint32_t,uint32_t,uint32_t*);
+
+int main(int argc, char* argv[])
+{
+ initRandomizer();
+ uint32_t m = 163;
+ //double x = static_cast<double>(m>>5);
+ double x = static_cast<double>( ((double)m) / 32);
+ uint32_t t = ceil(x);
+ uint32_t *A,*B,*C,*U,*V,*T1,*T2,*F,*R1,*R2,*R3,*R4;
+ long s = sizeof(uint32_t);
+ long bytes = s*t;
+ A = (uint32_t*) malloc(bytes);
+ B = (uint32_t*) malloc(bytes);
+ C = (uint32_t*) malloc(bytes);
+ U = (uint32_t*) malloc(bytes);
+ V = (uint32_t*) malloc(bytes);
+ T1 = (uint32_t*) malloc(bytes);
+ T2 = (uint32_t*) malloc(bytes);
+ F = (uint32_t*) malloc(bytes);
+ R1 = (uint32_t*) malloc(bytes);
+ R2 = (uint32_t*) malloc(bytes);
+ R3 = (uint32_t*) malloc(bytes);
+ R4 = (uint32_t*) malloc(bytes);
+
+ f2m_zero(t,A);
+ f2m_print(t,A);
+ if(f2m_is_zero(t,A))
+ printf("A is zero \n");
+
+ f2m_one(t,A);
+ f2m_print(t,A);
+ if(f2m_is_one(t,A))
+ printf("A is one \n");
+
+ uint32_t bit;
+ bit = f2m_biti(t,0,A);
+ if(bit == 1)
+ printf("Bit 1 of A is 1\n");
+ else
+ printf("Bit 1 of A is %u\n",bit);
+
+ if (f2m_is_equal(t,A,A) )
+ printf("A equal A\n");
+ else
+ printf("A not equal A ?!\n");
+ build_f(t,m,F);
+ uint32_t degF = f2m_deg(t,m,F);
+ printf("Deg(F) = %u\n",degF);
+ bool hasError = false;
+ for(uint32_t n = 0;n<10000;n++) {
+ f2m_rand(t,m,A);
+ /*f2m_rand(t,m,B);
+ f2m_rand(t,m,C);
+
+ f2m_mul(t,m,A,B,F,R1,T1,T2);
+ f2m_mul(t,m,R1,C,F,R2,T1,T2);
+
+ f2m_mul(t,m,B,C,F,R3,T1,T2);
+ f2m_mul(t,m,A,R3,F,R4,T1,T2);
+
+ if(f2m_is_equal(t,R2,R4))
+ printf("Mul works correctly\n");
+ else
+ printf("Mul is not working correctly\n");
+ */
+ f2m_inv(t,m,A,F,R1,U,V,T1,T2);
+ f2m_mul(t,m,A,R1,F,R2,T1,T2);
+
+ if(n%100 == 0){
+ printf("%u\n",n );
+ }
+
+ if(!f2m_is_one(t,R2))
+ {
+ hasError = true;
+ break;
+ }
+ }
+ if(!hasError)
+ printf("Inv works correctly\n");
+ else
+ printf("Inv is not working correctly\n");
+
+ //f2m_assign(t,A,B);
+ //printf("\n\n\n");
+ //f2m_print(t,B);
+
+ /*
+
+ f2m_and(t,A,A,C);
+
+ printf("A&A: \n");
+ f2m_print(t,C);
+
+ printf("A: \n");
+ f2m_print(t,A);
+
+ printf("B: \n");
+ f2m_print(t,B);
+
+ f2m_and(t,A,B,C);
+
+ printf("A&B: \n");
+ f2m_print(t,C);
+
+ printf("A << 1: \n");
+ f2m_shiftleft(t,A,B);
+ f2m_print(t,B);
+ uint32_t test[] = {0x1,0x0};
+ f2m_print(2,&test[0]);
+ for(int i=0;i<63;i++) {
+ f2m_shiftleft(2,&test[0],&test[0]);
+ f2m_print(2,&test[0]);
+ }
+ for(int i=0;i<63;i++) {
+ f2m_shiftright(2,&test[0],&test[0]);
+ f2m_print(2,&test[0]);
+ }
+ printf("0 OR 1: \n");
+ test[0] = 0x0;
+ test[1] = 0x0;
+ uint32_t test2[] = {0x1,0x0};
+ uint32_t test3[2];
+ f2m_or(2,&test[0],&test2[0],&test3[0]);
+ f2m_print(2,&test3[0]);
+
+ printf("1 XOR 1: \n");
+ test[0] = 0x1;
+ test[1] = 0x0;
+ test2[0] = 0x1;
+ test2[1] = 0x0;
+ f2m_xor(2,&test[0],&test2[0],&test3[0]);
+ f2m_print(2,&test3[0]);
+ */
+ getchar();
+ free(A);
+ free(B);
+ free(C);
+ free(F);
+ free(U);
+ free(V);
+ free(T1);
+ free(T2);
+ free(R1);
+ free(R2);
+ free(R3);
+ free(R4);
+ return 0;
+}
+
+void initRandomizer()
+{
+ srand(time(NULL));
+}
+uint32_t getRandomUint32()
+{
+ uint32_t resLow = rand();
+ uint32_t resHigh = rand();
+ uint32_t res;
+ res = resHigh << 15;
+ res = res | (resLow);
+ return res;
+}
+
+void f2m_rand(uint32_t t, uint32_t m, uint32_t *A)
+{
+ for(int i=t-1;i>=0;i--)
+ {
+ A[i]= getRandomUint32();
+ }
+
+ uint32_t mask = 0x0;
+ uint32_t unEvenBytes = m%32;
+ if (unEvenBytes != 0) {
+ for(uint32_t i=0;i<(unEvenBytes)-1;i++) {
+ mask |= (1<<i);
+ }
+ A[t-1] &= mask;
+ }
+}
+
+void f2m_print(uint32_t t, uint32_t *A)
+{
+ for(int i=t-1;i>=0;i--)
+ {
+ printf("%08X ",A[i]);
+ if(!(i%4))
+ printf("\n");
+ }
+}
+
+void f2m_assign(uint32_t t, uint32_t *A, uint32_t *B)
+{
+ for(int i=t-1;i>=0;i--)
+ {
+ B[i]=A[i];
+ }
+}
+void f2m_and(uint32_t t, uint32_t *A, uint32_t *B, uint32_t *C)
+{
+ for(int i=t-1;i>=0;i--)
+ {
+ C[i] = (B[i] & A[i]);
+ }
+}
+
+void f2m_or(uint32_t t, uint32_t *A, uint32_t *B, uint32_t *C)
+{
+ for(int i=t-1;i>=0;i--)
+ {
+ C[i] = (B[i] | A[i]);
+ }
+}
+
+void f2m_xor(uint32_t t, uint32_t *A, uint32_t *B, uint32_t *C)
+{
+ for(int i=t-1;i>=0;i--)
+ {
+ C[i] = (B[i] ^ A[i]);
+ }
+}
+
+void f2m_shiftleft(uint32_t t, uint32_t *A, uint32_t *B)
+{
+ for(int i=t-1;i>0;i--)
+ {
+ B[i] = ((A [i] << 1)| getbit(A[i-1],31));
+ }
+ B[0] = A [0] << 1;
+}
+void f2m_shiftright(uint32_t t, uint32_t *A, uint32_t *B)
+{
+ for(uint32_t n=0;n<(t-1);n++)
+ {
+ B[n] = ((A[n]>> 1)| (getbit(A[n+1],0)<<31));
+ }
+ B[t-1] = A[t-1]>> 1;
+}
+
+uint32_t getbit(uint32_t U, uint32_t i)
+{
+ if(i==0)
+ return U & 0x1;
+ else
+ return ((U>> i)& 0x1);
+}
+
+uint32_t f2m_bitm(uint32_t t, uint32_t m, uint32_t *A)
+{
+ /*
+ int modul = m%32;
+ if(modul!=0)
+ return getbit(A[t-1],(m%32)-1);
+ else
+ return getbit(A[t-1],31);
+ */
+ return f2m_biti(t,m,A);
+}
+
+uint32_t f2m_biti(uint32_t t,uint32_t i,uint32_t *A)
+{
+ return getbit(A[i / 32],i % 32);
+}
+void f2m_one(uint32_t t,uint32_t *A)
+{
+ for(uint32_t i=1; i<t; i++)
+ {
+ A[i] = 0;
+ }
+ A[0]=1;
+}
+void f2m_zero(uint32_t t,uint32_t *A)
+{
+ for(uint32_t i=0; i<t; i++)
+ {
+ A[i] = 0;
+ }
+}
+uint32_t f2m_is_equal(uint32_t t,uint32_t *A,uint32_t *B)
+{
+ for(uint32_t i=0; i<t; i++)
+ {
+ if(A[i] != B[i])
+ return 0;
+ }
+ return 1;
+}
+uint32_t f2m_is_one(uint32_t t,uint32_t *A)
+{
+ for(uint32_t i=1; i<t; i++)
+ {
+ if(A[i] != 0)
+ return 0;
+ }
+ if(A[0] != 1)
+ return 0;
+ return 1;
+}
+uint32_t f2m_is_zero(uint32_t t,uint32_t *A)
+{
+ for(uint32_t i=0; i<t; i++)
+ {
+ if(A[i] != 0)
+ return 0;
+ }
+ return 1;
+}
+void f2m_mul(uint32_t t,uint32_t m,uint32_t *A,uint32_t *B,uint32_t *F,uint32_t *C,uint32_t *T1,uint32_t *T2)
+{
+ f2m_assign(t,B,T1);
+ f2m_zero(t,T2);
+ for(uint32_t i=0;i<m-1;i++){
+ if( f2m_biti(t,m,T1) == 1 )
+ {
+ f2m_xor(t,T1, F ,T1);
+ }
+ if ( f2m_biti(t,i,A) == 1)
+ {
+ f2m_xor(t,T2,T1,T2);
+ }
+ f2m_shiftleft(t,T1,T1);
+ }
+ f2m_assign(t,T2,C);
+}
+
+uint32_t f2m_deg(uint32_t t,uint32_t m, uint32_t* A)
+{
+ /*
+ for(uint32_t i = t-1; i >= 0; i--)
+ {
+ if(A[i] != 0)
+ {
+ for(uint32_t x=31;x>=0;x--)
+ {
+ if( getbit(A[i],x) == 0x1 )
+ {
+ return (i*32)+x+1;
+ }
+ }
+ }
+ }
+ */
+ for(uint32_t pos=m;pos>=0;pos--)
+ {
+ if(f2m_biti(t,pos,A) == 0x1)
+ {
+ return pos;
+ }
+ }
+ return 0;
+}
+
+void f2m_inv(uint32_t t,uint32_t m,uint32_t *A,uint32_t *F,uint32_t *B,uint32_t *U,uint32_t *V,uint32_t *T1,uint32_t *T2)
+{
+ f2m_assign(t,A,U);
+ f2m_assign(t,F,V);
+ f2m_one(t,T1);
+ f2m_zero(t,T2);
+ while( !f2m_is_one(t,U) && !f2m_is_one(t,V) )
+ {
+ while(f2m_biti(t,0,U) == 0 && !f2m_is_zero(t,U) )
+ {
+ f2m_shiftright(t,U,U);
+ if(f2m_biti(t,0,T1) == 0 && !f2m_is_zero(t,T1) )
+ {
+ f2m_shiftright(t,T1,T1);
+ }
+ else
+ {
+ f2m_xor(t,T1,F,T1);
+ f2m_shiftright(t,T1,T1);
+ }
+ }
+ while(f2m_biti(t,0,V) == 0 && !f2m_is_zero(t,V) )
+ {
+ f2m_shiftright(t,V,V);
+ if(f2m_biti(t,0,T2) == 0 && !f2m_is_zero(t,T2) )
+ {
+ f2m_shiftright(t,T2,T2);
+ }
+ else
+ {
+ f2m_xor(t,T2,F,T2);
+ f2m_shiftright(t,T2,T2);
+ }
+ }
+ if(f2m_deg(t,m,U) > f2m_deg(t,m,V))
+ {
+ f2m_xor(t,U,V,U);
+ f2m_xor(t,T1,T2,T1);
+ }
+ else
+ {
+ f2m_xor(t,U,V,V);
+ f2m_xor(t,T1,T2,T2);
+ }
+ }
+ if(f2m_is_one(t,U))
+ {
+ f2m_assign(t,T1,B);
+ }
+ else
+ {
+ f2m_assign(t,T2,B);
+ }
+}
+void build_f(uint32_t t,uint32_t m,uint32_t* F)
+{
+ f2m_zero(t,F);
+ F[5] = 1<<3;
+ F[0] = 0xC9;
+ f2m_print(t,F);
+}
\ No newline at end of file diff --git a/Master/Public-Key-Algorithmen/Praktikumsbericht.docx b/Master/Public-Key-Algorithmen/Praktikumsbericht.docx Binary files differnew file mode 100644 index 0000000..5df042b --- /dev/null +++ b/Master/Public-Key-Algorithmen/Praktikumsbericht.docx diff --git a/Master/Public-Key-Algorithmen/Praktikumsbericht.pdf b/Master/Public-Key-Algorithmen/Praktikumsbericht.pdf Binary files differnew file mode 100644 index 0000000..62481a2 --- /dev/null +++ b/Master/Public-Key-Algorithmen/Praktikumsbericht.pdf diff --git a/Master/Public-Key-Algorithmen/main.c b/Master/Public-Key-Algorithmen/main.c new file mode 100644 index 0000000..51d92bb --- /dev/null +++ b/Master/Public-Key-Algorithmen/main.c @@ -0,0 +1,53 @@ +/*
+ * main.c
+ *
+ * Created on: 23.04.2010
+ * Author: eisenhauer
+ */
+#include "stdlib.h"
+#include "unistd.h"
+#include "stdio.h"
+
+#define HI(x)(x>>16)
+#define LO(x)(x&0x0000FFFF)
+
+void mulc(uint32_t* u,uint32_t* v,uint32_t a,uint32_t b)
+{
+ uint32_t t;
+ t=LO(a)*LO(b);
+ *v=LO(t);
+ t=HI(t)+HI(a)*LO(b);
+ *u=HI(t);
+ t=LO(t)+LO(a)*HI(b);
+ *v|=LO(t)<<16;
+ *u+=HI(t)+HI(a)*HI(b);
+}
+
+void mula(uint32_t *u,uint32_t *v,uint32_t a,uint32_t b)
+{
+ asm(
+ "mov %2, %%eax\n"
+ "mul %3\n"
+ "mov %%edx, %0\n"
+ "mov %%eax, %1"
+ : "=c"(*u),"=d"(*v)
+ : "a"(a),"b"(b)
+ );
+}
+
+int main(int args, char* argv[])
+{
+ uint32_t resLow;
+ uint32_t resHigh;
+ uint32_t a = 1261938865;
+ uint32_t b = 1446688886;
+
+ mulc(&resHigh,&resLow,a,b);
+ printf("%u * %u = %u %u\n",a,b,resHigh,resLow);
+ resHigh = 0;
+ resLow = 0;
+ printf("%u %u\n",resHigh,resLow);
+ mula(&resHigh,&resLow,a,b);
+ printf("%u * %u = %u %u\n",a,b,resHigh,resLow);
+ return EXIT_SUCCESS;
+}
diff --git a/Master/Public-Key-Algorithmen/main.cpp b/Master/Public-Key-Algorithmen/main.cpp new file mode 100644 index 0000000..6132c25 --- /dev/null +++ b/Master/Public-Key-Algorithmen/main.cpp @@ -0,0 +1,675 @@ +#include <stdlib.h>
+//#include <windows.h>
+#include <time.h>
+#include <stdio.h>
+#include <Math.h>
+
+
+typedef unsigned int uint32_t;
+
+
+void initRandomizer();
+uint32_t getRandomUint32(uint32_t length);
+
+void f2m_rand(uint32_t t, uint32_t m, uint32_t *A);
+void f2m_print(uint32_t t, uint32_t *A);
+void f2m_assign(uint32_t t, uint32_t *A, uint32_t *B);
+void f2m_and(uint32_t t, uint32_t *A, uint32_t *B, uint32_t *C);
+void f2m_or(uint32_t t, uint32_t *A, uint32_t *B, uint32_t *C);
+void f2m_xor(uint32_t t, uint32_t *A, uint32_t *B, uint32_t *C);
+void f2m_shiftleft(uint32_t t, uint32_t *A, uint32_t *B);
+void f2m_shiftright(uint32_t t, uint32_t *A, uint32_t *B);
+uint32_t getbit(uint32_t U, uint32_t i);
+uint32_t f2m_bitm(uint32_t t, uint32_t m, uint32_t *A);
+
+uint32_t f2m_biti(uint32_t t,uint32_t i,uint32_t *A);
+void f2m_one(uint32_t t,uint32_t *A);
+void f2m_zero(uint32_t t,uint32_t *A);
+uint32_t f2m_is_equal(uint32_t t,uint32_t *A,uint32_t *B);
+uint32_t f2m_is_one(uint32_t t,uint32_t *A);
+uint32_t f2m_is_zero(uint32_t t,uint32_t *A);
+void f2m_mul(uint32_t t,uint32_t m,uint32_t *A,uint32_t *B,uint32_t *F,uint32_t *C,uint32_t *T1,uint32_t *T2);
+void f2m_inv(uint32_t t,uint32_t m,uint32_t *A,uint32_t *F,uint32_t *B,uint32_t *U,uint32_t *V,uint32_t *T1,uint32_t *T2);
+uint32_t f2m_deg(uint32_t,uint32_t,uint32_t*);
+void build_f(uint32_t,uint32_t,uint32_t*);
+
+void f2m_montgomery(uint32_t t,uint32_t m,uint32_t* k,uint32_t* xP,uint32_t* F,uint32_t* b,uint32_t* X1,uint32_t* Z1,uint32_t* X2,
+uint32_t* Z2,uint32_t* T,uint32_t* S,uint32_t* M1,uint32_t* M2);
+uint32_t f2m_reconstruct_point(
+ uint32_t t,
+ uint32_t m,
+ uint32_t* F,
+ uint32_t* xP,
+ uint32_t* yP,
+ uint32_t* X1,
+ uint32_t* Z1,
+ uint32_t* X2,
+ uint32_t* Z2,
+ uint32_t* xQ,
+ uint32_t* yQ,
+ uint32_t* A1,
+ uint32_t* A2,
+ uint32_t* A3,
+ uint32_t* A4
+);
+bool f2m_diffie(uint32_t t,uint32_t m,uint32_t* F,uint32_t* b,uint32_t *xP,uint32_t* yP,uint32_t* k,uint32_t *d);
+
+int main(int argc, char* argv[])
+{
+ initRandomizer();
+ uint32_t m = 163;
+ //double x = static_cast<double>(m>>5);
+ double x = static_cast<double>( ((double)m) / 32);
+ uint32_t t = 6; //static_cast<uint32_t>(ceil(x));
+ uint32_t *X1,*Z1,*X2,*Z2,*T,*S,*M1,*M2,*F,*b,*xP,*yP,*k,*xQ,*yQ,*tmpInv,*x1,*x2;
+ long s = sizeof(uint32_t);
+ long bytes = s*t;
+ X1 = (uint32_t*) malloc(bytes);
+ Z1 = (uint32_t*) malloc(bytes);
+ X2 = (uint32_t*) malloc(bytes);
+ Z2 = (uint32_t*) malloc(bytes);
+ F = (uint32_t*) malloc(bytes);
+ T = (uint32_t*) malloc(bytes);
+ S = (uint32_t*) malloc(bytes);
+ M1 = (uint32_t*) malloc(bytes);
+ M2 = (uint32_t*) malloc(bytes);
+ b = (uint32_t*) malloc(bytes);
+ xP = (uint32_t*) malloc(bytes);
+ yP = (uint32_t*) malloc(bytes);
+ k = (uint32_t*) malloc(bytes);
+ xQ = (uint32_t*) malloc(bytes);
+ yQ = (uint32_t*) malloc(bytes);
+ tmpInv = (uint32_t*) malloc(bytes);
+ x1 = (uint32_t*) malloc(bytes);
+ x2 = (uint32_t*) malloc(bytes);
+
+ /*
+ f2m_zero(t,A);
+ f2m_print(t,A);
+ if(f2m_is_zero(t,A))
+ printf("A is zero \n");
+
+ f2m_one(t,A);
+ f2m_print(t,A);
+ if(f2m_is_one(t,A))
+ printf("A is one \n");
+
+ uint32_t bit;
+ bit = f2m_biti(t,0,A);
+ if(bit == 1)
+ printf("Bit 1 of A is 1\n");
+ else
+ printf("Bit 1 of A is %u\n",bit);
+
+ if (f2m_is_equal(t,A,A) )
+ printf("A equal A\n");
+ else
+ printf("A not equal A ?!\n");
+ */
+ //build_f(t,m,F);
+ //uint32_t degF = f2m_deg(t,m,F);
+ //printf("Deg(F) = %u\n",degF);
+ /*
+ bool hasError = false;
+ for(uint32_t n = 0;n<10000;n++) {
+ f2m_rand(t,m,xP);
+ //f2m_rand(t,m,B);
+ //f2m_rand(t,m,C);
+
+ //f2m_mul(t,m,A,B,F,R1,T1,T2);
+ //f2m_mul(t,m,R1,C,F,R2,T1,T2);
+
+ //f2m_mul(t,m,B,C,F,R3,T1,T2);
+ //f2m_mul(t,m,A,R3,F,R4,T1,T2);
+ //
+ //if(f2m_is_equal(t,R2,R4))
+ // printf("Mul works correctly\n");
+ //else
+ // printf("Mul is not working correctly\n");
+
+ f2m_inv(t,m,xP,F,S,T,X1,M1,M2);
+ f2m_mul(t,m,xP,S,F,X1,M1,M2);
+
+ if(n%100 == 0){
+ printf("%u\n",n );
+ }
+
+ if(1 != f2m_is_one(t,X1))
+ {
+ hasError = true;
+ break;
+ }
+ }
+ if(!hasError)
+ printf("Inv works correctly\n");
+ else
+ printf("Inv is not working correctly\n");
+ */
+ //f2m_assign(t,A,B);
+ //printf("\n\n\n");
+ //f2m_print(t,B);
+
+ /*
+
+ f2m_and(t,A,A,C);
+
+ printf("A&A: \n");
+ f2m_print(t,C);
+
+ printf("A: \n");
+ f2m_print(t,A);
+
+ printf("B: \n");
+ f2m_print(t,B);
+
+ f2m_and(t,A,B,C);
+
+ printf("A&B: \n");
+ f2m_print(t,C);
+
+ printf("A << 1: \n");
+ f2m_shiftleft(t,A,B);
+ f2m_print(t,B);
+ uint32_t test[] = {0x1,0x0};
+ f2m_print(2,&test[0]);
+ for(int i=0;i<63;i++) {
+ f2m_shiftleft(2,&test[0],&test[0]);
+ f2m_print(2,&test[0]);
+ }
+ for(int i=0;i<63;i++) {
+ f2m_shiftright(2,&test[0],&test[0]);
+ f2m_print(2,&test[0]);
+ }
+ printf("0 OR 1: \n");
+ test[0] = 0x0;
+ test[1] = 0x0;
+ uint32_t test2[] = {0x1,0x0};
+ uint32_t test3[2];
+ f2m_or(2,&test[0],&test2[0],&test3[0]);
+ f2m_print(2,&test3[0]);
+
+ printf("1 XOR 1: \n");
+ test[0] = 0x1;
+ test[1] = 0x0;
+ test2[0] = 0x1;
+ test2[1] = 0x0;
+ f2m_xor(2,&test[0],&test2[0],&test3[0]);
+ f2m_print(2,&test3[0]);
+ */
+
+ // Prakt 4 Verify Montgomery impl.
+ build_f(t,m,F);
+ b[5] = 0x00000002; b[4] = 0x0A601907; b[3]=0xB8C953CA; b[2]=0x1481EB10; b[1]=0x512F7874; b[0]=0x4A3205FD;
+ xP[5] = 0x00000003; xP[4] = 0xF0EBA162; xP[3]=0x86A2D57E; xP[2]=0xA0991168; xP[1]=0xD4994637; xP[0]=0xE8343E36;
+ yP[5] = 0x00000000; yP[4] = 0xD51FBC6C; yP[3]=0x71A0094F; yP[2]=0xA2CDD545; yP[1]=0xB11C5C0C; yP[0]=0x797324F1;
+ k[5] = 0x00000001; k[4] = 0x367D5331; k[3]=0x3A3A028C; k[2]=0x0BF1F5B4; k[1]=0x34B7C146; k[0]=0x627801B3;
+
+ f2m_montgomery(t,m,k,xP,F,b,X1,Z1,X2,Z2,T,S,M1,M2);
+
+ f2m_inv(t,m,Z1,F,tmpInv,T,S,M1,M2);
+ f2m_mul(t,m,X1,tmpInv,F,x1,T,S);
+ printf("\nx1 = X1/Z1:\n");
+ f2m_print(t,x1);
+
+ f2m_inv(t,m,Z2,F,tmpInv,T,S,M1,M2);
+ f2m_mul(t,m,X2,tmpInv,F,x2,T,S);
+ printf("\nx2 = X2/Z2:\n");
+ f2m_print(t,x2);
+
+ f2m_reconstruct_point(t,m,F,xP,yP,X1,Z1,X2,Z2,xQ,yQ,T,S,M1,M2);
+ printf("\nxQ: ");
+ f2m_print(t,xQ);
+ printf("\nyQ: ");
+ f2m_print(t,yQ);
+ printf("\n");
+
+ // Prakt 4
+
+ // Prakt 5
+ uint32_t *d;
+ d = (uint32_t*) malloc(sizeof(uint32_t)*t);
+ k = (uint32_t*) malloc(sizeof(uint32_t)*t);
+ f2m_rand(t, m, d);
+ f2m_rand(t, m, k);
+
+ printf("\n Diffie: %s",(f2m_diffie(t,m,F,b,xP,yP,k,d)?"true":"false"));
+
+ free(d);
+ // Prakt 5
+
+ getchar();
+ free(X1);
+ free(Z1);
+ free(X2);
+ free(Z2);
+ free(F);
+ free(b);
+ free(T);
+ free(S);
+ free(M1);
+ free(M2);
+ free(k);
+ free(xP);
+ free(yP);
+ free(xQ);
+ free(yQ);
+ free(tmpInv);
+ free(x1);
+ free(x2);
+ return 0;
+}
+
+void initRandomizer()
+{
+ srand(static_cast<unsigned int>(time(NULL)));
+}
+uint32_t getRandomUint32()
+{
+ uint32_t resLow = rand();
+ uint32_t resHigh = rand();
+ uint32_t res;
+ res = resHigh << 15;
+ res = res | (resLow);
+ return res;
+}
+
+void f2m_rand(uint32_t t, uint32_t m, uint32_t *A)
+{
+ for(int i=t-1;i>=0;i--)
+ {
+ A[i]= getRandomUint32();
+ }
+
+ uint32_t mask = 0x0;
+ uint32_t unEvenBytes = m%32;
+ if (unEvenBytes != 0) {
+ for(uint32_t i=0;i<(unEvenBytes)-1;i++) {
+ mask |= (1<<i);
+ }
+ A[t-1] &= mask;
+ }
+}
+
+void f2m_print(uint32_t t, uint32_t *A)
+{
+ for(int i=t-1;i>=0;i--)
+ {
+ printf("%08X ",A[i]);
+ //if(!(i%4))
+ // printf("\n");
+ }
+}
+
+void f2m_assign(uint32_t t, uint32_t *A, uint32_t *B)
+{
+ for(int i=t-1;i>=0;i--)
+ {
+ B[i]=A[i];
+ }
+}
+void f2m_and(uint32_t t, uint32_t *A, uint32_t *B, uint32_t *C)
+{
+ for(int i=t-1;i>=0;i--)
+ {
+ C[i] = (B[i] & A[i]);
+ }
+}
+
+void f2m_or(uint32_t t, uint32_t *A, uint32_t *B, uint32_t *C)
+{
+ for(int i=t-1;i>=0;i--)
+ {
+ C[i] = (B[i] | A[i]);
+ }
+}
+
+void f2m_xor(uint32_t t, uint32_t *A, uint32_t *B, uint32_t *C)
+{
+ for(int i=t-1;i>=0;i--)
+ {
+ C[i] = (B[i] ^ A[i]);
+ }
+}
+
+void f2m_shiftleft(uint32_t t, uint32_t *A, uint32_t *B)
+{
+ for(int i=t-1;i>0;i--)
+ {
+ B[i] = ((A [i] << 1)| getbit(A[i-1],31));
+ }
+ B[0] = A [0] << 1;
+}
+void f2m_shiftright(uint32_t t, uint32_t *A, uint32_t *B)
+{
+ for(uint32_t n=0;n<(t-1);n++)
+ {
+ B[n] = ((A[n]>> 1)| (getbit(A[n+1],0)<<31));
+ }
+ B[t-1] = A[t-1]>> 1;
+}
+
+uint32_t getbit(uint32_t U, uint32_t i)
+{
+ if(i==0)
+ return U & 0x1;
+ else
+ return ((U>> i)& 0x1);
+}
+
+uint32_t f2m_bitm(uint32_t t, uint32_t m, uint32_t *A)
+{
+ /*
+ int modul = m%32;
+ if(modul!=0)
+ return getbit(A[t-1],(m%32)-1);
+ else
+ return getbit(A[t-1],31);
+ */
+ return f2m_biti(t,m,A);
+}
+
+uint32_t f2m_biti(uint32_t t,uint32_t i,uint32_t *A)
+{
+ return getbit(A[i / 32],i % 32);
+}
+void f2m_one(uint32_t t,uint32_t *A)
+{
+ for(uint32_t i=1; i<t; i++)
+ {
+ A[i] = 0;
+ }
+ A[0]=1;
+}
+void f2m_zero(uint32_t t,uint32_t *A)
+{
+ for(uint32_t i=0; i<t; i++)
+ {
+ A[i] = 0;
+ }
+}
+uint32_t f2m_is_equal(uint32_t t,uint32_t *A,uint32_t *B)
+{
+ for(uint32_t i=0; i<t; i++)
+ {
+ if(A[i] != B[i])
+ return 0;
+ }
+ return 1;
+}
+uint32_t f2m_is_one(uint32_t t,uint32_t *A)
+{
+ for(uint32_t i=1; i<t; i++)
+ {
+ if(A[i] != 0)
+ return 0;
+ }
+ if(A[0] != 1)
+ return 0;
+ return 1;
+}
+uint32_t f2m_is_zero(uint32_t t,uint32_t *A)
+{
+ for(uint32_t i=0; i<t; i++)
+ {
+ if(A[i] != 0)
+ return 0;
+ }
+ return 1;
+}
+void f2m_mul(uint32_t t,uint32_t m,uint32_t *A,uint32_t *B,uint32_t *F,uint32_t *C,uint32_t *T1,uint32_t *T2)
+{
+ f2m_assign(t,B,T1);
+ f2m_zero(t,T2);
+ for(uint32_t i=0;i<m;i++){
+ if( f2m_biti(t,m,T1) == 1 )
+ {
+ f2m_xor(t,T1, F ,T1);
+ }
+ if ( f2m_biti(t,i,A) == 1)
+ {
+ f2m_xor(t,T2,T1,T2);
+ }
+ f2m_shiftleft(t,T1,T1);
+ }
+ f2m_assign(t,T2,C);
+}
+
+uint32_t f2m_deg(uint32_t t,uint32_t m, uint32_t* A)
+{
+ /*
+ for(uint32_t i = t-1; i >= 0; i--)
+ {
+ if(A[i] != 0)
+ {
+ for(uint32_t x=31;x>=0;x--)
+ {
+ if( getbit(A[i],x) == 0x1 )
+ {
+ return (i*32)+x+1;
+ }
+ }
+ }
+ }
+ */
+ for(uint32_t pos=m;pos>=0;pos--)
+ {
+ if(f2m_biti(t,pos,A) == 0x1)
+ {
+ return pos;
+ }
+ }
+ return 0;
+}
+
+void f2m_inv(uint32_t t,uint32_t m,uint32_t *A,uint32_t *F,uint32_t *B,uint32_t *U,uint32_t *V,uint32_t *T1,uint32_t *T2)
+{
+ f2m_assign(t,A,U);
+ f2m_assign(t,F,V);
+ f2m_one(t,T1);
+ f2m_zero(t,T2);
+ while( !f2m_is_one(t,U) && !f2m_is_one(t,V) )
+ {
+ while(f2m_biti(t,0,U) == 0 && !f2m_is_zero(t,U) )
+ {
+ f2m_shiftright(t,U,U);
+ if(f2m_biti(t,0,T1) == 0 && !f2m_is_zero(t,T1) )
+ {
+ f2m_shiftright(t,T1,T1);
+ }
+ else
+ {
+ f2m_xor(t,T1,F,T1);
+ f2m_shiftright(t,T1,T1);
+ }
+ }
+ while(f2m_biti(t,0,V) == 0 && !f2m_is_zero(t,V) )
+ {
+ f2m_shiftright(t,V,V);
+ if(f2m_biti(t,0,T2) == 0 && !f2m_is_zero(t,T2) )
+ {
+ f2m_shiftright(t,T2,T2);
+ }
+ else
+ {
+ f2m_xor(t,T2,F,T2);
+ f2m_shiftright(t,T2,T2);
+ }
+ }
+ if(f2m_deg(t,m,U) > f2m_deg(t,m,V))
+ {
+ f2m_xor(t,U,V,U);
+ f2m_xor(t,T1,T2,T1);
+ }
+ else
+ {
+ f2m_xor(t,U,V,V);
+ f2m_xor(t,T1,T2,T2);
+ }
+ }
+ if(f2m_is_one(t,U))
+ {
+ f2m_assign(t,T1,B);
+ }
+ else
+ {
+ f2m_assign(t,T2,B);
+ }
+}
+void build_f(uint32_t t,uint32_t m,uint32_t* F)
+{
+ f2m_zero(t,F);
+ F[5] = 1<<3;
+ F[0] = 1<<7|1<<6|1<<3|1;
+ //f2m_print(t,F);
+}
+
+void f2m_montgomery(uint32_t t,uint32_t m,uint32_t* k,uint32_t* xP,uint32_t* F
+ ,uint32_t* b,uint32_t* X1,uint32_t* Z1,uint32_t* X2,
+uint32_t* Z2,uint32_t* T,uint32_t* S,uint32_t* M1,uint32_t* M2)
+{
+ f2m_one(t,X1); f2m_zero(t,Z1); /*1*/
+ f2m_assign(t,xP,X2); f2m_one(t,Z2); /*2*/
+ for(int i = m;i >= 1; i--) /*3*/
+ {
+ if(f2m_biti(t,i-1,k) == 1) /*4*/
+ {
+ f2m_mul(t,m,X1,Z2,F,T,M1,M2); /*5*/
+ f2m_mul(t,m,X2,Z1,F,S,M1,M2); /*6*/
+ f2m_mul(t,m,T,S,F,X1,M1,M2); /*7*/
+ f2m_xor(t,T,S,S); /*8*/
+ f2m_mul(t,m,S,S,F,Z1,M1,M2); /*9*/
+ f2m_mul(t,m,xP,Z1,F,T,M1,M2); /*10*/
+ f2m_xor(t,X1,T,X1); /*11*/
+ f2m_mul(t,m,X2,X2,F,T,M1,M2); /*12*/
+ f2m_mul(t,m,Z2,Z2,F,S,M1,M2); /*13*/
+ f2m_mul(t,m,S,T,F,Z2,M1,M2); /*14*/
+ f2m_mul(t,m,S,S,F,S,M1,M2); /*15*/
+ f2m_mul(t,m,S,b,F,S,M1,M2); /*16*/
+ f2m_mul(t,m,T,T,F,X2,M1,M2); /*17*/
+ f2m_xor(t,X2,S,X2); /*18*/
+ }
+ else /*19*/
+ {
+ f2m_mul(t,m,X2,Z1,F,T,M1,M2); /*20*/
+ f2m_mul(t,m,X1,Z2,F,S,M1,M2); /*21*/
+ f2m_mul(t,m,T,S,F,X2,M1,M2); /*22*/
+ f2m_xor(t,T,S,S); /*23*/
+ f2m_mul(t,m,S,S,F,Z2,M1,M2); /*24*/
+ f2m_mul(t,m,xP,Z2,F,T,M1,M2); /*25*/
+ f2m_xor(t,X2,T,X2); /*26*/
+ f2m_mul(t,m,X1,X1,F,T,M1,M2); /*27*/
+ f2m_mul(t,m,Z1,Z1,F,S,M1,M2); /*28*/
+ f2m_mul(t,m,S,T,F,Z1,M1,M2); /*29*/
+ f2m_mul(t,m,S,S,F,S,M1,M2); /*30*/
+ f2m_mul(t,m,S,b,F,S,M1,M2); /*31*/
+ f2m_mul(t,m,T,T,F,X1,M1,M2); /*32*/
+ f2m_xor(t,X1,S,X1); /*33*/
+ }
+ }
+}
+uint32_t f2m_reconstruct_point(
+ uint32_t t,
+ uint32_t m,
+ uint32_t* F,
+ uint32_t* xP,
+ uint32_t* yP,
+ uint32_t* X1,
+ uint32_t* Z1,
+ uint32_t* X2,
+ uint32_t* Z2,
+ uint32_t* xQ,
+ uint32_t* yQ,
+ uint32_t* A1,
+ uint32_t* A2,
+ uint32_t* A3,
+ uint32_t* A4
+)
+{
+ uint32_t step = 0;
+
+ if( f2m_is_zero(t,Z1) == 1 )
+ return 0;
+ if( f2m_is_zero(t,Z2) == 1 )
+ {
+ f2m_assign(t,xP,xQ);
+ f2m_xor(t,xP,yP,yQ);
+ return 1;
+ }
+
+ uint32_t* R1 = (uint32_t*) malloc(sizeof(uint32_t) * t);
+ f2m_mul(t,m,Z1,Z2,F,xQ,A1,A2);
+ f2m_mul(t,m,xP,xP,F,yQ,A1,A2);
+ f2m_xor(t,yQ,yP,yQ);
+ f2m_mul(t,m,xQ,yQ,F,yQ,A1,A2);
+ f2m_mul(t,m,xQ,xP,F,xQ,A1,A2);
+ f2m_inv(t,m,xQ,F,R1,A1,A2,A3,A4);
+ f2m_assign(t,R1,xQ);
+ f2m_mul(t,m,Z2,xP,F,Z2,A1,A2);
+ f2m_xor(t,Z2,X2,Z2);
+ f2m_mul(t,m,Z1,xP,F,X2,A1,A2);
+ f2m_xor(t,X2,X1,X2);
+ f2m_mul(t,m,X2,Z2,F,Z2,A1,A2);
+ f2m_xor(t,yQ,Z2,yQ);
+ f2m_mul(t,m,yQ,xQ,F,yQ,A1,A2);
+ f2m_inv(t,m,Z1,F,xQ,A1,A2,A3,A4);
+ f2m_mul(t,m,xQ,X1,F,xQ,A1,A2);
+ f2m_xor(t,xP,xQ,Z2);
+ f2m_mul(t,m,yQ,Z2,F,yQ,A1,A2);
+ f2m_xor(t,yQ,yP,yQ);
+
+ free(R1);
+
+ return 1;
+}
+bool f2m_diffie(uint32_t t,uint32_t m,uint32_t* F,uint32_t* b,uint32_t *xP,uint32_t* yP,uint32_t* k,uint32_t *d)
+{
+ bool retVal = false;
+ uint32_t *X1,*Z1,*X2,*Z2,*T,*S,*M1,*M2,*xQ1,*yQ1,*xQ2,*yQ2,*xTmp,*yTmp;
+ X1 = (uint32_t*) malloc(sizeof(uint32_t)*t);
+ Z1 = (uint32_t*) malloc(sizeof(uint32_t)*t);
+ X2 = (uint32_t*) malloc(sizeof(uint32_t)*t);
+ Z2 = (uint32_t*) malloc(sizeof(uint32_t)*t);
+ T = (uint32_t*) malloc(sizeof(uint32_t)*t);
+ S = (uint32_t*) malloc(sizeof(uint32_t)*t);
+ M1 = (uint32_t*) malloc(sizeof(uint32_t)*t);
+ M2 = (uint32_t*) malloc(sizeof(uint32_t)*t);
+
+ xQ1 = (uint32_t*) malloc(sizeof(uint32_t)*t);
+ yQ1 = (uint32_t*) malloc(sizeof(uint32_t)*t);
+ xQ2 = (uint32_t*) malloc(sizeof(uint32_t)*t);
+ yQ2 = (uint32_t*) malloc(sizeof(uint32_t)*t);
+ xTmp = (uint32_t*) malloc(sizeof(uint32_t)*t);
+ yTmp = (uint32_t*) malloc(sizeof(uint32_t)*t);
+
+ f2m_montgomery(t,m,d,xP,F,b,X1,Z1,X2,Z2,T,S,M1,M2);
+ f2m_reconstruct_point(t,m,F,xP,yP,X1,Z1,X2,Z2,xTmp,yTmp,T,S,M1,M2);
+ f2m_montgomery(t,m,k,xTmp,F,b,X1,Z1,X2,Z2,T,S,M1,M2);
+ f2m_reconstruct_point(t,m,F,xTmp,yTmp,X1,Z1,X2,Z2,xQ1,yQ1,T,S,M1,M2);
+
+ f2m_montgomery(t,m,k,xP,F,b,X1,Z1,X2,Z2,T,S,M1,M2);
+ f2m_reconstruct_point(t,m,F,xP,yP,X1,Z1,X2,Z2,xTmp,yTmp,T,S,M1,M2);
+ f2m_montgomery(t,m,d,xTmp,F,b,X1,Z1,X2,Z2,T,S,M1,M2);
+ f2m_reconstruct_point(t,m,F,xTmp,yTmp,X1,Z1,X2,Z2,xQ2,yQ2,T,S,M1,M2);
+
+ if ( (1 == f2m_is_equal(t,xQ1,xQ2)) && (1 == f2m_is_equal(t,yQ1,yQ2)) )
+ {
+ retVal = true;
+ }
+
+ free(X1);
+ free(Z1);
+ free(X2);
+ free(Z2);
+ free(T);
+ free(S);
+ free(M1);
+ free(M2);
+ free(xQ1);
+ free(yQ1);
+ free(xQ2);
+ free(yQ2);
+ free(xTmp);
+ free(yTmp);
+
+ return retVal;
+}
\ No newline at end of file diff --git a/Master/Public-Key-Algorithmen/pka_klausurvorbereitung.pdf b/Master/Public-Key-Algorithmen/pka_klausurvorbereitung.pdf Binary files differnew file mode 100644 index 0000000..582d0c2 --- /dev/null +++ b/Master/Public-Key-Algorithmen/pka_klausurvorbereitung.pdf diff --git a/Master/Public-Key-Algorithmen/ss2010_public_key_algorithmen_praktikum.pdf b/Master/Public-Key-Algorithmen/ss2010_public_key_algorithmen_praktikum.pdf Binary files differnew file mode 100644 index 0000000..865ab4b --- /dev/null +++ b/Master/Public-Key-Algorithmen/ss2010_public_key_algorithmen_praktikum.pdf |