<<

. 3
( 8)



>>



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/*printf("Round %03d: %081x %081x sk: %081x %08lx\n",
i/2,d[0l,d[ll,sk[il,skCi+ll); *!
d[ll -= sk[i+ll;
rc = d[Ol & 31;
d[ll = ROTR32(dCll,rc);
d[l] '= d[Ol;

dCO1 -= sk[il;
rc = d[ll & 31;
drol = ROTR32(dCOl,rc);
d[Ol '= d[ll;
I
d[O] -= c->xkCOl;
d[l] -= c->xkCll;
d+=2;



void rc5-key(rc5-ctx *c, ul *key, int keylen){
u4 *pk,A,B; I* padded key *I
int xk-len, pk-len, i, num-steps,rc;
ul *cp;

xk-len = c->nr*2 + 2;
pk-len = keylen/4;
if((keylen%4)!=0) pk-len += 1;

pk = (˜4 *) malloc(pk-len * 4);
if(pk==NULL) I
printf("An error occurred!\n");
exit(-1);


/* Initialize pk -- this should work on Intel machines, anyway.... */
for(i=O;i<pk-len;i++) pk[i]=O;
cp = (ul *)pk;
for(i=O;i<keylen;i++) cp[i]=key[i];

/* Initialize xk. */
c->xkCOl = Oxb7e15163; /* P32 */
for(i=l;i<xk-len;i++) c->xk[i] = c->xk[i-11 + Ox9e3779b9; /* Q32 */

/* TESTING */
A=B=O;
for(i=O;i<xk-len;i++) 1
A = A + c->xk[i];
B=B^ c->xk[i];


/* Expand key into xk. */
if(pk-len>xk-len) num-steps = 3*pk_len;else num-steps = 3*xk_len;

A=B=O;
for(i=O;i<num-steps;i++)l
A = c->xk[i%xk-lenl = ROTL32(c->xkCi%xk-len] + A + B,3);
rc = (A+B) & 31;




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B = pk[i%pk-len] = ROTL32(pk[i%pk_lenl + A + B,rc);

I
/* c lobber sensitive data before deallocating memory. */
for-( i=O;i<pk-len;i++) pk[i] =O;

free (pk);
I

void main(void)(
rc5-ctx c;
u4 data[81;
char key[l = "ABCDE";
int i;




for(i=O;i<8;i++) data[il = i;
rc5_init(&c,lO); /* 10 rounds */
rc5_key(&c,key,5);

rc5_encrypt(&c,data,4);
printf("Encryptions:\n'I;
for(i=O;i<8;i+=2) printf("Block %Old = %081x %081x\n",
i/2,data[il,data[i+ll);
rc5_decrypt(&c,data,2);
rc5_decrypt(&c,data+4,2);
printf("Decryptions:\n"I;
for(i=O;i<8;i+=2) printf("Block %Old = %081x %081x\n",
i/2,data[il,data[i+ll);




A5
typedef struct 1
unsigned long rl,r2,r3;
I a5-ctx;

static int thresholdcrl, r2, r3)
unsigned int rl;
unsigned int r2;
unsigned int r3;

int total;

total = (((t-1 >> 9) & 0x1) == 1) +
(((t-2 >> 11) & 0x1) == 1) +
(((t-3 >> 11) & 0x1) == 1);

if (total > 1)
return (0);




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A5


else
return (1);


unsigned long clock-rl(ct1, rl)
int ctl;
unsigned long rl;

unsigned long feedback;

ctl I\= ((t-1 >> 9) & 0x1);
if (ctl)

feedback = (r-1 >> 18) h (r-1 >> 17) h (t-1 >> 16) h (r-1 >> 13);
rl = (t-1 << 1) & Ox7ffff;
if (feedback & 0x01)
rl A= 0x01;

return (t-1);


unsigned long clock-r2(ctl, r2)
int ctl;
unsigned long r2;

unsigned long feedback;

ctl A= ((r-2 >> 11) & 0x1);
if (ctl)

feedback = (r2 >> 21) h (r2 >> 20) h (r-2 >> 16) n (r-2 >> 12);
t-2 = (t-2 << 1) & Ox3fffff;
if (feedback & 0x01)
r2 A= 0x01;

return (t-2);


unsigned long clock-r3(ctl, r3)
int ctl;
unsigned long r3;

unsigned long feedback;

ctl A= ((t-3 >> 11) & 0x1);
if (ctl)
(
feedback = (r3 >> 22) A (t-3 >> 21) A (r-3 >> 18) A (t-3 >> 17);
r3 = (r3 << 1) & Ox7fffff;
if (feedback & 0x01)
r3 A= 0x01;
1
return (r-3);




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Source Code


int keystreamckey, frame, alice, bob)
unsigned char *key; /* 64 bit session key */
unsigned long frame; /* 22 bit frame sequence number */
unsigned char *alice; /* 114 bit Alice to Bob key stream */
unsigned char *bob; /* 114 bit Bob to Alice key stream */

unsigned long rl; /* 19 bit shift register */
unsigned long r2; /* 22 bit shift register */
unsigned long r3; /* 23 bit shift register */
int i; /* counter for loops */
int clock...ctl; /* xored with clock enable on each shift register */
unsigned char *ptr; /* current position in keystream */
unsigned char byte; /* byte of keystream being assembled */
unsigned int bits; /* number of bits of keystream in byte */
unsigned int bit; /* bit output from keystream generator */

/* Initialise shift registers from session key */

rl = (keyLO 1 (key[ll << 8) 1 (key[21 << 16) ) & Ox7ffff;
r2 = ((keyL21 >> 3) 1 (keyC31 << 5) 1 (key[4] << 13) I (key[S] << 21)) &
Ox3fffff;
r3 = ((keyL51 >> 1) I (key[61 << 7) ) (key[71 << 15) ) & Ox7fffff;

/* Merge frame sequence number into shift register state, by xor'ing it
* into the feedback path
*/

for (i=O;i<22;i++)

clock-ctl = thresholdcr1, r2, r2);
rl = clock-rl(clock-ctl, rl);
r2 = clock-r2(clock_ctl, r2);
r3 = clock-r3(clock_ctl, r3);
if (frame & 1)
1
rl A= 1;
r2 A= 1;
r3 h= 1.
I '
frame = frame >> 1;


/* Run shift registers for 100 clock ticks to allow frame number to
* be diffused into all the bits of the shift registers
*/

for (i=O;i<lOO;i++)

clock-ctl = thresholdcr1, r2, r2);
rl = clock-rl(clock-ctl, rl);
r2 = clock-r2(clock_ctl, r2);
r3 = clock-r3(clock_ctl, r3);
I

/* Produce 114 bits of Alice->Bob key stream */




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ptr = alice;
bits = 0;
byte = 0;
for (i=O;i<ll4;i++)
i
clock-ctl = thresholdcr1, t-2, r2);
rl = clock-rl(clock-ctl, rl);
r2 = clock-r2(clock_ctl, r2);
r3 = clock-r3(clock_ctl, r3);

bit = ((t-1 >> 18) * (r-2 >> 21) h (t-3 >> 22)) & 0x01;
byte = (byte << 1) 1 bit;
bits++;
if (bits == 8)
1
*ptr = byte;
ptr++;
bits = 0;
byte = 0;
I
I
if (bits)
*ptr = byte;

/* Run shift registers for another 100 bits to hide relationship between
* Alice->Bob key stream and Bob->Alice key stream.
*/

for (i=O;i<lOO;i++)
1
clock-ctl = thresholdcr1, r2, r2);
rl = clock-rl(clock-ctl, rl);
r2 = clock-r2(clock_ctl, r2);
r3 = clock-r3(clock_ctl, r3);
I

/* Produce 114 bits of Bob->Alice key stream */

ptr = bob;
bits = 0;
byte = 0;
for (i=O;i<ll4;i++)

clock-ctl = thresholdcrl, r2, r2);
rl = clock-rl(clock-ctl, rl);
r2 = clock-r2(clock_ctl, r2);
r3 = clock-r3(clock_ctl, r3);

bit = ((t-1 >> 18) h (r2 >> 21) A (t-3 >> 22)) & 0x01;
byte = (byte << 1) ( bit;
bits++;
if (bits == 8)

*ptr = byte;




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Source Code


ptr++;
bits = 0;
byte = 0;

t
if (bits)
*ptr = byte;

return (0);



void a5_key(a5_ctx *c, char *k)l
c->rl = k[01<<11˜k[11<<3 I k[21>>5 ; /* 19 */
c->r2 = k[21<<17lk[31<<9 I k[41<<1 I k[51>>7; /* 22 */
c->r3 = k[51<<15lk[61<<8 I k[71 ; I* 23 "I


I* Step one bit in A5, return 0 or 1 as output bit. *I
int a5LstepCa5Lctx *c)(
int control;
control = thresholdcc->rl,c->r2,c->r3);
c->rl = clock-rl(control,c->rl);
c->r2 = clock-r2(control,c->rZ);
c->r3 = clock-r3(control,c->r3);
return( (c->rl^c->r2^c->r3)&1);


/* Encrypts a buffer of len bytes. *I
void a5-encrypt(a5Lctx *c, char *data, int 1en)l
int i,j;
char t;

for(i=O;i<len;i++){
for(j=O;j<8;j++) t = t<<l I a5LstepCc);
data[il^=t;



void a!Y_decrypt(a5_ctx *c, char *data, int 1en)l
a5_encrypt(c,data,len);


void main(void)i
a5Lctx c;
char data[lOOl;
char key[l = l1,2,3,4,5,6,7,8);
int i,flag;

for(i=O;i<lOO;i++) data[il = i;

a5_key(&c,key);
a5_encrypt(&c,data,lOO);

a5_key(&c,key);




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SEAL


a5_decrypt(&c,data,l);
a5_decrypt(&c,data+l,99);

flag = 0;
for(i=O;i<lOO;i++) if(data[il!=i)flag = 1;
if(flag)printf("Decrypt failed\n"); else printf("Decrypt succeeded\n");
I



SEAL
#undef SEAL-DEBUG

#define ALG-OK 0
#define ALG-NOTOK 1
#define WORDS-PER-SEAL-CALL 1024

typedef struct {
long tL5201; I* 512 rounded up to a multiple
unsigned of 5 + 5*/
unsigned long s[2651; I* 256 rounded up to a multiple of 5 + 5*/
unsigned long r[201; /* 16 rounded up to multiple of 5 *I
unsigned long counter; I* 32-bit synch value. *I
unsigned long ks-buf[WORDS-PER-SEAL-CALL];
int ks-pos;
I seal-ctx;

#define ROT2(x) (((x) >> 2) 1 C(x) << 30))
#define ROT9(x) (c(x) >> 9) 1 C(x) << 23))
#define ROT8(x) (c(x) >> 8) 1 c(x) << 24))
#define ROTlGCx) (c(x) >> 16) 1 c(x) << 16))
#define ROT24Cx) (c(x) >> 24) I ((x1 << 8))
#define RDT27Cx) (((x1 >> 27) I c(x) << 5))

(cp[ll
#define WORD(cp) ((cp[Ol << 24) << 16)l(cp[21 << 8)l(cpC31))

#define FlCx, y, z) (((x) & (˜1) 1 cc-(x)1 & (z)))
#define F2(x, y, z) ((x)^(y)^(z)
#define F3(x, y, z) (((x1 & (˜1) 1 ((xl & (z)) I C(y) & (z)))
#define F4(x, y, z) ((x)^(y)^(z)

int g(in, i, h)
unsigned char *in;
int i;
unsigned long *h;
1
unsigned long ho;
unsigned long hl;
unsigned long h2;
unsigned long h3;
unsigned long h4;
unsigned long a;
unsigned long b;
unsigned long c;
unsigned long d;
unsigned long e;




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Source Code


unsigned char *kp;
unsigned long wL801;
unsigned long temp;

kp = in;
h0 = WORDCkp); kp += 4;
hl = WORDCkp); kp += 4;
h2 = WORDCkp); kp += 4;
h3 = WORDCkp); kp += 4;
h4 = WORDCkp); kp += 4;

w[Ol = i;
for (i=l;i<l6;i++)
w[il = 0;
for (i=16;i<8O;i++)
w[i] = w[i-31Aw[i-81Aw[i-14l^w[i-161;

a = ho;
b = hl;
c = h2;
d = h3;
e = h4;

for (i=O;i<2O;i++)
i
temp = ROT27Ca) + Fl(b, c, d) + e + w[i] + Ox5a827999;
e= d;
d= c;
c= ROT2Cb);
b= a;
a= temp;

for (i=2O;i<4O;i++)
I
1
d) + e + w[il + OxkK%bal;
temp = ROT27Ca) + F2(b, c,
e= d.
d= c;
c= ROT2Cb);
b= a;
a= temp;

for (i=4O;i<6O;i++)
1
d) + e + w[il + Ox8flbbcdc;
temp = ROT27(a) + F3(b, c,
e= d;
d= c;
c= ROT2Cb);
b= a;
a= temp;
1
for (i=6O;i<8O;i++)
1
temp = ROT27Ca) + F4(b, c, d) + e + w[i 1 + Oxca62cld6;
e = d;
d = c;




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SEAL


c = ROTPCb);
b = a;
a = temp;
1
h[OI = hO+a;
h[lI = hl+b;
h[21 = h2+c;
h[31 = h3+d;
h[4] = h4+e;

return (ALG-OK);
I

unsigned long gammaca, i)
unsigned char *a;
int i;
I
unsigned long h[51;

(void) g(a, i/5, h);
return h[i % 51;
1

int seal-initcseal-ctx *result, unsigned char *key)
i
int i;
unsigned long h[51;

for (i=O;i<51O;i+=5)
g(key, i/5, &(result->t[il));
I* horrible special case for the end *I
g(key, 51015, h);
for (i=51O;i<512;i++)
result->t[il = h[i-5101;
I* 0x1000 mod 5 is +l, so have horrible special case for the s tart *I
g(key, (-1+0x1000)/5, h);
for (i=O;i<4;i++)
result->s[il = h[i+lI;
for (i=4;i<254;i+=5)
g(key, (i+Ox1000)/5, &(result->s[i]));
I* horrible special case for the end *I
g(key, (254+0x1000)/5, h);
for (i=254;i<256;i++)
result->s[il = h[i-2541;
I* 0x2000 mod 5 is +2, so have horrible special case at the start *I
g(key, (-2+0x2000)/5, h);
for (i=O;i<3;i++)
result->r[il = h[i+2];
for (i=3;i<13;i+=5)
g(key, (i+Ox2000)/5, &(result->r[il));
I* horrible special case for the end *I
g(key, (13+0x2000)/5, h);
for (i=13;i<16;i++)
result->r[il = h[i-131;
return (ALG-OK);




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int seal(seal-ctx *key, unsigned long in, unsigned long *out)
,
int i;
int j;
int 1;
unsigned long a;
unsigned long b;
unsigned long c;
unsigned long d;
unsigned short p;
unsigned short q;
unsigned long nl;
unsigned long n2;
unsigned long n3;
unsigned long n4;
unsigned long *wp;

wp = out;

for (1=0;1<4;1++)
1
a = in h key->rC4*11;
b = ROT8Cin) A key->r[4*1+11;
c = ROTlGCin) A key->r[4*1+21;
d = ROT24Cin) A key->r[4*1+31;

for (j=O;j<2;j++)
,
p = a & Ox7fc;
b += key->t[pl41;
a = ROT9Ca);

p = b & Ox7fc;
c += key->t[p/41;
b = RDT9Cb);

p = c & Ox7fc;
d += key->t[pl41;
c = ROT9Cc);

p = d & Ox7fc;
a += key->t[p/4];
d = ROT9Cd);


nl = d;
n2 = b;
n3 = a;
n4 = c;

p = a & Ox7fc;
b += key->t[p/4];




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SEAL


a = ROT9Ca);

p = b & Ox7fc;
c += key->tCp/41;
b = ROT9Cb):

p = c & Ox7fc;
d += key->tCp/41;
c = ROT9Cc):

p = d & Ox7fc;
a += key->tCp/41;
d = ROT9Cd);

I* This generates 64 32-bit words, or 256 bytes of keystream. *I
for (i=O;i<64;i++)

p = a & Ox7fc;
b += key->t[p/41;
a = ROT9Ca);
b h= a;

q = b & Ox7fc;
c A= key->t[q/41;
b = ROT9Cb);
c += b;

p = (p+c) & Ox7fc;
d += key->t[p/41;
c = ROT9Cc);
d h= c;

q = (q+d) & Ox7fc;
a h= key->t[q/4];
d = ROT9Cd);
a += d;

p = (p+a) & Ox7fc;
b h= key->t[p/41;
a = ROT9Ca);

q = (q+b) & Ox7fc;
c += key->tCq/41;
b = ROT9Cb);

p = (p+c) & Ox7fc;
d II= key->t[p/41;
c = ROT9Cc);

q = (q+d) & Ox7fc;
a += key->tCq/41;
d = ROT9Cd);

= b + key->s[4*il;
*wp




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Source Code


wp++;
*wp = c n key->s[4*i+ll;
wp++;
*wp = d + key->s[4*i+21;
wp++;
*wp = a n key->s[4*i+31;
wp++;

if (i & 1)

a += n3;
c += n4;

else

a += nl;
c += n2;




return (ALGGOK);


/* Added call to refill ks-buf and reset counter and ks-pos. */
void seal-refill-buffer(seal_ctx *c)(
seal(c,c->counter,c->ks-buf);
c->counter++;
c->ks-pos = 0;
I

void seal-keycseal-ctx *c, unsigned char *key){
seal-init(c,key);
c->counter = 0; /* By default, init to zero. */
c->ks-pos = WORDS-PER-SEAL-CALL;
/* Refill keystream buffer on next call. */


/* This encrypts the next w words with SEAL. */
void seal-encrypt(seal_ctx *c, unsigned long *data-ptr, int w)l
int i;

for(i=O;i<w;i++){
if(c->ks-pos>=WORDS-PER-SEAL-CALL) seal-refill-buffer(c);
data-ptr[i]^=c->ks-buf[c->ks_posI;
c->ks_pos++;



void seal-decrypt(seal-ctx *c, unsigned long *data-ptr, int w) {
seal_encrypt(c,data-ptr,w);
1

void seal-resynch(seal-ctx *c, unsigned long synch-word){
c->counter = synch-word;




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SEAL


c->ks-pos = WORDS-PER-SEAL-CALL;


void main(void)L
seal-ctx sc;
unsigned long buf[lOOOl,t;
int i,flag;
unsigned char key[l =
.1,12,13,14,15,16,1 .7,18,191;
10,1,2,3,4,5,6,7,8,9,10,1

printf("l\n");
seal-key(&sc,key);

printf("2\n");
for(i=O;i<lOOO;i++) buf[il=O;
printf("3\n");
seal˜encrypt(&sc,buf,lOOO);
printf("4\n");
t = 0;
for(i=O;i<lOOO;i++) t = t h buf[il;
printf("XOR of buf is %08lx.\n",t);

seal-key(&sc,key);
seal-decrypt(&sc,buf,l);
seal-decrypt(&sc,buf+l,999);
flag = 0;
for(i=O;i<lOOO;i++) if(buf[il!=O)flag=l;
if(flag) printf("Decrypt failed.\n");
else printf("Decrypt succeeded.\n");




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References


Cryptology-CRYPTO ˜87 Proceedings,
1. ABA Bank Card Standard, “Management
and Use of Personal Information Num- Springer-Verlag, 1988, pp. 224-230.
9. C.M. Adams and S.E. Tavares, “The Struc-
bers,” Aids from ABA, Catalog no. 207213,
tured Design of Cryptographically Good S-
American Bankers Association, 1979.
Boxes,” fournal of Cryptology, v. 3, n. 1,
2. ABA Document 4.3, “Key Management
Standard,” American Bankers Association, 1990, pp. 27-41.
10. C.M. Adams and S.E. Tavares, “Designing
1980.
S-Boxes for Ciphers Resistant to Differen-
3. M. Abadi, J. Feigenbaum, and J. Kilian,
“On Hiding Information from an Oracle,” tial Cryptanalysis,” Proceedings of the 3rd
Symposium on State and Progress of
Proceedings of the 19th ACM Symposium
on the Theory of Computing, 1987, pp. Research in Cryptography, Rome, Italy,
195-203. 15-16 Feb 1993, pp. 181-190.
Il. W. Adams and D. Shanks, “Strong Primal-
4. M. Abadi, J. Feigenbaum, and J. Kilian,
ity Tests That Are Not Sufficient,” Mathe-
“On Hiding Information from an Oracle,”
matics of Computation, v. 39, 1982, pp.
fournal of Computer and System Sciences,
v. 39, n. 1, Aug 1989, pp. 21-50. 255300.
5. M. Abadi and R. Needham, “Prudent Engi- 12. W.W. Adams and L.J. Goldstein, Introduc-
neering Practice for Cryptographic Proto- tion to Number Theory, Englewood Cliffs,
cols,” Research Report 125, Digital Equip- N.J.: Prentice-Hall, 1976.
ment Corp Systems Research Center, Jun 13. B.S. Adiga and P. Shankar, “Modified Lu-
1994. Lee Cryptosystem,” Electronics Letters, v.
6. CM. Adams, “On Immunity Against 21, n. 18,29 Aug 1985, pp. 794795.
Biham and Shamir™s ˜Differential Crypt- 14. L.M. Adleman, “A Subexponential Algo-
analysis,™ ” Information Processing Let- rithm for the Discrete Logarithm Problem
ters, v. 41, 14 Feb 1992, pp. 77-80. with Applications to Cryptography,” Pro-
7. C.M. Adams, “Simple and Effective Key ceedings of the IEEE 20th Annual Sympo-
Scheduling for Symmetric Ciphers,” Work- sium of Foundations of Computer Science,
shop on Selected Areas in Cryptography- 1979, pp. 5560.
Workshop Record, Kingston, Ontario, 5-6 15. L.M. Adleman, “On Breaking Generalized
May 1994, pp. 129-133. Knapsack Public Key Cryptosystems,”
Proceedings of the 15th ACM Symposium
8. C.M. Adams and H. Meijer, “Security-
on Theory of Computing, 1983, pp. 402-
Related Comments Regarding McEliece™s
Public-Key Cryptosystem,” Advances in 412.




Page 673
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References


16. L.M. Adleman, “Factoring Numbers Using 28. S.G. Akl, “Digital Signatures: A Tutorial
Singular Integers,” Proceedings of the 23rd Survey,” Computer, v. 16, n. 2, Feb 1983,
Annual ACM Symposium on the Theory pp. 15-24.
of Computing, 1991, pp. 64-71. 29. S.G. Akl, “On the Security of Compressed
17. L.M. Adleman, “Molecular Computation Encodings,” Advances in Cryptology: Pro-
of Solutions to Combinatorial Problems,” ceedings of Crypto 83, Plenum Press, 1984,
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