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The PSP KIRK Crypto Engine is a security hardware device that is embedded into the TACHYON main IC chip. It is a bus master and can DMA to/from main DDR RAM memory, operating independantly of the CPU. It is interfaced via memory mapped registers at base of 0xBDE00000 ([[SPOCK Crypto Engine]] on the other hand is mapped to 0xBDF00000). It is capable of performing AES encryption, decryption, SHA1 Hash, pseudo random number generation, and signature generation and verifications (ECDSA) and CMAC.
The PSP KIRK Crypto Engine is a security hardware device that is embedded into the TACHYON main IC chip. It is a bus master and can DMA to/from main DDR RAM memory, operating independantly of the CPU. It is intefaced via memory mapped registers at base of 0xBDE00000 ([[SPOCK Crypto Engine]] on the other hand is mapped to 0xBDF00000). It is capable of performing AES encryption, decryption, SHA1 Hash, pseudo random number generation, and signature generation and verifications (ECDSA) and CMAC.
 
Most of the static keys used by the engine (plus the private key for Kirk command 1, which is not present on the chip) have been found through the PS3 hacks or glitching and can be found on the [[Keys]] page.
 
= Invocation =
 
All of the Kirk commands can be used using the function sceUtilsBufferCopyWithRange, which takes five arguments:
*the output buffer (if there is one, NULL otherwise)
*the output buffer size (if there is one, 0 otherwise)
*the input buffer (if there is one, NULL otherwise)
*the input buffer size (if there is one, 0 otherwise)
*the index of the command (as detailed below).
 
= Elliptic curves =
 
The PSP uses ECDSA for public-key cryptography. Elliptic curves are known for being fast and only requiring small keys, contrary to other public-key cryptography algorithms. They are still considered to be very secure, even for the 160-bit curves used by the PSP, unless a mistake is made when using them.
 
These curves have been designed by Sony only for the console. They are not vulnerable to any known attack.
 
Both use the usual Weierstrass form.
 
== Elliptic curve for Kirk commands 1/2/3/0xA ==
 
This curve is used for the ECDSA verification of Kirk commands 1, 2, 3 and 0xA.
 
<pre>
p = 0xFFFFFFFFFFFFFFFF0001B5C617F290EAE1DBAD8F
G = (0x2259ACEE15489CB096A882F0AE1CF9FD8EE5F8FA, 0x604358456D0A1CB2908DE90F27D75C82BEC108C0)
n = 0xFFFFFFFFFFFFFFFF00000001FFFFFFFFFFFFFFFF
a = -3
b = 0x65D1488C0359E234ADC95BD3908014BD91A525F9
</pre>
 
The public key is hardcoded, and is equal to: (0xED9CE58234E61A53C685D64D51D0236BC3B5D4B9, 0x049DF1A075C0E04FB344858B61B79B69A63D2C39).
 
== Elliptic curve for the other commands ==
 
This curved is used for Kirk commands 0xC, 0xD, 0xE, 0x10 and 0x11.
 
<pre>
p = 0xFFFFFFFFFFFFFFFEFFFFB5AE3C523E63944F2127
G = (0x128EC4256487FD8FDF64E2437BC0A1F6D5AFDE2C, 0x5958557EB1DB001260425524DBC379D5AC5F4ADF)
n = 0xFFFFFFFFFFFFFFFF00000001FFFFFFFFFFFFFFFF
a = -3
b = 0xA68BEDC33418029C1D3CE33B9A321FCCBB9E0F0B
</pre>
 
These commands allow to do operations with any public key. For the latest [[iplloader]] version which adds an additional ECDSA verification of the XOR of the block hashes, the public key which is hardcoded in the iplloader is (0xBC660611A70BD7F2D140A48215C096D11D2D4112, 0xF0E9379AC4E0D387C542D091349DD15169DD5A87).
 
== Code sample ==
 
Below is an example of how to manipulate these curves using the ecpy python library.
 
<pre>
import ecpy.curves
 
psp_curve_cmd1 = {
    'name':      "psp_curve_cmd1",
    'type':      "weierstrass",
    'size':      160,
    'field':    0xFFFFFFFFFFFFFFFF00000001FFFFFFFFFFFFFFFF,
    'generator': (0x2259ACEE15489CB096A882F0AE1CF9FD8EE5F8FA, 0x604358456D0A1CB2908DE90F27D75C82BEC108C0),
    'order':    0xFFFFFFFFFFFFFFFF0001B5C617F290EAE1DBAD8F,
    'cofactor':  1,
    'a':        -3,
    'b':        0x65D1488C0359E234ADC95BD3908014BD91A525F9,
}
 
psp_curve_cmd17 = {
    'name':      "psp_curve_cmd17",
    'type':      "weierstrass",
    'size':      160,
    'field':    0xFFFFFFFFFFFFFFFF00000001FFFFFFFFFFFFFFFF,
    'generator': (0x128EC4256487FD8FDF64E2437BC0A1F6D5AFDE2C, 0x5958557EB1DB001260425524DBC379D5AC5F4ADF),
    'order':    0xFFFFFFFFFFFFFFFEFFFFB5AE3C523E63944F2127,
    'cofactor':  1,
    'a':        -3,
    'b':        0xA68BEDC33418029C1D3CE33B9A321FCCBB9E0F0B,
}
 
crv1 = ecpy.curves.WeierstrassCurve(psp_curve_cmd1)
crv17 = ecpy.curves.WeierstrassCurve(psp_curve_cmd17)
 
pt1 = ecpy.curves.Point(0xED9CE58234E61A53C685D64D51D0236BC3B5D4B9, 0x049DF1A075C0E04FB344858B61B79B69A63D2C39, crv1)
pt17 = ecpy.curves.Point(0xbc660611a70bd7f2d140a48215c096d11d2d4112, 0xf0e9379ac4e0d387c542d091349dd15169dd5a87, crv17)
 
# verify the Kirk command 1 ECDSA private key
crv1_g = ecpy.curves.Point(0x2259ACEE15489CB096A882F0AE1CF9FD8EE5F8FA, 0x604358456D0A1CB2908DE90F27D75C82BEC108C0, crv1)
assert(crv1.mul_point(crv1.generator, 0xF392E26490B80FD889F2D9722C1F34D7274F983D) == pt1)
</pre>
 
= Slotted Keys =
The KIRK ROM can access different keys which are slotted in what might be some kind of secure enclave. There are slots for both AES and ECDSA keys.
 
== AES slotted keys ==
{| class="wikitable"
|+
!Id
!Content
!Do we have it?
|-
|0
|KIRK command 0 (Kbooti from Devkit) decryption key
|No
|-
|1
|KIRK command 0 (Kbooti from Devkit) CMAC key
|No
|-
|2
|KIRK command 1 (IPL) decryption key
|Yes
|-
|3
|KIRK command 2 (DRM) decryption key
|No
|-
|4~0x83
|KIRK commands 4/7 decryption keys (128 possible ones)
|Yes
|}
 
== ECDSA slotted keys ==
Note: public keys take two slots (for both coordinates), and private keys take only one.
{| class="wikitable"
|+
!Id
!Content
!Do we have it?
|-
|0/1
|KIRK command 1 (IPL) public key (used to verify valid IPLs)
|Yes (including the private key!)
|-
|2/3
|KIRK command 2 (DRM) public key (used to verify data passed to KIRK command 2)
|No
|-
|4
|KIRK command 3 (DRM) private key (used by command 2 to sign data for command 3)
|No
|-
|5/6
|KIRK command 3 (DRM) public key (used by command 3 to verify data coming from command 2)
|No
|}
 
= PSP Individual Keys =
 
Kirk commands 2, 3, 5, 6, 8, 9, 0x10 and 0x12 use individual (per-console) seeds to generate individual keys. The base per-console seed is the Fuse ID (6 bytes), which is transformed into a 0x30-byte buffer named unofficially "individual key mesh". The PSP individual key mesh is used to generate various final individual keys depending on a seed parameter.
 
== PSP Individual Key Mesh ==
 
=== Structure ===
 
<source lang="c">
typedef struct ScePspIndividualKeyMesh { // size is 0x30
    SceUInt8 derivation_seed_0[0x10]; // a seed used to derive final keys with derivation_key
    SceUInt8 derivation_seed_1[0x10]; // a seed used to derive final keys with derivation_key
    SceUInt8 derivation_key[0x10]; // AES128 key used to derive final keys from seed_0 and seed_1
} ScePspIndividualKeyMesh;
</source>
 
=== Algorithm ===
 
To generate the individual key mesh of a specific PSP, provided its [[Fuse ID]], execute the following code.
 
<source lang="c">
void gen_psp_individual_key_mesh(ScePspIndividualKeyMesh *key_mesh) {
  int i, k;
  u8 subkey_1[0x10], subkey_2[0x10];
  rijndael_ctx aes_ctx;
  u8 fuse_id[8];
 
  // Byte-reverse the Fuse ID
  u32 g_fuse90 = *(u32 *)0xBC100090;
  u32 g_fuse94 = *(u32 *)0xBC100094;
  fuse_id[7] = g_fuse90 &0xFF;
  fuse_id[6] = (g_fuse90>>8) &0xFF;
  fuse_id[5] = (g_fuse90>>16) &0xFF;
  fuse_id[4] = (g_fuse90>>24) &0xFF;
  fuse_id[3] = g_fuse94 &0xFF;
  fuse_id[2] = (g_fuse94>>8) &0xFF;
  fuse_id[1] = (g_fuse94>>16) &0xFF;
  fuse_id[0] = (g_fuse94>>24) &0xFF;
  rijndael_set_key(&aes_ctx, ids_master_key, 128); // set ids_master_key as AES key
 
  for (i = 0; i < 0x10; i++) // initialize the subkeys using the Fuse ID
    subkey_2[i] = subkey_1[i] = fuse_id[i % 8];
 
  for (i = 0; i < 3; i++) { // encrypt first subkey three times, and decrypt second subkey three times
    rijndael_encrypt(&aes_ctx, subkey_1, subkey_1);
    rijndael_decrypt(&aes_ctx, subkey_2, subkey_2);
  }
 
  rijndael_set_key(&aes_ctx, subkey_1, 128); // set subkey_1 as AES key
 
  for (i = 0; i < 3; i++) { // encrypt 3, 6 and 9 times subkey_2 to obtain the final key mesh
    for (k = 0; k < 3; k++)
      rijndael_encrypt(&aes_ctx, subkey_2, subkey_2);
    memcpy(key_mesh[i * 0x10], subkey_2, 0x10);
  }
}
 
typedef struct {
unsigned char buf1[8]; // 0
unsigned char buf2[8]; // 8
unsigned char buf3[8]; // 0x10
} SomeStructure;
 
void gen_psp_individual_key_mesh_official_implementation(SomeStructure *ss, ScePspIndividualKeyMesh *key_mesh) {
  byte bVar1;
  byte *dst;
  int idx;
  int j;
  byte *src;
  byte subkey_2[16];
  byte subkey_1[16];
  uint ctx[64];
  uint ctx2[64];
 
  AES_set_encrypt_key_2(g_ids_master_key, 128, ctx); // set g_ids_master_key as AES key
  AES_set_decrypt_key_2(g_ids_master_key, 128, ctx2); // set g_ids_master_key as AES key
 
  idx = 0; // initialize the subkeys using the Fuse ID
  do {
    bVar1 = ss[idx + ((int)(idx + ((uint)(idx >> 0x1f) >> 0x1d)) >> 3) * -8];
    src = subkey_2 + idx;
    dst = subkey_1 + idx;
    idx = idx + 1;
    *src = bVar1;
    *dst = bVar1;
  } while (idx < 0x10);
 
  idx = 2; // encrypt first subkey three times, and decrypt second subkey three times
  do {
    AES_encrypt_2(subkey_1, subkey_1, ctx);
    idx = idx - 1;
    AES_decrypt_2(subkey_2, subkey_2, ctx2);
  } while (-1 < idx);
 
  AES_set_encrypt_key_2(subkey_1, 128, ctx); // set subkey_1 as AES key
 
  idx = 0; // encrypt three times each one of the three first blocks
  do {
    j = 2;
    do {
      j = j - 1;
      AES_encrypt_2(subkey_2, subkey_2, ctx);
    } while (-1 < j);
    dst = key_mesh + idx * 0x10;
    j = 0;
    do {
      src = subkey_2 + j;
      j = j + 1;
      *dst = *src;
      dst = dst + 1;
    } while (j < 0x10);
    idx = idx + 1;
  } while (idx < 3);
}
</source>
 
== Final PSP Individual Keys ==
 
=== Algorithm ===
 
In some Kirk commands, the individual key mesh is used along with a seed parameter to generate a final individual key using the following algorithm.
 
<syntaxhighlight lang="c">
void make_perconsole_key(u8 output[16], int seed_param, ScePspIndividualKeyMesh *key_mesh) {
    if (seed_param & 1)
        memcpy(output, key_mesh->derivation_seed_1, 16);
    else
        memcpy(output, key_mesh->derivation_seed_0, 16);
 
    // Encrypt the result several times depending on the seed parameter
    rijndael_set_key(&aes_ctx, key_mesh->derivation_key);
    seed_param = (seed_param / 2) + 1;
    while ((seed_param--) >= 0) {
        rijndael_encrypt(&aes_ctx, output);
    }
}
</syntaxhighlight>
 
=== Seed Parameter Per Command ===
 
{| class="wikitable"
|+
!Seed parameter
!Usage
|-
|0
|Kirk commands 2 (encryption) & 3 (decryption) (the real encryption and CMAC keys are random, but this per-console key is used to encrypt them)
|-
|1
|Kirk command 5 (encryption) & 8 (decryption)
|-
|2
|Kirk command 6 (encryption) & 9 (decryption)
|-
|3
|Kirk command 16
|-
|4
|Kirk command 18
|-
|5
|Unused
|-
|6
|RNG buffer reseeding
|}
 
== PSP Individual Key Mesh Certificate ==
 
There exists a PSP Individual Key Mesh Certificate stored in both PSP flashData.prx and in PS Vita cmep keyrings 0x601 and 0x602 (in endian-swapped fashion). It contains the individual key mesh followed by the Fuse ID from which it was generated and ends with a hash.
 
=== Structure ===
 
<source lang="C">
typedef struct ScePspIndividualKeyMeshCert { // size is 0x40
    ScePspIndividualKeyMesh key_mesh;
    SceUInt8 fuse_id[8]; // endianness to precise
    SceUInt8 reserved[4]; // could be arbitrary but in practice always zeroed
    SceUInt32 hash; // the hash algorithm is in PSP Jig Kick flashData.prx
} ScePspIndividualKeyMeshCert;
</source>
 
=== Algorithm ===
 
To generate the ScePspIndividualKeyMeshCert of a specific PSP, provided its [[Fuse ID]], execute the following code.
 
<source lang="C">
void gen_psp_individual_key_mesh_certificate_hash(ScePspIndividualKeyMeshCert *cert) {
  byte bVar1;
  uint uVar2;
  int iVar3;
  byte *pbVar4;
  uint uVar5;
  uint uVar6;
  byte *pbVar7;
  uint uVar8;
  byte bVar9;
  int idx;
  int offset;
  byte *pbVar11;
  byte local_60 [80];
  byte m [16];
  uint uVar10;
 
  pbVar11 = local_60;
  m[0] = 1;
  m[1] = 0xf;
  m[2] = 0x36;
  m[3] = 0x78;
  m[4] = 0x40;
 
  offset = 0;
  do {
    pbVar4 = cert + offset;
    pbVar7 = local_60 + offset;
    offset = offset + 1;
    *pbVar7 = *pbVar4;
  } while (offset < 0x3c);
 
  offset = 0x3c;
  do {
    pbVar7 = local_60 + offset;
    offset = offset + 1;
    *pbVar7 = 0;
  } while (offset < 0x40);
 
  offset = 0;
  do {
    bVar1 = *pbVar11;
 
    idx = 0;
    do {
      uVar8 = (uint)m[idx];
      iVar3 = idx + 0x40;
      uVar10 = 0;
      bVar9 = 0;
      uVar2 = (uint)bVar1;
      while (uVar8 != 0) {
        uVar6 = uVar2 << 1;
        uVar5 = uVar8 & 1;
        uVar8 = (int)uVar8 >> 1;
        if (uVar5 != 0) {
          uVar10 = uVar10 ^ uVar2;
        }
        bVar9 = (byte)uVar10;
        uVar2 = uVar6;
        if ((uVar6 & 0x100) != 0)
          uVar2 = uVar6 ^ 0x11d;
      }
      idx = idx + 1;
      local_60[iVar3] = bVar9;
    } while (idx < 5);
 
    idx = 0;
    do {
      pbVar7 = pbVar11 + idx;
      iVar3 = idx + 0x40;
      idx = idx + 1;
      *pbVar7 = *pbVar7 ^ local_60[iVar3];
    } while (idx < 5);
 
    idx = offset + 1;
    pbVar11 = local_60 + offset + 1;
    offset = idx;
  } while (idx < 0x3c);
 
  offset = 0x3c;
  do {
    pbVar11 = local_60 + offset;
    pbVar7 = cert + offset;
    offset = offset + 1;
    *pbVar7 = *pbVar11;
    *pbVar11 = 0;
  } while (offset < 0x40);
 
  return;
}
 
void gen_psp_individual_key_mesh_certificate(SomeStructure *ss, byte *data_for_0x38, ScePspIndividualKeyMeshCert *cert) { 
  gen_psp_key_mesh(cert->key_mesh);
 
  for (int idx = 0; idx < 8; idx++)
    cert->fuse_id[idx] = ss[idx];
 
  for (int idx = 0; idx < 4; idx++)
    cert->reserved[idx] = data_for_0x38[idx];
 
  gen_psp_individual_key_mesh_certificate_hash(cert);
 
  return 0;
}
 
typedef struct U64 {
unsigned int low;
unsigned int high;
} U64;
 
int CreateSomeStructure(SomeStructure *ss) {
U64 fuse_id;
int i;
 
memcpy(&fuse_id, &g_fuse_id, 8);
 
memset(ss->buf1, 0, 8);
memset(ss->buf2, 0xFF, 8);
 
memcpy(ss->buf3, &fuse_id.high, 4);
memcpy(ss->buf3+4, &fuse_id.low, 4);
 
for (i = 0; i < 4; i++) {
ss->buf1[3-i] = ss->buf3[i];
ss->buf1[7-i] = ss->buf3[4+i];
}
 
return 0;
}
 
uint gen_psp_individual_seed_helper(ScePspIndividualKeyMeshCert *cert) {
  SomeStructure ss;
  CreateSomeStructure(&ss);
  int data_for_0x38 = 0;
  gen_psp_individual_key_mesh_certificate(&ss, &data_for_0x38, cert)
  return 0;
}
</source>
 
= Mapping Structure =
<pre>
0xBDE00000 = Kirk Signature
0xBDE00004 = Kirk Version
0xBDE00008 = Kirk Error
0xBDE0000C = Kirk Proc Phase
0xBDE00010 = Kirk CMD Number
0xBDE00014 = Kirk Result
0xBDE00018 = Unknown?
0xBDE0001C = Kirk Status
0xBDE00020 = Kirk Status Asynchronous
0xBDE00024 = Kirk Status Asynchronous End
0xBDE00028 = Kirk Status End
0xBDE0002C = Kirk Source Address
0xBDE00030 = Kirk Destination Address
</pre>


= Commands =
= Commands =


On PSP there are 19 Kirk commands. On PSVita, there are these 19 commands plus some new commands to support bigger keys (192 bits for example). See [https://wiki.henkaku.xyz/vita/F00D_Commands#gcauthmgr_sm.self F00D commands].
On PSP there are 18 KIRK commands. On PSVita, there are these 18 commands plus some new commands to support bigger keys (192 bits for example). See [https://wiki.henkaku.xyz/vita/F00D_Commands#gcauthmgr_sm.self F00D commands].


Kirk commands are called with the same 5 arguments (outbuf, outbuf_size, inbuf, inbuf_size, service_number (which is the command ID)). Depending on the service number used, the expectations of the inbuf or outbuf vary and are detailed below.
KIRK functions are called with the same 5 arguments (outbuf, outbuf_size, inbuf, inbuf_size, service_number (which is the command ID)). Depending on the service number used, the expectations of the inbuf or outbuf vary and are detailed below.


== Table ==
== Table ==
Line 505: Line 16:
! scope="col"| Input size
! scope="col"| Input size
! scope="col"| Output size
! scope="col"| Output size
! scope="col"| Result
! scope="col"| Used in
! scope="col"| Used in
! scope="col"| Uses perconsole key fuse based algo?
! scope="col"| Uses slot key? (if yes, specify)
|-
| 0
| KIRK_CMD_DECRYPT_BOOTROM
| Decryption of the psp devkit kbooti bootrom (no inverse)
| encrypted kbooti size+0x12
| decrypted kbooti bootrom size
| tachsm.o
| {{no}}
| {{Slot0_AES_1_CMAC}}
|-
|-
| 1
| 1
| KIRK_CMD_DECRYPT_PRIVATE
| KIRK_CMD_DECRYPT_PRIVATE
| Super-Duper decryption (no inverse)
| Super-Duper decryption (no inverse)
| buf_size+0x90
| buf_size+0x40
| buf_size
| buf_size
| memlmd, mesg_led, bootrom
|
| {{no}}
| memlmd, mesg_led
| {{Slot2_AES_CMAC}}
|-
|-
| 2
| 2
| KIRK_CMD_DNAS_ENCRYPT
| KIRK_CMD_2
| Encrypt Operation for DNAS (inverse of command 3)
| Encrypt Operation (inverse of cmd 3)
| buf_size+0x90
|  
| buf_size
|  
| mesg_led
|  
| {{yes}}
|  
| {{Slot3_AES}}
|-
|-
| 3
| 3
| KIRK_CMD_DNAS_DECRYPT
| KIRK_CMD_3
| Decrypt Operation for DNAS (inverse of command 2)
| Decrypt Operation (inverse of cmd 2)
| buf_size+0x90
|  
| buf_size
|  
| mesg_led
|  
| {{yes}}
|  
| {{no}}
|-
|-
| 4
| 4
| KIRK_CMD_ENCRYPT_STATIC
| KIRK_CMD_ENCRYPT_IV_0
| Encrypt Operation (inverse of command 7) (key=static)
| Encrypt Operation (inverse of cmd 7) (IV=0)
| buf_size+0x14
| buf_size+0x14
| buf_size+0x14
| buf_size+0x14
| chnnlsv, memab, openpsid
|
| {{no}}
| chnnlsv, memab
| {{Slot4_AES}}
|-
|-
| 5
| 5
| KIRK_CMD_ENCRYPT_PERCONSOLE
| KIRK_CMD_ENCRYPT_IV_FUSE
| Encrypt Operation (inverse of command 8) (key=per-console)
| Encrypt Operation (inverse of cmd 8) (IV=FuseID)
| buf_size+0x14
| buf_size+0x14
| buf_size+0x14
| buf_size+0x14
| openpsid, chnnlsv, psheet since PSP FW 2.81 for PGD, ?openpsid for IDPS Certificates?
|  
| {{yes}}
| chnnlsv, psheet since PSP FW 2.81 for PGD, ?openpsid for IDS Certificates?
| {{no}}
|-
|-
| 6
| 6
| KIRK_CMD_ENCRYPT_USER
| KIRK_CMD_ENCRYPT_IV_USER
| Encrypt Operation (inverse of command 9) (key=user-defined)
| Encrypt Operation (inverse of cmd 9) (IV=UserDefined)
| buf_size+0x24
|  
| buf_size+0x34
|  
| power, inside a kl4e blob, IPL (stage 2)
|  
| {{yes}}
|  
| {{no}}
|-
|-
| 7
| 7
| KIRK_CMD_DECRYPT_STATIC
| KIRK_CMD_DECRYPT_IV_0
| Decrypt Operation (inverse of command 4) (key=static)
| Decrypt Operation (inverse of cmd 4) (IV=0)
| buf_size+0x14
| buf_size+0x14
| buf_size+0x14
| buf_size+0x14
| memlmd, mesg_led,chnnlsv, memab, openpsid, bootrom
|
| {{no}}
| memlmd, mesg_led,chnnlsv, memab
| {{Slot4_AES}}
|-
|-
| 8
| 8
| KIRK_CMD_DECRYPT_PERCONSOLE
| KIRK_CMD_DECRYPT_IV_FUSE
| Decrypt Operation (inverse of command 5) (key=per-console)
| Decrypt Operation (inverse of cmd 5) (IV=FuseID)
| buf_size+0x14
| buf_size+0x14
| buf_size+0x14
| buf_size+0x14
| memlmd, chnnlsv, psheet since PSP FW 2.81 for PGD
|  
| {{yes}}
| chnnlsv, psheet since PSP FW 2.81 for PGD
| {{no}}
|-
|-
| 9
| 9
| KIRK_CMD_DECRYPT_USER
| KIRK_CMD_DECRYPT_IV_USER
| Decrypt Operation (inverse of command 6) (key=user-defined)
| Decrypt Operation (inverse of cmd 6) (IV=UserDefined)
| buf_size+0x34 (header + key)
|  
| buf_size
|  
| power, inside a kl4e blob, IPL (stage 2)
|  
| {{yes}}
|  
| {{no}}
|-
|-
| 10 (0xA)
| 10 (0xA)
| KIRK_CMD_PRIV_SIGVRY
| KIRK_CMD_PRIV_SIGVRY
| Private Signature Verify (checks for private SCE signature)
| Private Signature Verify (checks for private SCE sig)
| buf_size+0x90
|  
| 0
|  
|
|  
|  
| {{yes}}
| {{no}}
|-
|-
| 11 (0xB)
| 11 (0xB)
Line 612: Line 103:
| SHA1 Hash
| SHA1 Hash
| buf_size >= 0x14
| buf_size >= 0x14
| 0x14
| ?0x14?
| memlmd, mesg_led, memab, chkreg, openpsid, bootrom
|
| {{no}}
| memlmd, mesg_led, memab
| {{no}}
|-
|-
| 12 (0xC)
| 12 (0xC)
| KIRK_CMD_ECDSA_GENKEY
| KIRK_CMD_MUL1
| ECDSA Generate Private/Public Key Pair
| ECDSA Generate Keys
| 0
| 0
| 0x3C
| 0x3C
| memab, openpsid
|  
| {{no}}
| memab
| {{no}}
|-
|-
| 13 (0xD)
| 13 (0xD)
| KIRK_CMD_ECDSA_MUL
| KIRK_CMD_MUL2
| ECDSA Multiply Point
| ECDSA Multiply Point
| 0x3C
| 0x3C
| 0x3C
| 0x3C
| memab, openpsid
|  
| {{no}}
|  
| {{no}}
|-
|-
| 14 (0xE)
| 14 (0xE)
Line 640: Line 128:
| 0
| 0
| 0x14
| 0x14
| mesg_led, chnnlsv, memab, semawm, openpsid
|
| {{no}}
| mesg_led, chnnlsv, memab, semawm
| {{no}}
|-
|-
| 15 (0xF)
| 15 (0xF)
| KIRK_CMD_SEED
| KIRK_CMD_15
| Seed the Kirk internal RNG buffer
| (absolutely no idea – could be KIRK initialization)
| 0x1C
|  
| 0x1C
|  
|  
| IPL
| IPL
| {{yes}}
| {{no}}
|-
|-
| 16 (0x10)
| 16 (0x10)
Line 658: Line 144:
| 0x34
| 0x34
| 0x28
| 0x28
| memab, openpsid (used for IDStorage Certificates ECDSA)
|  
| {{yes}}
| memab
| {{no}}
|-
|-
| 17 (0x11)
| 17 (0x11)
| KIRK_CMD_SIGVRY
| KIRK_CMD_SIGVRY
| ECDSA Signature Verification
| Signature Verification (checks for generated signatures)
| 0x64
| 0x64
| 0
| 0
| memab, memlmd, mesg_led, openpsid (checks for generated signatures, used for IDStorage Certificates ECDSA)
|  
| {{no}}
| memab
| {{no}}
|-
|-
| 18 (0x12)
| 18 (0x12)
| KIRK_CMD_CERTVRY
| KIRK_CMD_CERTVRY
| Certificate Verification
| Certificate Verification (IDStorage Certificates CMAC)
| 0xB8
| 0xB8
| 0
| 0
| openpsid, memab, chkreg (used for IDStorage Certificates AES-CMAC)
|
| {{yes}}
| openpsid, memab
| {{no}}
|}
|}


== Command 0x0: decrypt kbooti ==
== Command 1: decryption and authentication ==
This command is only used by devkits to decrypt the kbooti, ie the devkit's Bootrom. It supposedly can only be run at a very early stage. The very short header is as follows.
{| class="wikitable"
|+
!Address
!Size
!Description
|-
|0x0
|16
|CMAC of the body, computed using AES slotted key 1
|-
|0x10
|2
|Size of the body
|-
|0x12
|...
|Body, encrypted using AES slotted key 0
|}
The command is very simple and acts as follows:
 
# Verify the command is run at an early stage
# Read the body size and check it's non-zero
# Verify the CMAC of the body using AES slotted key 1
# While computing the CMAC, verify the body size didn't change
# Decrypt body using AES slotted key 0
 
== Commands 0x1, 0x2, 0x3 & 0xA: decryption and authentication ==


=== Overview ===
=== Overview ===


These three functions take very similar inputs, as they all do signature verification and decryption.
There are two versions of this service: AES CMAC Verification, and ECDSA Verification. They use the header section of the input buffer slightly differently as follows.
 
* Command 1 is used to decrypt the IPL blocks.
* Command 2 is used to decrypt DRMBB and reencrypt them using a (random key encrypted with a) per-console key to generate data to pass to command 3.
* Command 3 decrypts data encrypted by command 2.
* Command 0xA takes the same data as commands 1, 2 and 3 but only does the signature verification for the header (not for the body) and no decryption (or reencryption).
 
There are two versions of this service: AES CMAC verification, and ECDSA verification. They use the header section of the input buffer slightly differently.
 
In both cases, the total header length is 0x90. The 0x10..0x60 bytes depend on the signature mode.
 
'''Metadata Header Structure (Length 0x90)''':
{| class="wikitable"
|-
! Address !! Size !! Description
|-
|0x00
|0x10
|Decryption key, encrypted with another key depending on the command
|-
|0x10
|0x50
|Signature information, depends on the signature mode (see below)
|-
| 0x60  || 4    || Set to 1, 2 or 3 depending on the command
|-
| 0x64  || 4    || Bit 0 is 0 if block is AES CMAC-signed, 1 if it is ECDSA-signed
Bit 1 is used by command 2 to determine if the resulting Kirk 3 block should be AES CMAC-signed (0) or ECDSA-signed (1)
|-
| 0x68  || 4    || Bit 0 indicates all input data (including the full header) should be wiped if the body signature check fails
|-
| 0x6C  || 4    || 0 for retail version and 0xFFFFFFFF for dev versions
|-
| 0x70  || 4    || Length of decrypted data
|-
| 0x74  || 4    || Length of the padding after the header and before the real data
|-
| 0x78  || 24    || Unused
|}


=== AES CMAC Version ===
=== AES CMAC Version ===


'''Signature Structure (Length 0x60)''':
'''Key Header Structure (Length 0x60)''':
{| class="wikitable"
*0x00-0x0F is decryption key (but stored encrypted with AES128, is not PLAINTEXT key)
|-
*0x10-0x1F is CMAC key (but again, derived ver not plain)
! Address !! Size !! Description
*0x20-0x2F is header hash (CMAC)
|-
*0x30-0x3F is data hash (CMAC)
| 0x10 || 16 || CMAC key, encrypted with the the same key as the decryption key (at 0x00)
*0x40-0x5F is 0
|-
| 0x20 || 16 || Header hash (CMAC)
|-
| 0x30 || 16 || Data hash (CMAC)
|-
| 0x40 || 32 || 0
|}


==== Verification process ====
'''Metadata Header Structure (Length 0x30)''':


The CMAC key at 0x10 is decrypted using a key which depends on the command and is the same as the decryption key at 0x00 (see below). It is decrypted using AES-CBC (so offset 0x00 is used as the IV).
*0x60-0x63 is set to 1 to indicate KIRK1 Verification
*0x64-0x67 is 0 to indicate AES CMAC Version
*0x68-0x6B is 0
*0x6C-0x6F is 0 for retail versions and 0xFFFFFFFF for dev versions
*0x70-0x73 is length of decrypted data
*0x74-0x77 is length of padding after Metadata header before real data starts
*0x78-0x8F is 0


The CMAC of the header from offset 0x60 and size 0x30 is computed. Kirk then checks the data size & offset (at 0x70 and 0x74) didn't change from what was previously read (possibly to avoid data being overwritten while being processed). The value is then checked against the value at 0x20.
==== Decryption process ====


If this fails, the command returns KIRK_HEADER_SIG_INVALID. Otherwise, except for command 10, it proceeds with the full data CMAC, computed from header offset 0x60 to the end of the body contents. The value is checked against the value at 0x30.
The first 0x20 bytes of the Key Header is decrypted with the KIRK 1 Stored AES Key. This was allegedly discovered by Datel by decapping the chip and reversing engineering the algorithms and keys. This was also recovered through the failure in PS3 cryptography by decrypting the isolated module in the PSP emulator on the PS3.


If this second check fails, and the LSB of 0x68 is set to 1, all the input data is wiped (set to zero's). In both cases, if the check fails, it then returns KIRK_HEADER_SIG_INVALID.
The first two blocks (0x20 bytes at offset 0) are decrypted with the KIRK 1 AES Key. The first block is the AES Key used for decrypting the main data. The second block is used to decrypt the next two blocks (0x20 bytes at offset 0x20). These represent the Metadata Header CMAC and the Data CMAC. They are checked against the AES CMAC of the header section and the AES CMAC of the data section.


=== ECDSA Version ===
=== ECDSA Version ===


'''Key Header Structure (Length 0x60)''':
'''Key Header Structure (Length 0x60)''':
{| class="wikitable"
*0x00-0x0F is decryption key (but stored encrypted with AES128, is not PLAINTEXT key)
|-
*0x10-0x23 is header ECDSA sig r
! Address !! Size !! Description
*0x24-0x37 is header ECDSA sig s
|-
*0x38-0x4b is data ECDSA sig r
| 0x10 || 0x14 || Header ECDSA signature r
*0x4c-0x5f is data ECDSA sig s
|-
| 0x24 || 0x14 || Header ECDSA signature s
|-
| 0x38 || 0x14 || Data ECDSA signature r
|-
| 0x4C || 0x14 || Data ECDSA signature s
|}
 
==== Verification process ====
 
The ECDSA version is slightly different. The header from offset 0x60 with size 0x30 is hashed and the header signature is verified. Similarly to CMAC, it then verifies values at 0x70 and 0x74 didn't change. It then acts similarly to the CMAC version with the data signature, including the possible data wiping.


=== Commands 1 & 3 ===
'''Metadata Header Structure (Length 0x30)''':
Commands 1 and 3 work exactly the same. The only difference is that the ECDSA public key comes from slots 0/1 for command 1, and 5/6 for command 3. Also, the AES key, used for decrypting the decryption & CMAC keys, is a static key in keyslot 2 for command 1, and a per-console key with seed 0 for command 3.


# Verify that the command mode at 0x60 matches the current command
*0x60-0x63 is set to 1 to indicate KIRK1 Verification
# Read the body size and data offset and verify that the body size is non-zero
*0x64-0x67 is set to 1 to indicate ECDSA version
# Get or compute the AES key
*0x68-0x6B is 0
# Check the signature mode at 0x64, and check the header & the data signature as specified above depending on the signature mode
*0x6C-0x6F is 0 for retail versions and 0xFFFFFFFF for dev versions
# Decrypt the decryption key at 0x00 using the key from step 3.
*0x70-0x73 is length of decrypted data
# Decrypt the data using AES-CBC with a null IV.
*0x74-0x77 is length of padding after Metadata header before real data starts
*0x78-0x8F is 0


=== Command 2 ===
==== Decryption process ====
Command 2 is a bit more complicated as it re-encrypts data for command 3.


# Follow steps 1-5 from above, using key slots 2/3 for the ECDSA key and key slot 3 for the AES key
The ECDSA version is slightly different. Only the first block (0x10 bytes) is decrypted with the Kirk 1 AES Key. It is used to decrypt the main data section just as in the AES CMAC version. Rather than a CMAC, the Metadata header is checked by SHA1 hashing its 0x30 bytes and checking the signature components through a ECDSA Verify call. The Data section is also checked via SHA1 of the entire data through a ECDSA Verify call.
# Copy the input header (including padding) to the output
# Change offset 0x60 (command) to command 3
# Change offset 0x64 to 0 or 1 depending on the second bit of the input value at 0x64 (which determines if the output of command 2 should be ECDSA or CMAC-signed)
# Decrypt the body of the data similarly to commands 1 & 3
# Generate a random key and encrypt it with per-console key (seed = 0), and store the result at 0x00
# If in CMAC mode for the output, do the same for the CMAC key at 0x10 (encrypt using CBC mode and data at 0x00 as the IV)
# Encrypt the body in CBC mode with a null IV
# Generate a valid CMAC or ECDSA signature for the output. For ECDSA, this uses the private key stored in key slot 4 (and is the private counterpart of slots 5/6 used by command 3).


=== Command 0xA ===
The ECDSA curve parameters used for this ECDSA Verification are as follows.
Its behavior is very simple:


# Determine if the input is data for command 1, 2 or 3 depending on the command mode. (If it is another value, return an error.)
p=FFFFFFFFFFFFFFFF00000001FFFFFFFFFFFFFFFF
# Get or compute AES and ECDSA public keys depending on the command
# Check the signature similarly to the other commands.


== Commands 4~9: AES encrypt & decrypt ==
NP=FFFFFFFFFFFFFFFF0001B5C617F290EAE1DBAD8F


All these commands do AES128-CBC encryption/decryption with an IV equal to 0. The encryption operands take a header as an input along with the raw data, and generate encrypted data along with a header corresponding to the matching decryption command. Decryption commands output the raw decrypted data.
a=-3


- Commands 4 (encryption) and 7 (decryption) use a one of the 128 keys stored in the Kirk chip and available on the [[Keys]] page, index being given by the keyseed field (which must be between 0x00 and 0x7F), with console-specific modifications for some keyseeds
b=65D1488C0359E234ADC95BD3908014BD91A525F9


- Commands 5 (encryption) and 8 (decryption) use a per-console key derived from the key mesh
'''Base Point''':
Gx=2259ACEE15489CB096A882F0AE1CF9FD8EE5F8FA
Gy=604358456D0A1CB2908DE90F27D75C82BEC108C0


- Commands 6 (encryption) and 9 (decryption) use a key derived from a random key and data stored at 0x14, the random key being encrypted with a per-console key so that command 9 can decrypt
'''Public Point''':
Px=ED9CE58234E61A53C685D64D51D0236BC3B5D4B9
Py=049DF1A075C0E04FB344858B61B79B69A63D2C39


In all cases, data is prefixed with a 0x14-byte long header (except for commands 6 and 9 where it is longer).
== Command 2 (DRM encrypt) ==
{| class="wikitable"
|-
! Address !! Size !! Description
|-
| 0x00 || 4 || Mode: must be 4 for encryption (commands 4/5/6), 5 for decryption (commands 7/8/9)
|-
| 0x04 || 8 || Unused
|-
| 0x0C || 1 || Only used by commands 4/7: keyseed
|-
|0x0D
|1
|Submode: the 3 LSBs are 0 for commands 4/7, 1 for commands 5/8 and 2 for commands 6/9
|-
|0x0E
|2
|Unused
|-
| 0x10 || 4 || Size of the following data
|-
|0x14
|16
|Only for commands 6/9: additional key
|-
|0x24
|16
|Only for command 9: reencrypted encryption key
|}


=== Commands 4/7 ===
This command is mostly unknown.
The behavior of these commands is:
The input data passed to KIRK is first checked (presumably CMAC), then decrypted, and re-encrypted with the console unique private key.
Having that common key would allow legit creation of DRM BB install packages.


# Read the header
== Command 3 ==
# Verify the mode and submode match the current command
# Read the body size and check that it is non-zero
# Get the AES key at key slot 4 + <keyseed>. Command 4 can only encrypt with keyseeds 0..0x3F while command 7 can decrypt with keyseeds 0..0x7F.
# Derive the key for some keyseeds using per-console parameters:
## If the key mesh's derivation key MSB is 1 and keyseed is in the 0x20..0x2f or 0x6c, 0x7b range, invert the bits of the last word (4 bytes) of the key
## If the keyseed is in the 0x27..0x2f or 0x73..0x7b range, XOR the first word of the key with the key mesh derivation key
# For command 4, copy the input header to the output, just replacing mode 4 with 5, and encrypt the body from offset 0x14 using AES-CBC with a null IV and the key determined at step 5.
# For command 7, decrypt the data and output it without a header


=== Commands 5/8 ===
== Command 4 ==
The behavior of these commands is identical to commands 4/7, except it uses per-console key computed from the key mesh with seed 1.


=== Commands 6/9 ===
== Command 5 ==
For both commands, steps 1-3 are the same as above, but differ afterwards.


Command 6 works like this:
== Command 6 ==


# Copy the 0x24-byte long header to the output, just replacing the mode from 4 to 5
== Command 7 ==
# Generate a random buffer and encrypt it using per-console key with seed 2. Write the result of the operation at 0x24.
# Encrypt the random buffer using the key at 0x14
# Use the result of step 3 to encrypt the data, then output it


Command 9 is the logical counterpart:
== Command 8 ==


# Decrypt data at 0x24 with the per-console key with seed 2
== Command 9 ==
# Reencrypt the data of the previous step with the key located at offset 0x14
# Decrypt the data using the result of step 2 as a key


== Command 0xB: SHA1 ==
== Command 10 ==


This command computes the SHA1 of the input. The input must be prefixed with a 4-byte header giving the length of the buffer. Output is 0x14-byte long.
== Command 11 ==


== Command 0xC: ECDSA key pair generation ==
== Command 12: ECDSA key pair generation ==


This command generates a random private key and computes the associated public key. See above for the parameters of the elliptic curve.
Elliptic Curve Math formula : <math>y^2 = x^3 +ax +b mod p</math> with NP points on the curve


This returns the following into the keypair buffer, of size 0x3C (each value is 0x14 bytes long):
p = FFFFFFFFFFFFFFFF00000001FFFFFFFFFFFFFFFF
*0x00 - randomly generated private key
*0x14 - Public Key point x value
*0x28 - Public Key point y value


== Command 0xD: ECDSA point multiplication ==
N= FFFFFFFFFFFFFFFEFFFFB5AE3C523E63944F2127


This command multiplies an elliptic curve point by a scalar. See above for the parameters of the elliptic curve.
a= -3


Input (size 0x3c):
b= A68BEDC33418029C1D3CE33B9A321FCCBB9E0F0B
*0x00 - scalar k
*0x14 - point x value P.x
*0x28 - point y value P.y


Output (size 0x28):
'''Base Point''':
*0x00 - point x value (kP).x
*0x14 - point y value (kP).y


The result is a new point (x and y are each 0x14 bytes long).
Gx= 128EC4256487FD8FDF64E2437BC0A1F6D5AFDE2C


== Command 0xE: PRNG ==
Gy= 5958557EB1DB001260425524DBC379D5AC5F4ADF


This function takes no input and generates an ECDSA private key similarly to command 12, but without computing the associated public key. (This is basically getting random data, but within the range given by the order of the curve.)
'''Invocation''':


== Command 0xF: Seed RNG buffer ==
<pre>
This function seeds the Kirk 32-byte RNG buffer used to generate all the random data coming from Kirk.
u8 keypair[0x3c]
sceUtilsBufferCopyWithRange(keypair,0x3c,0,0,0xC);
</pre>


It takes as an input and output data of size 0x1c:
This returns the following into the keypair buffer (each value is 0x14 bytes long):
*0x00 - randomly generated private key
*0x14 - Public Key point x value
*0x28 - Public Key point y value


* 0x00 - 64-bit counter - increased by 1 in the output
Basically function 0xC generates a random number < N and multiplies it to the base point G to get the new public key.
* 0x08 - seed data (0x14 bytes long) - used for seeding as an input, and contains fresh reseeded data for the output


Seeding works this way:
== Command 13: point multiplication ==


# Increment the input counter
Elliptic Curve Math formula : <math>y^2 = x^3 +ax +b mod p</math> with NP points on the curve
# Set the first 0x14 bytes of the PRNG seed to the input seed data, XOR'ed with a SHA1 of data coming from a true random number generator
# Initialize the 32-byte RNG buffer to two empty words, and two words taken from the input data at offsets 0x00 and 0x04
# Do a reseeding (see below)
# Output the bytes contained in the first 0x14 bytes of the PRNG seed after the reseeding


Reseeding is then done by all operations requiring random data and works this way:
p = FFFFFFFFFFFFFFFF00000001FFFFFFFFFFFFFFFF


# Encrypt RNG buffer with AES per-console key with seed 6
NP= FFFFFFFFFFFFFFFEFFFFB5AE3C523E63944F2127
# Set the last half of the PRNG seed (0x14 bytes) to the contents RNG buffer
# Regenerate data with the PRNG
The functions requiring random data then use some parts of the PRNG state ("seed" (first 0x28 bytes of the PRNG state) or "result" (last 0x14 bytes of the PRNG state)) as random data to be used.


== Command 0x10: ECDSA signature generation ==
a= -3


This command generates an ECDSA signature of a SHA1 hash (0x14 buffer) using an encrypted private key. It is used to verify IdStorage IDPS certificates.
b= A68BEDC33418029C1D3CE33B9A321FCCBB9E0F0B


Input is:
'''Base Point''':
*0x00: 0x20-byte long encrypted buffer containing the private key
*0x20: the message hash.


The output is a 0x28-byte long signature (r and s, both 0x14-byte long).
Gx= 128EC4256487FD8FDF64E2437BC0A1F6D5AFDE2C


The private key buffer is encrypted with the per-console key with seed 3. The command simply decrypts it, verifies that the scalar is valid (non-zero and less than the order of the curve), and outputs the resulting signature.
Gy= 5958557EB1DB001260425524DBC379D5AC5F4ADF


== Command 0x11: ECDSA signature verification ==
'''Invocation''':


This command verifies an ECDSA signature. It is used to verify IdStorage IDPS certificates.
<pre>
u8 buffer[0x3C]
u8 newpoint[0x28]
memcpy(buffer, multiplier, 0x14);
memcpy(buffer+0x14, pointx, 0x14);
memcpy(buffer+0x28, pointy, 0x14);
sceUtilsBufferCopyWithRange(newpoint,0x28,buffer,0x3c,0xD);
</pre>


It takes no output, and takes as an input:
The result is a new point(x and y are each 0x14 bytes long).
* 0x00: public key
* 0x28: signed message hash
* 0x3C: signature r
* 0x50: signature s


The result of the operation is given by the return value (0 on success, KIRK_ECDSA_DATA_INVALID on failure to verify the signature).
To test this, you can call 0xC service and copy the first 0x14 bytes to a new buffer, then copy the Gx and Gy values after that. Calling 0xD with the new buffer will return the values of x and y that were generated by the 0xC call.


== Command 0x12: verify certificate ==
== Command 14 ==


This command verifies an AES-CBC-MAC (OMAC1) signature. It is used to verify [[IDStorage#IDStorage_certified_sections|ID Storage certificates]].
== Command 15 ==


This command has no output.
== Command 16 ==


It takes as input an [[IDStorage#IDStorage_certified_sections|ID Storage certificate]] read from [[IDStorage]].
== Command 17 ==


<source lang="C">
== Command 18 ==
typedef struct kirk_command_0x12_input{
ids_cert_psp certificate;
} kirk_command_0x12_input;
</source>


It uses per-console key with seed 4.
= Library =


= Error codes =
== Calling commands using KIRK registers ==
 
<pre>
    0×00: Success
    0×01: Kirk not enabled
    0×02: Invalid mode
    0×03: Invalid header signature
    0×04: Invalid data signature
    0×05: Invalid ECDSA data
    0x0C: Kirk not seeded
    0x0D: Invalid operation (out of 1-18 range)
    0x0E: Invalid encryption keyseed
    0x0F: Invalid decryption keyseed
    0×10: Invalid data size (equals 0) (sign/cipher operations)
</pre>
 
= Code Samples =


* [https://github.com/DaveeFTW/iplsdk/tree/master/src/kirk]
* [https://github.com/DaveeFTW/iplsdk/tree/master/src/kirk]
Line 1,022: Line 347:
* [http://uofw.github.io/upspd/docs/SilverSpring_Blog/my.malloc.us/silverspring/kirk-crypto-engine/index.html]
* [http://uofw.github.io/upspd/docs/SilverSpring_Blog/my.malloc.us/silverspring/kirk-crypto-engine/index.html]


= Open problems =
= Notes =


* The private key corresponding to the latest version Bootrom public key is unknown.
In 2008 SilverSpring wrote:
* Keys related to Kirk commands 0, 2 and 3 are unknown. (See above for details.)
<pre>
* The Kirk's internal PRNG is deterministic but its function is unknown.
Currently what is known about the cipher is that it is:
* Elliptic curves have additional parameters specified in the code, which are unknown.
a block cipher operating in CBC mode
an all zero 128-bit initialization vector
128-bit block and key sizes
cmd4/7 uses a static key that is identical in all PSP’s
cmd5/8 uses a key based off the fuseID making all operations unique per PSP
cmd6/9 uses a user-defined 128-bit key
cmd1/2/3 uses the block cipher but also signature algorithms
the remaining KIRK cmd’s do not use the block cipher (sig, hash, & prng algo’s)
</pre>
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