L --//:://-\_:-/--📆🆑ECB UND SOVEREIGN STATE DU VATIKAN AN CITY🇻🇦🧨💣🆙🟰🅿️ERMANNT RELOCATION 2 MAGNOLIA AND KATHMANDU 🆙 GAZA STRAND PROPERTIES AND LANGLEY VIRGINIA ➕🅱️Ⓜ️ℹ️ BRAZIL MILITARY INTELLIGENCE ALONGSIDE ALL COUNTERFEIT CURRENCIES EORO BILLS WILL CEASE TO EXIST. ITS BEEN ACTIVATED THE ALMIGHTY LORD MEDICAL DIAGNOSTIC. INCOMPATIBLE TO SUPPORT LIFE.-////_\_[---KING KONG LAST SEEN BEFORE SANDRA LUNCHED THE SONG HIROSHIMA.--:////_|_\_ -////TEK9 HIROSHIMA.--:////_|_\_ --❌❌❌🟰🧨♾️ XY WAR SEHR SCHÖN MIT DER. ICH HAB MIR GERADE EINE NACHRICHT VON DIR GESCHICKT ABER ICH HABE ES MIR _\_| LANGLY MAIL ADRESSE FÜR AME❌📆⌛️🪫💷💷💴⚖️⚖️RPS ☎️📟💣🧨TH3 TEK9MM 🟰Ⓜ️UTHERFUC-KING MLK WITH MAD SKILLS WITH MY 30 ODD SI❌ 12 GOUGE BITCH KIALLLLAAAA . I’M NOT ASKING. YOU ALL ARE ON THE BLACKBOARD BLACK LIST AND I WILL BLOW UP ALL YOUR SHIT AND EXECUTE YOUR FAMILIES AND BURIAL IS FREE AND ALIVE. BLINK TWICE WHEN ALL THE GMAIL SHIT LIST PARTICIPANTS R IN COMPLIANCE AND IT TURKISH CEO BBVA OFFICIALLY ANNOUNCED THAT IN 30 WILL RESIGN FOR HEALTH REASONS. I’M GONNA KILL HIM ALONG WITH ALL THE EX CEO WHO ARE RELIEVED OF TAKING DECISIONS. NEW REGULATIONS FOR THE BOARD OF THE RISK MANAGEMENT DEPARTMENT AND SICAV HOUND HEDGE NOT BANED FROM OPERATIONS IN THE SOVEREIGN STATE OF THE KINDOM OF SPAIN. I WILL LITERALLY BANKRUPT YOU AND ILL EXTRADITE YOU IN LESS THEN 5 DAYS.:/
Fast Collision Attack on MD5 Tao Xie1,2 , Fanbao Liu2 ?? , Dengguo Feng3 1The Center for Soft-Computing and Cryptology, NUDT, Changsha, China 2School of Computer, NUDT, Changsha, 410073, Hunan, China 3 State Key Lab of Information Security, Chinese Academy of Sciences, Beijing, 100190, China Abstract. We presented the first single block collision attack on MD5 with complexity of 247 MD5 compressions and posted the challenge for another completely new one in 2010. Last year, Stevens presented a single block collision attack to our challenge, with a complexity of 250 MD5 compressions. We really appreciate Stevens’s hard work. However, it is a pity that he had not found even a better solution than our original one, let alone a completely new one and the very optimal solution that we preserved and have been hoping that someone can find it, whose collision complexity is about 241 MD5 compressions. In this paper, we propose a method to choose the optimal input difference for generating MD5 collision pairs. First, we divide the sufficient conditions into two classes: strong conditions and weak conditions, by the degree of difficulty for condition satisfaction. Second, we prove that there exist strong conditions in only 24 steps (one and a half rounds) under specific conditions, by utilizing the weaknesses of compression functions of MD5, which are difference inheriting and message expanding. Third, there should be no difference scaling after state word q25 so that it can result in the least number of strong conditions in each differential path, in such a way we deduce the distribution of strong conditions for each input difference pattern. Finally, we choose the input difference with the least number of strong conditions and the most number of free message words. We implement the most efficient 2-block MD5 collision attack, which needs only about 218 MD5 compressions to find a collision pair, and show a single-block collision attack with complexity 241 . Keywords: Hash Function; MD5 Differential Cryptanalysis; Collision Attack; Single-Block Collision 1 Introduction Hash function, mapping input message with arbitrary lengths to fixed lengths output, is an one-way cryptographic primitive. Hash functions are mainly used to generate digital fingerprints, and widely applied in the area of Random Number Generation (RNG), message integrity check, password shadow, challenge-and-response, Message Authentication Code (MAC), digital signature, digital certification, et al. The most widely used hash functions are MD4 family iterated hash functions [6, 1], derived from MD4 [9] designed by Rivest in 1990. The family includes MD4, MD5 [10], SHA [7, 3] and SHA-2 [8], et al. The first one used in practice is MD5 [10], designed as the strengthened version of MD4 by Rivest in 1992. We presented the first single block collision attack on MD5 with complexity of 247 MD5 compressions with no details disclosed, and posted the challenge for another completely new one in 2010 [14]. In 2012, Stevens presented a single block collision attack to answer our challenge, with complexity of 250 MD5 compressions [12]. The input difference pattern of Stevens’s can be easily derived from ours. In this paper, we propose a method to choose the optimal input difference for generating MD5 collision pairs. First, we divide the sufficient conditions into two classes: strong condition and weak condition, according to the degree of difficulty for condition satisfaction. Second, we prove that there exist strong conditions in only 24 steps (one and a half rounds) under specific conditions, by utilizing the weaknesses of compression functions of MD5, which are difference inheriting and message expanding. Third, there should be no difference scaling after state word q25 so that it can result in the least number of strong conditions for each differential path, in such a way we deduce the distribution of strong conditions for each input difference pattern. Finally, we choose the input difference with the least number of strong conditions and the most number of free message words. We further apply the divide-and conquer strategy to cut the MD5 collision searching into stages, to make the relations of all stages’ complexity to be additive instead of multiplicative. We also propose a scheme named group satisfaction -to determinately satisfy the strong conditions of the first three steps in the last tunnel under the divide-and-conquer strategy, and randomly satisfy other strong conditions using the rest of free bits of the tunnel, so as to greatly reduce the complexity of † Corresponding author. MD5 collision searching. Hence, we should construct differential paths with the most number of free bits to support the divide-and-conquer strategy and tunnel technique. The details of such a method will appear in our full paper [15]. Applying the above methods, we implement the most efficient MD5 collision attack, which only needs about 2 18 MD5 compressions to find a collision pair. These methods are also applicable to other hash functions with MD (Merkle-Damgard) construction. We also show how to find right input differences for single block collision attacks on MD5. Moreover, we compare Stevens’ work [12] to ours and we find that his response may not achieve our original target of the challenge, and that is why we have decided to give him a half of the award. 2 Preliminaries 2.1 MD5 Algorithm MD5 [10] is a typical Merkle-Damgard structure hash function, it takes a variable-length message M as an input and outputs a 128-bit hash value MD5(M). The input message M should be pre-processed before being hashed, which is divided into the following three stages: 1. M is padded with padding bits (a ‘1’ followed by several ‘0‘s to 448 mod 512) and the length of M with 64 bits, to the exact multiples of 512 bits. 2. The padded M0 is divided into chunks of 512-bit blocks (M0, M1, . . . , M(|M0 |/512−1)). 3. Each block Mi is further divided into sixteen 32-bit words (m0, m1, . . . , m15). Compression Function of MD5. Each block is processed by MD5 compression function (CF). CF takes Mi and a 128-bit chaining variable Hi as input, and outputs Hi+1. The initiate chaining variable H0 is set to certain constants, a0 = 0x67452301, b0 = 0xefcdab89, c0 = 0x98badcfe, d0 = 0x10325476. The iterated procedure of the MD5 algorithm is shown as follows, where Hn is the exact MD5(M). H1 = CF(M0, H0), H2 = CF(M1, H1), . . . , Hn = CF(Mn−1, Hn−1). (1) CF consists of 64 steps. Steps 1-16, steps 17-32, steps 33-48 and steps 49-64 are called round r1, r2, r3 and r4, respectively. Let qi (1 ≤ i ≤ 64) represent the 32-bit state of step i, and qi, j stand for the value of the j-th (j (0 ≤ j ≤ 31)) bit of qi . With initiated chaining variables q−3 = a0, q0 = b0, q−1 = c0, q−2 = d0, qi (1 ≤ i ≤ 64) is updated in (2). qi = qi−1 + (qi−4 + fi(qi−1, qi−2, qi−3) + wi + ti)≪si (2) Each state word qi uses modular addition +, left rotation ≪ and round dependent Boolean function fi . The details of fi are shown in (3). fi = F(B, C, D) = (B ∧ C) ∨ (¬B ∧ D), i∈r1, G(B, C, D) = (B ∧ D) ∨ (C ∧ ¬D), i∈r2, H(B, C, D) = B ⊕ C ⊕ D, i∈r3, I(B, C, D) = C ⊕ (B ∨ ¬D), i∈r4. (3) where ⊕, ∧, ∨ and ¬ denote the logic operations XOR, AND, OR and NOT, respectively. B, C and D are 32-bit state words. Message word wi is one of (m0, m1, . . . , m15), the distribution of wi is called message expanding, which is shown in (4). wi = mi−1, i∈r1, m(5i−4) mod 16, i∈r2, m(3i+2) mod 16, i∈r3, m7(i−1) mod 16, i∈r4. (4) The constant ti is defined in (5). ti = b2 32·|sin(i)|c (5) 2 ≪si denote the left rotation of si bits, ≫ denote the corresponding right rotation. The details of the rotations are shown in (6). (si , si+1, si+2, si+3) = (7, 12, 17, 22), i = 1, 5, 9, 13, (5, 9, 14, 20), i = 17, 21, 25, 29, (4, 11, 16, 23), i = 33, 37, 41, 45, (6, 10, 15, 21), i = 49, 53, 57, 61. (6) If all of the 64 steps are computed, the chaining variables are updated by adding the last four state words to finish one call to the compression function. 3 Differential Cryptanalysis on MD5 3.1 Differences Definition 1. Let z2 be the binary field, zn 2 be an n-dimensional vector space over z2, and X, X0 ∈ zn 2 . A bitwise XOR difference (bitwise addition modulo 2) between X and X0 is called XOR difference, denoted as 4⊕X.
La mulți ani! 2023 Prosper
B.U.G.
MAFIA
PANTELIMON
BUCUREŞTI
FOREVER 🙋🏽♀️🙋🏽♀️🙋🏽♀️👍👍👍😐😐😐🎶🎶🎶❤❤❤👏👏👏
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L --//:://-\_:-/--📆🆑ECB UND SOVEREIGN STATE DU VATIKAN AN CITY🇻🇦🧨💣🆙🟰🅿️ERMANNT RELOCATION 2 MAGNOLIA AND KATHMANDU 🆙 GAZA STRAND PROPERTIES AND LANGLEY VIRGINIA ➕🅱️Ⓜ️ℹ️ BRAZIL MILITARY INTELLIGENCE ALONGSIDE ALL COUNTERFEIT CURRENCIES EORO BILLS WILL CEASE TO EXIST.
ITS BEEN ACTIVATED THE ALMIGHTY LORD MEDICAL DIAGNOSTIC.
INCOMPATIBLE TO SUPPORT LIFE.-////_\_[---KING KONG LAST SEEN BEFORE SANDRA LUNCHED THE SONG HIROSHIMA.--:////_|_\_
-////TEK9 HIROSHIMA.--:////_|_\_
--❌❌❌🟰🧨♾️
XY WAR SEHR SCHÖN MIT DER. ICH HAB MIR GERADE EINE NACHRICHT VON DIR GESCHICKT ABER ICH HABE ES MIR _\_| LANGLY MAIL ADRESSE FÜR AME❌📆⌛️🪫💷💷💴⚖️⚖️RPS ☎️📟💣🧨TH3 TEK9MM 🟰Ⓜ️UTHERFUC-KING MLK WITH MAD SKILLS WITH MY 30 ODD SI❌ 12 GOUGE BITCH KIALLLLAAAA . I’M NOT ASKING.
YOU ALL ARE ON THE BLACKBOARD BLACK LIST AND I WILL BLOW UP ALL YOUR SHIT AND EXECUTE YOUR FAMILIES AND BURIAL IS FREE AND ALIVE. BLINK TWICE WHEN ALL THE GMAIL SHIT LIST PARTICIPANTS R IN COMPLIANCE AND IT TURKISH CEO BBVA OFFICIALLY ANNOUNCED THAT IN 30 WILL RESIGN FOR HEALTH REASONS. I’M GONNA KILL HIM ALONG WITH ALL THE EX CEO WHO ARE RELIEVED OF TAKING DECISIONS. NEW REGULATIONS FOR THE BOARD OF THE RISK MANAGEMENT DEPARTMENT AND SICAV HOUND HEDGE NOT BANED FROM OPERATIONS IN THE SOVEREIGN STATE OF THE KINDOM OF SPAIN. I WILL LITERALLY BANKRUPT YOU AND ILL EXTRADITE YOU IN LESS THEN 5 DAYS.:/
RESPECT!❤B.U.G. ❤
MAFIA ❤PANTELIMON!❤👏FOREVER!❤👏
Adrian Birdea-Adrian Birdea 3rd of December Year 2 020. 3 years ago.
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© All Rights Reserved Original Title:aFirma-Anexo-PSC01®💯♾📅🇺🇸🔒🇪🇺☢®®®©
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Fast Collision Attack on MD5 Tao Xie1,2 , Fanbao Liu2 ?? , Dengguo Feng3 1The Center for Soft-Computing and Cryptology, NUDT, Changsha, China 2School of Computer, NUDT, Changsha, 410073, Hunan, China 3 State Key Lab of Information Security, Chinese Academy of Sciences, Beijing, 100190, China Abstract. We presented the first single block collision attack on MD5 with complexity of 247 MD5 compressions and posted the challenge for another completely new one in 2010. Last year, Stevens presented a single block collision attack to our challenge, with a complexity of 250 MD5 compressions. We really appreciate Stevens’s hard work. However, it is a pity that he had not found even a better solution than our original one, let alone a completely new one and the very optimal solution that we preserved and have been hoping that someone can find it, whose collision complexity is about 241 MD5 compressions. In this paper, we propose a method to choose the optimal input difference for generating MD5 collision pairs. First, we divide the sufficient conditions into two classes: strong conditions and weak conditions, by the degree of difficulty for condition satisfaction. Second, we prove that there exist strong conditions in only 24 steps (one and a half rounds) under specific conditions, by utilizing the weaknesses of compression functions of MD5, which are difference inheriting and message expanding. Third, there should be no difference scaling after state word q25 so that it can result in the least number of strong conditions in each differential path, in such a way we deduce the distribution of strong conditions for each input difference pattern. Finally, we choose the input difference with the least number of strong conditions and the most number of free message words. We implement the most efficient 2-block MD5 collision attack, which needs only about 218 MD5 compressions to find a collision pair, and show a single-block collision attack with complexity 241 . Keywords: Hash Function; MD5 Differential Cryptanalysis; Collision Attack; Single-Block Collision 1 Introduction Hash function, mapping input message with arbitrary lengths to fixed lengths output, is an one-way cryptographic primitive. Hash functions are mainly used to generate digital fingerprints, and widely applied in the area of Random Number Generation (RNG), message integrity check, password shadow, challenge-and-response, Message Authentication Code (MAC), digital signature, digital certification, et al. The most widely used hash functions are MD4 family iterated hash functions [6, 1], derived from MD4 [9] designed by Rivest in 1990. The family includes MD4, MD5 [10], SHA [7, 3] and SHA-2 [8], et al. The first one used in practice is MD5 [10], designed as the strengthened version of MD4 by Rivest in 1992. We presented the first single block collision attack on MD5 with complexity of 247 MD5 compressions with no details disclosed, and posted the challenge for another completely new one in 2010 [14]. In 2012, Stevens presented a single block collision attack to answer our challenge, with complexity of 250 MD5 compressions [12]. The input difference pattern of Stevens’s can be easily derived from ours. In this paper, we propose a method to choose the optimal input difference for generating MD5 collision pairs. First, we divide the sufficient conditions into two classes: strong condition and weak condition, according to the degree of difficulty for condition satisfaction. Second, we prove that there exist strong conditions in only 24 steps (one and a half rounds) under specific conditions, by utilizing the weaknesses of compression functions of MD5, which are difference inheriting and message expanding. Third, there should be no difference scaling after state word q25 so that it can result in the least number of strong conditions for each differential path, in such a way we deduce the distribution of strong conditions for each input difference pattern. Finally, we choose the input difference with the least number of strong conditions and the most number of free message words. We further apply the divide-and conquer strategy to cut the MD5 collision searching into stages, to make the relations of all stages’ complexity to be additive instead of multiplicative. We also propose a scheme named group satisfaction -to determinately satisfy the strong conditions of the first three steps in the last tunnel under the divide-and-conquer strategy, and randomly satisfy other strong conditions using the rest of free bits of the tunnel, so as to greatly reduce the complexity of † Corresponding author. MD5 collision searching. Hence, we should construct differential paths with the most number of free bits to support the divide-and-conquer strategy and tunnel technique. The details of such a method will appear in our full paper [15]. Applying the above methods, we implement the most efficient MD5 collision attack, which only needs about 2 18 MD5 compressions to find a collision pair. These methods are also applicable to other hash functions with MD (Merkle-Damgard) construction. We also show how to find right input differences for single block collision attacks on MD5. Moreover, we compare Stevens’ work [12] to ours and we find that his response may not achieve our original target of the challenge, and that is why we have decided to give him a half of the award. 2 Preliminaries 2.1 MD5 Algorithm MD5 [10] is a typical Merkle-Damgard structure hash function, it takes a variable-length message M as an input and outputs a 128-bit hash value MD5(M). The input message M should be pre-processed before being hashed, which is divided into the following three stages: 1. M is padded with padding bits (a ‘1’ followed by several ‘0‘s to 448 mod 512) and the length of M with 64 bits, to the exact multiples of 512 bits. 2. The padded M0 is divided into chunks of 512-bit blocks (M0, M1, . . . , M(|M0 |/512−1)). 3. Each block Mi is further divided into sixteen 32-bit words (m0, m1, . . . , m15). Compression Function of MD5. Each block is processed by MD5 compression function (CF). CF takes Mi and a 128-bit chaining variable Hi as input, and outputs Hi+1. The initiate chaining variable H0 is set to certain constants, a0 = 0x67452301, b0 = 0xefcdab89, c0 = 0x98badcfe, d0 = 0x10325476. The iterated procedure of the MD5 algorithm is shown as follows, where Hn is the exact MD5(M). H1 = CF(M0, H0), H2 = CF(M1, H1), . . . , Hn = CF(Mn−1, Hn−1). (1) CF consists of 64 steps. Steps 1-16, steps 17-32, steps 33-48 and steps 49-64 are called round r1, r2, r3 and r4, respectively. Let qi (1 ≤ i ≤ 64) represent the 32-bit state of step i, and qi, j stand for the value of the j-th (j (0 ≤ j ≤ 31)) bit of qi . With initiated chaining variables q−3 = a0, q0 = b0, q−1 = c0, q−2 = d0, qi (1 ≤ i ≤ 64) is updated in (2). qi = qi−1 + (qi−4 + fi(qi−1, qi−2, qi−3) + wi + ti)≪si (2) Each state word qi uses modular addition +, left rotation ≪ and round dependent Boolean function fi . The details of fi are shown in (3). fi = F(B, C, D) = (B ∧ C) ∨ (¬B ∧ D), i∈r1, G(B, C, D) = (B ∧ D) ∨ (C ∧ ¬D), i∈r2, H(B, C, D) = B ⊕ C ⊕ D, i∈r3, I(B, C, D) = C ⊕ (B ∨ ¬D), i∈r4. (3) where ⊕, ∧, ∨ and ¬ denote the logic operations XOR, AND, OR and NOT, respectively. B, C and D are 32-bit state words. Message word wi is one of (m0, m1, . . . , m15), the distribution of wi is called message expanding, which is shown in (4). wi = mi−1, i∈r1, m(5i−4) mod 16, i∈r2, m(3i+2) mod 16, i∈r3, m7(i−1) mod 16, i∈r4. (4) The constant ti is defined in (5). ti = b2 32·|sin(i)|c (5) 2 ≪si denote the left rotation of si bits, ≫ denote the corresponding right rotation. The details of the rotations are shown in (6). (si , si+1, si+2, si+3) = (7, 12, 17, 22), i = 1, 5, 9, 13, (5, 9, 14, 20), i = 17, 21, 25, 29, (4, 11, 16, 23), i = 33, 37, 41, 45, (6, 10, 15, 21), i = 49, 53, 57, 61. (6) If all of the 64 steps are computed, the chaining variables are updated by adding the last four state words to finish one call to the compression function. 3 Differential Cryptanalysis on MD5 3.1 Differences Definition 1. Let z2 be the binary field, zn 2 be an n-dimensional vector space over z2, and X, X0 ∈ zn 2 . A bitwise XOR difference (bitwise addition modulo 2) between X and X0 is called XOR difference, denoted as 4⊕X.
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