“Given the initial value IV0 : A0 = 0x67452301, B0 = 0xefcdab89,
C0 = 0x98badcfe, D0 = 0x10325476,
on an IBM P690, it takes about one hour to find the M and M’, and after that it takes only 15 seconds to 5 minutes to find Ni and Ni’
M’ = M + DC1, DC1 = (0, 0, 0, 0, 231, …, 215, …, 231, 0)
Ni’ = Ni + DC2, DC2 = (0, 0, 0, 0, 231, …, -215, …, 231, 0)
(Non-zeros at position 5, 12 and 15)
such that, MD5(M, Ni) = MD5(M’, Ni’).”
A Chinese woman stood at the podium of the 24th International Cryptology Conference in 2004 and calmly presented this statement to the assembled audience. Within minutes the amazed audience was on its feet to acknowledge one of the most significant breakthroughs in cryptography in the new century. What Wang Xiaoyun had presented to them was an elegant and audacious attack on the computer security procedure called MD5. Before she spoke, it was assumed by all the mathematicians present that it would take a million years of supercomputer time to crack a security code like MD5. Now, this woman proved she could unscramble any MD5 code in an hour using merely a personal computer. From an ordinary child to an international decoder of the digital world, Wang achieved this remarkable feat by living her life with determination.
Wang grew up in an average family in Zhucheng, China: her mother was a farmer and her father was an elementary school mathematics teacher. As a high school student, Wang excelled in physics and dreamed of becoming an accomplished physicist like Madam Curie. Unfortunately, she did not perform well on the national college entrance examinations in physics, so she entered the Mathematics Department at Shandong University instead.
After receiving her bachelor’s degree in mathematics, Wang pursued her doctorate degree in number theory under the mentorship of the famous mathematician, Pan Chengdong. Honoring the scholarly Confucian tradition at Shandong University, Wang studied tirelessly for ten years and obtained a solid foundation in analytical mathematics. After receiving her Ph.D. degree, she was offered a high-paying job in the technology industry but turned it down in favor of pursuing pure mathematics in an academic setting.
With her strong background in analytical mathematics, Wang was attracted to the field of cryptography for her research work with a special interest in hash algorithms. A hash algorithm is a mathematical procedure for deriving a “fingerprint” from a block of data. It is used in almost every aspect of digital security, such as computer passwords, digital signatures, and credit card processing. Cryptographic hash algorithms are designed to be resistant to a “collision”; that is, it should be computationally impossible for a person to find two documents that yield the same hash value. Hash algorithms present such difficult problems to researchers that ninety-nine percent of the people who focus on this field can work for many years without result. But this did not stop Wang. To test her abilities, she targeted MD5 and SHA-1, the two most widely-used computer security procedures in the United States. MD5 was devised by Ronald Rivest of the Massachusetts Institute of Technology in 1991. SHA-1 was devised by the U.S. National Security Agency in 1995. For ten years, working with her eight-person research team, Wang applied her mind to the problem of decoding MD5 and SHA-1.
Wang’s commitment to mathematics is not just a matter of pragmatic duty. Her relationship with mathematics is passionate, and she has a rare ability to express this commitment in language which gives us a glimpse into her world. Attempting to convey what mathematics means to her, she said: “Once mathematics becomes instinctive to us, we view numbers as beautiful musical notes.” To Wang, mathematics is truly like the sound of music flowing in her mind. Many of Wang’s fellow academics have left their universities to earn larger salaries in the business world. But Wang and her team insulated themselves from the culture of ambition and greed, focusing instead on contributing to the field of mathematics.
As Wang took her analytical skills and computational capacities to higher and higher levels, she was still able to balance her personal life and her work. She was a devoted mother, raising her daughter and helping her with her homework. She invited her research team into her home, cooked meals for them, and worked with them late into the night. Her approach to her work and life was collegial. She did not make herself the center of attention on use her skills to find a high-paying job. Speaking of her academic life, she said “Our lives are like a relay race. One person’s research life is short, but we can extend our lives through our students and our student’s students, passing on the baton until one of us finally reaches the summit.”
Six months after announcing her successful “attack” on MD5 at the Cryptology Conference, Wang repeated her astounding performance by breaking into SHA-1, considered to be the apex of computer security applications. Security industry professionals around the world were shocked again, and many voiced concerns about the ability of a Chinese national to decode sensitive information: the economic implications of breaking these codes were staggering. Responding to these concerns, Wang said “We are not hackers. Our work is to find the deficiencies in the existing digital security system so developers can design more secure hash algorithms.”
Wang is not only on the cutting edge in her academic field, she is on the cutting edge of women’s role in society. In ten years, using her profound gift for analytical thought, Wang surpassed the capacity of a supercomputer. Modestly, Want said “This comes from my ten years’ rigorous training in number theory and a woman’s perseverance. There is no other secret.” As a woman who has transcended the expectations of her own society and of her professional community, Wang Xiaoyun is an example and an inspiration to women everywhere.
About the student:
Currently a freshman at Eden Prairie High School, I am taking Advanced Placement Statistics and have studied Computer Science. Along with my high school coursework, I am also enrolled in Calculus through the University of Minnesota Talented Youth Mathematics Program (UMTYMP). To me, it is amazing to see how scientists and engineers can use mathematics to govern, build, and modify our world, and it is beautiful to see how mathematics can be used to describe the universe in which we live. Through my own studies, I hope to advance our increasing use of mathematics in shaping our world.